# Algebra 2 Flashcards, test questions and answers

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### We've found 24 Algebra 2 tests

Algebra 1
Algebra 2
Annual Interest Rate
Five Years Ago
Growth
The New York Times
Years

Writing Exponential Functions Given Initial Amount and Percent of Change – Flashcards 12 terms
Kolby Cobb

12 terms
Preview

Writing Exponential Functions Given Initial Amount and Percent of Change – Flashcards

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Write an exponential function for Initial amount: 62 19% increase

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Write an exponential function for Initial amount: 75 25% decrease

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Write an exponential function for Initial amount: 90 3.2% increase

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Write an exponential function for Initial amount: 16 2.5% decrease

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Write an exponential function for Initial amount: 25 30% decrease

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Write an exponential function for Initial amount: 51 150% increase

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Write an exponential function for Initial amount: 32 10% decrease

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Write an exponential function for Initial amount: 45 0.5% increase

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Write an exponential function for Initial amount: 6500 20% increase

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Write an exponential function for Initial amount: 30 15% decrease

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Write an exponential function for Initial amount: 15 3% decrease

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Write an exponential function for Initial amount: 450 2% increase

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Algebra
Algebra 1
Algebra 2

Algebra 8 Chapter 10 Vocabulary – Flashcards 35 terms
Tara Rose

35 terms
Preview

Algebra 8 Chapter 10 Vocabulary – Flashcards

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An expression which is the sum of terms of the form ax^k, where k is a nonnegative integer

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polynomial

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The form of a polynomial ax^n + bx^(n-1) + ... + qx + r

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standard form

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The name for the exponent of the variable in a term of a polynomial

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degree

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The largest degree of any of the terms of a polynomial.

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degree of a polynomial

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When a polynomial is written in standard form, the coefficient of the first term is the ____.

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leading coefficient

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A polynomial with only one term is called a ____.

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monomial

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A polynomial with two terms is called a ____.

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binomial

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A polynomial with three terms is called a ____.

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trinomial

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The growth of a polynomial is ____ in a monomial of degree zero.

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constant

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The growth of a polynomial is ____ in a monomial of degree one.

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linear

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The growth of a polynomial is ____ in a polynomial of degree two.

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quadratic

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The growth of a polynomial is ____ in a polynomial of degree three.

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cubic

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The growth of a polynomial is ____ in a polynomial of degree four.

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quartic

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Which is the constant term in 2x^3 + 5x^2 - 4^x + 7 ???

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7

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Which is the leading coefficient in 2x^3 + 5x^2 - 4^x + 7 ???

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2

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What is the degree of the polynomial in 2x^3 + 5x^2 - 4^x + 7 ???

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3

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What is the degree of the 2nd monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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2

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What is the degree of the third monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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1

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What is the coefficient of the third monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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4

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What is the coefficient of the fourth monomial in 2x^3 + 5x^2 - 4^x + 7 ???

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7

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What does FOIL stand for?

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First Outer Inner Last

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What is the sum and difference pattern?

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(a+b)(a-b) = a^2 - b^2

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What pattern? (a+b)(a-b) = a^2 - b^2

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sum and difference

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What pattern? (a+b)^2 = a^2 + 2ab + b^2

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square of a binomial

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What pattern? (a-b)^2 = a^2 - 2ab + b^2

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square of a binomial

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A polynomial is in ____ if it is written as the product of two or more linear factors.

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factored form

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Zero Product Property: Let 'a' and 'b' be real numbers. If ____, then 'a' = 0 or 'b' = 0

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ab=0

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What property? LPr

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zero property

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What pattern? a^2 - b^2 = (a+b)(a-b)

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difference of two squares

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What is the difference of two squares pattern?

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a^2 - b^2 = (a+b)(a-b)

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What pattern? a^2 + 2ab + b^2 = (a+b)^2

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perfect square trinomial

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What pattern? a^2 - 2ab + b^2 = (a-b)^2

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perfect square trinomial

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A polynomial is ___ if it is not the product of polynomials having integer coefficients

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prime

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To factor a monomial completely, write it as the product of 1.) ____ and 2.) prime factors with at least two terms

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monomial factors

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To factor a monomial completely, write it as the product of 1.) monomial factors and 2.) ____

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prime factors with at least two terms

Algebra 1
Algebra 2

Algebra 2 B- Lesson 3: Rational Functions and Their Graphs – Flashcards 12 terms
Maddison Bailey

12 terms
Preview

Algebra 2 B- Lesson 3: Rational Functions and Their Graphs – Flashcards

question

Suppose that w and t vary inversely and that t=1/5 when w=4. Write a function that models the inverse variation, and find t when w=9.

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t=4/5w; 4/45

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Suppose that y varies directly with x and inversely with z, and y=18 when x=15 and z=5. Write the equation that models the relationship. Then find y when x=21 and z=7.

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y=6x/z; 18

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Graph the function y=13/6x

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Graph C

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Sketch the asymptotes, and graph the function y= 5/(x-2) +3

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Graph C

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This graph of a function is translation of y=4/x. what is an equation for the function?

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4/x+6 +2

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Find any points of discontinuity for the rational function y=(x+6)(x+2)(x+8)/(x+9)(x+7)

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x=-9, x=-7

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Describe the vertical asymptote(s) and hole(s) for the graph of y=(x+2)(x+4)/(x+4)(x+1)

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asymptote: x=-1 and hole: x=-4

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Find the horizontal asymptote of the graph of y=3x^6-7x+10/8x^5+9x+10

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There is no horizontal asymptote

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What is the graph of the rational function? y=-3x+5/-5x+2

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Graph A

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The amount of oil used by a ship traveling at a uniform speed varies jointly with the distance and the square of the speed. The ship uses 30 barrels of oil in traveling 85 miles at 42 mi/h. How many barrels of oil are used when the ship travels 26 miles at 54 mi/h? Round your answer to the nearest tenth of a barrel, if necessary.

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15.2 barrels.

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The yearbook committee is distributing yearbooks to students by class. Each class has approximately the same number of students. The table shows the number of volunteers who helped to distribute the yearbooks to each of the four classes and the time needed to distribute the yearbooks. What function models the data?

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nt=440

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You want to mix a 5% blue dye with a 20% blue dye to make a 12% blue dye. The function y=100(0.05)+x(0.2)/100+x gives the concentration y of the blue dye after you add x mL of the 20% dye to 100 mL of the 5% dye. How much of the 20% dye must you add to get a dye that is 12% concentrated?

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87.5 mL

Algebra 1
Algebra 2

Algebra I: Write Linear Equations – Flashcards 25 terms
Noah Thomson

25 terms
Preview

Algebra I: Write Linear Equations – Flashcards

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slope intercept form

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where m is the slope and (x1, y1) is a point on the line This is another format for straight line equations. Use when you know a point and the slope; it helps find the y-intercept

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point slope form

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the y-coordinate of the point where the line crosses the y-axis

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y - intercept

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1 - Write ƒ(0) = 5 as (0, 5) and ƒ(4) = 17 as (4, 17) 2 - Calculate the slope using the formula 3 - The y-intercept is 5 because the line crosses at (0,5) Write in slope intercept form: y = mx + b

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How to Write a Linear Function Ex: Write an equation for the linear function ƒ with the values ƒ(0) = 5 and ƒ(4) = 17.

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1 - Identify the slope m. You can use the slope formula if you know two points on the line. 2 - Find the y-intercept. You can substitute the slope and the coordinates (x, y) of a point on the line in y = mx + b. Then solve for b. 3 - Write an equation using y = mx + b

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How to Write an Equation of a Line in Slope-Intercept Form

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can be used to find the x- and y-intercepts. Ax + By = C A, B, C are integers (no fractions or decimals) A should be positive

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Standard Form

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Slope Formula

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the slope and the y-intercept

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What do you need to graph a line?

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plug the slope and a point into y = mx + b solve for b Write the equation

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Write the equation of a line that passes through the point with the given slope

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use the formula to find the slope plug the slope and a point into y = mx + b solve for b Write the equation

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Write the equation of a line in slope intercept form that passes through two points

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the statement formed by exchanging the hypothesis and conclusion of a conditional statement (the opposite)

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converse

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If two nonvertical lines in the same plane have the same slope, then they are parallel. If two nonvertical lines in the same plane are parallel, then they have the same slope.

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Parallel Lines

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1 - Identify the slope (in this case = 3) 2 - Use the slope and the point to solve for b in y = mx + b 3 - Write the equation using y = mx + b

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To Write an Equation of a Parallel Line: Write an equation of the line that passes through (-3, -5) and is parallel to the line y = 3x - 1

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If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular. If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.

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Perpendicular Lines

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write all equations in slope-intercept form ( y = mx + b) compare their m value: if the same, then parallel; if negative reciprocals, then perpendicular

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To determine whether lines are parallel or perpendicular

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is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.

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Scatter Plot

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y tends to increase, as x increases

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Positive Correlation

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y tends to decrease, as x increases

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Negative Correlation

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x and y have no apparent relationship

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Relatively No Correlation

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The line that most closely follows a trend in data is called the best-fitting line.

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Line of Best Fit

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the process of finding the best-fitting line to model a set of data; you can use technology to do this

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Linear Regression

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using a line or its equation to approximate a value between two known values

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Linear Interpolation

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1 - Make a scatter plot of the data 2 - Graph the best fitting line

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Interpolate Using an Equation

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using a line or its equation to approximate a value outside the range of known values

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Linear Extrapolation

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for the function ƒ, any number x such that ƒ(x) = 0

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Zeros of a Function

Algebra 2
Measure Of Central Tendency

AQR Unit 4 – Flashcards 70 terms
Ewan Tanner

70 terms
Preview

AQR Unit 4 – Flashcards

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1. A yogurt shop offers 6 different flavors of frozen yogurt and 12 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?

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72

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2. In how many different orders can you line up 8 cards on a table?

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40,320

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3. There are 10 students participating in a spelling bee. In how many ways can the students who go first and second in the bee be chosen?

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90 ways

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4. Evaluate 60C3/15C3

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6,844/91

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5. There are 6 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for 0, 1, 2, 3, or 4 judges. In how many different ways can a person vote?

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57

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1. A bag contains 6 red marbles, 6 white marbles, and 4 blue marbles. Find P (red or blue).

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5/8

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2. A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day. Carry out a simulation of 20 trials using the random number table below to find the probability that the osprey will actually catch a fish on all of the next three days. Explain your method. 945 025 354 793 236 106 746 981 105 012 832 180 250 871 835 793 726 864 496 947

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Using the digits 0-6 to represent a caught fish, the probability of catching a fish on each of the next three days is 35%.

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3. This is a spinner used in a board game. What is the probability that the spinner will land on a multiple of 3 and 4?

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3/8

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4. What is the theoretical probability of being dealt exactly three 4s in a 5-card hand from a standard 52- card deck?

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94/54145

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5. If a dart hits the target at random, what is the probability that it will land in the shaded region?

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1/16

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1. Which are dependent events?

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Taking two marbles from a box without replacing the first marble

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2. Suppose Q and R are independent events. Find P(Q and R). P(Q) = 0.41, P(R) = 0.44

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0.1804

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3. You roll a six-sided number cube. Which events are mutually exclusive?

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Rolling an even number and an odd number

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4. Suppose S and T are mutually exclusive events. Find P(S or T). P(S) = 20%, P(T) = 22%

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42%

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5. A jar contains 7 blue cubes, 4 blue spheres, 5 green cubes, and 6 green spheres. If you select an object at random, what is the probability that the object is green or a cube?

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9/11

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1. Suppose Ruth Ann has 3 routes she can travel between the school to the library, and 5 routes from the library to her home. How many routes are there from Ruth Ann's school to her home with a stop at the library?

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15

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2. Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny?

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696

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3. Evaluate 7C6

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7

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4. In how many ways can 3 singers be selected from 5 who came to an audition?

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10

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6. A spinner is numbered from 1 through 10 with each number equally likely to occur. What is the probability of obtaining a number less than 2 or greater than 7 in a single spin?

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2/5

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7. On the following dartboard, the radius of the bullseye (area A) is 4 inches. The radius of each concentric circle is 4 inches more than the circle inside it. If a person throws randomly onto the dartboard, what is the probability that the dart will hit in area B?

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3/16

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8. Two urns contain white balls and yellow balls. The first urn contains 9 white balls and 9 yellow balls and the second urn contains 8 white balls and 3 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?

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4/11

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9. If all possible results are equally likely, what is the probability that a spin of the spinner will land on an upper case letter or a consonant?

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0.9

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10. Joey's sock drawer is unorganized and contains 3 black dress socks, 5 black ankle socks, 7 brown dress socks, and 6 brown ankle socks. What is the probability that Joey will blindly reach into his sock drawer and pull out a sock that is brown or a dress sock?

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16/21

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11. The table shows the results of a survey of students in two math classes. Find P(more than 1 hour of TV | 6th period class). Round to the nearest thousandth. Did You Watch More Than One Hour of TV Last Night?

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0.565

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12. The probability that a city bus is ready for service when needed is 84%. The probability that a city bus is ready for service and has a working radio is 67%. Find the probability that a bus chosen at random has a working radio given that it is ready for service. Round to the nearest tenth of a percent.

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79.8%

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13. A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.

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0.241

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1. Find the mean, median, and mode of the data set. Round to the nearest tenth. 15, 13, 9, 9, 7, 1, 11, 10, 13, 1, 13

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Mean = 9.3 Median = 10 Mode = 13

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2. Find the outlier in the set of data. 17, 13, 16, 18, 38, 14, 21, 24

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38

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3. Over the first five years of owning a car, Gina drove about 12,700 miles the first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and 13,075 the fifth year. a. Find the mean, median, and mode of this data. b. Explain which measure of central tendency will best predict how many miles Gina will drive in the sixth year.

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Mean = 13,156 Median = 12,700 No mode The median is the best choice because it is not skewed by the high outlier

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4. Make a box-and-whisker plot of the data. 24, 18, 29, 21, 16, 23, 13, 11

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A

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5. Find the values of the 30th and 90th percentiles of the data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20

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30th percentile = 7 90th percentile = 19

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1. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth. 92, 97, 53, 90, 95, 98

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Mean = 87.5 Variance = 245.6 Standard deviation = 15.7

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2. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth.

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Mean = 47.6 Variance = 31 Standard deviation = 5.6

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3. Susan keeps track of the number of tickets sold for each play presented at the community theater. Within how many standard deviations of the mean do all the values fall? 135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85

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2

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4. The graph below displays how many pieces of candy Timmy and his five friends each received last Halloween. Within how many standard deviations of the mean do the values fall?

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2

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1. A citizens' group wants to determine peoples' opinions about a new road. The members of the group conduct a survey at the largest mall in the city. Which best describes the sampling method used by the citizens' group?

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Convenience sample

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2. The town council must decide how to allocate next year's budget. They survey a sample of the town population to determine residents' preferences. Which survey question shows the least bias?

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Do you think we should plant gardens in the park or buy new park benches?

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3. You want to determine what percentage of working adults in your neighborhood regularly ride the bus to work. Which sampling method and survey question are best?

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Go to every fifth house and ask the working adults, "How many times per week do you ride the bus to work?"

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4. A researcher tags 20 squirrels in a wood. The next month, she returns to the wood and observes a sample of 12 squirrels, 5 of which are tagged, and a sample of 25 squirrels, 9 of which are tagged. If the two samples are representative of the squirrel population, which is the best estimate of the number of squirrels in the wood?

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50

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1. A survey of high school juniors found that 82% of students plan on attending college. If you pick three students at random, what is the probability that at least two plan on attending college? Round to the nearest percent.

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91%

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2. A poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. If 10 voters are selected at random, what is the probability that exactly five of them will vote in favor of the initiative?

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5.1%

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3. Use the Binomial Theorem to find the binomial expansion of the expression. (s - 5v)^5

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C

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4. A recent poll found that 45% of eligible voters are planning to vote in favor of a new by-law. Suppose you randomly survey six voters. What is the probability that at least three of the voters plan to vote in favor of the new by-law?

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55.8%

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1. Find the mean, median, and mode of the data set. Round to the nearest tenth. Test scores on a math exam: 88, 89, 65, 62, 83, 63, 84, 63, 74, 64, 71, 82, 66, 88, 79, 60, 86, 63, 93, 99, 60, 85

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Mean = 75.8 Median = 76.5 Mode = 63

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2. Make a boxandwhisker plot of the data. Average daily temperatures in Tucson, Arizona, in December: 67, 57, 52, 51, 64, 58, 67, 58, 55, 59, 66, 50, 57, 62, 58, 50, 58, 50, 60, 63

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A

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3. Find the values of the 30th and 90th percentiles of the data. 129, 113, 200, 100, 105, 132, 100, 176, 146, 152

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30th percentile = 105 90th percentile = 176

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4. What are the mean, variance, and standard deviation of these values? Round to the nearest tenth. 11, 11, 3, 1, 11, 11

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Mean = 8 Variance = 18.3 Standard deviation = 4.3

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5. Mrs. Jones Algebra 2 class scored very well on yesterday's quiz. With one exception, everyone received an A. Within how many standard deviations of the mean do all the quiz grades fall? 91, 92, 94, 88, 96, 99, 91, 93, 94, 97, 95, 97

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2

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6. According to one study, 61% of the population swallow at least one spider per year in their sleep. Based on this study, what is the probability that exactly 7 of 10 randomly selected people have swallowed at least one spider in their sleep in the last year.

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22%

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7. Use the Binomial Theorem to find the binomial expansion of the expression. (d-5)^6

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D

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8. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay from $600 to $749 per month.

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93%

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9. The scores on an exam are normally distributed with a mean of 77 and a standard deviation of 10. What percent of the scores are greater than 87?

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16%

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10. A grocery store will only accept yellow onions that are at least 3 in. in diameter. A grower has a crop of onions with diameters that are normally distributed with a mean diameter of 3.25 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store?

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84%

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1. In how many ways can 12 basketball players be listed in a program?

answer

479,001,600

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2. Evaluate 9P4

answer

3,024

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3. The Booster Club sells meals at basketball games. Each meal comes with a choice of hamburgers, pizza, hot dogs, cheeseburgers, or tacos, and a choice of root beer, lemonade, milk, coffee, tea, or cola. How many possible meal combinations are there?

answer

30

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4. Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn's results?

answer

11/20

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5. Teesha is in the French club. There are 29 students in the club. The French teacher will pick two students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide?

answer

27/29

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6. A game uses 26 tiles, lettered from A to Z. To start, you randomly choose a set of 5 tiles. What is the theoretical probability of drawing exactly 2 vowels (A, E, I, O, or U) in your set of 5? Round to the nearest percent.

answer

20%

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7. A dartboard consists of two concentric circles. The probability of hitting the inner circle is 16%. If the outer circle has a diameter of 20 inches, what is the radius of the inner circle?

answer

4 inches

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8. Eli has 7 black pens and 5 blue pens in his desk drawer. He also has 3 yellow highlighters, 2 green highlighters, and 5 pink highlighters in his pencil case. If he chooses one pen and one highlighter without looking, what is the probability that he will get a black pen and he will not get a green highlighter?

answer

46.7%

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9. Using a sixteen-sided number cube, what is the probability that you will roll an even number or an odd prime number? The number 1 isn't an odd prime. Round to three decimals.

answer

0.813

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10. Each person in a group of students was identified by year and asked when he or she preferred taking classes: in the morning, afternoon, or evening. The results are shown in the table. Find the probability that the student preferred afternoon classes given he or she is a junior. Round to the nearest thousandth.

answer

0.464

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11. The probability that a dessert sold at a certain cafe contains chocolate is 73%. The probability that a dessert containing chocolate also contains nuts is 25%. Find the probability that a dessert chosen at random contains nuts given that it contains chocolate. Round to the nearest tenth of a percent.

answer

34.2%

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12. An airline has 81% of its flights depart on schedule. It has 69% of its flights depart and arrive on schedule. Find the probability that a flight that departs on schedule also arrives on schedule.

answer

0.85

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13. Find the values of the 30th and 90th percentiles of the data. 18, 9, 7, 5, 11, 7, 17, 20, 19, 2, 17, 12, 5, 1, 13, 12, 11, 15, 16, 20

answer

30th percentile = 7 90th percentile = 19

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14. Use the Binomial Theorem to find the binomial expansion of the expression. (d + 3)7

answer

A

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15. The bar graph shows the rents paid per month for apartments in an urban neighborhood. The curve shows that the rents are normally distributed. Estimate the percent of apartment residents who pay less than $650 per month.

answer

30%

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16. Betty's Bite-Size Candies are packaged in bags. The number of candies per bag is normally distributed, with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint, a sample of bags is checked, and 4 bags contain fewer than 47 candies. How many bags were probably taken as samples?

answer

25 bags

Algebra 1
Algebra 2
Completing The Square
Greater Than Zero

Algebra 2: Midterm Exam (study guide) – Flashcards 50 terms
Roman Peck

50 terms
Preview

Algebra 2: Midterm Exam (study guide) – Flashcards

question

What is the number of real solutions? - x² + 9x + 7 = 0

answer

use b^2-4ac

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What is the number of real solutions? 8x² - 11x = -3

answer

use b^2-4ac

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What is the number of real solutions? x² = -7x + 7

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use b^2-4ac

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What is the number of real solutions? - 4x² - 4 = 8x

answer

use b^2-4ac

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What is the expression in factored form? 2x² + 16x + 30

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2(x+3)(x+5)

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What is the expression in factored form? - 4x² + 8x + 32

answer

__________________

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What is the expression in factored form? 3x² + 26x + 35

answer

__________________

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What is the expression in factored form? 9x² - 18x + 9

answer

__________________

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What is the expression in factored form? x² - 64

answer

__________________

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What are the solutions of the quadratic equation? x² - 9x + 18 = 0

answer

__________________

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What are the solutions of the quadratic equation? 3x² + 25X + 42 = 0

answer

__________________

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What are the solutions of the quadratic equation? 4x² - 18x + 20 = 0

answer

__________________

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Solve by using tables. Give each answer to a most two decimal places. 2x² + 5x - 3 = 0

answer

__________________

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Solve by using tables. Give each answer to a most two decimal places. - 7x² - 2 = -10x

answer

__________________

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What is the solution of each equation? 3x² = 21

answer

__________________

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What is the solution of each equation? 108x² =147

answer

__________________

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Solve the equation. x² + 18x + 81 = 25

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__________________

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Solve the equation. x² - 8x + 16 = 16

answer

__________________

question

Solve the equation. 0.125r - 0.0625 + 0.25r = 0.25 + r

answer

__________________

question

Solve the equation. - 5y - 9 = - ( y - 1 )

answer

__________________

question

Solve the quadratic equation by completing the square. x² + 10x + 14 = 0

answer

__________________

question

Solve the quadratic equation by completing the square. - 3x² + 7x = - 5

answer

__________________

question

Rewrite the equation in vertex form. Name the vertex and y- intercept. y = 3/5x² + 30x + 382

answer

__________________

question

Use the quadratic formula to solve the equation. - 2x² - 5x + 5 = 0

answer

__________________

question

Use the quadratic formula to solve the equation. 2x² + x - 4 = 0

answer

__________________

question

Use the quadratic formula to solve the equation. - 4 x² + x = - 4

answer

__________________

question

Simplify the number using the imaginary unit i. √(-144)

answer

__________________

question

Simplify the number using the imaginary unit i. √(-360)

answer

__________________

question

Simplify the expression. (-1 + 6i) + ( -4 + 2i)

answer

__________________

question

Simplify the expression. (1 + 2i) - (5 + 3i)

answer

__________________

question

Simplify the expression. (-5i) (6i)

answer

__________________

question

Simplify the expression. (6 - 4i) (-1 + 6i)

answer

__________________

question

Simplify the expression. -1+3i ------------ 4 - i

answer

__________________

question

Simplify the expression. -5 +4i ----------- -6i

answer

__________________

question

What are the solutions? 9x² + 16 = 0

answer

__________________

question

What are the solutions? ½ x² - x + 5 = 0

answer

__________________

question

Which algebraic expression models the given word phrase? 40 fewer than a number t

answer

__________________

question

Which algebraic expression models the given word phrase? You start with $15.00 and save $8.00 each week. What algebraic expression models the total amount you save?

answer

__________________

question

Write an algebraic model for the situation and evaluate it for the given information? You are going shopping for some new sweaters, t-shirts, and pants. Sweater (s) cost $30, t-shirts (t) cost $19, and pants (p) cost $18. What algebraic expression models the total cost of the clothes that you buy? Suppose you bought 26 sweaters, 9 t-shirts, and 23 pairs of pants. How much did you spend?

answer

__________________

question

Is the relation a function? {(15, 11), (5, 1), (4,11) ,(9,9),(5,5)}

answer

__________________

question

What is the slope of the line that passes through the given points? (-12,12) and (2,4)

answer

__________________

question

What is the slope of the line that passes through the given points? (7,-9) and (7,-1)

answer

__________________

question

What is an equation of the line in slope intercept form? m = ½ and the y-intercept is (0,-2)

answer

__________________

question

see graph

answer

__________________

question

Write the equation in slope intercept form. What are the slope and y-intercept? -8x +3x = -10

answer

__________________

question

Write the equation in slope intercept form. What are the slope and y-intercept? ¾x + 4/5y = 4

answer

__________________

question

What is the graph of the equation? 3x - y = 3

answer

__________________

question

What is the graph of the equation? -5x + 5y =4

answer

__________________

question

Write an equation of the line, in point-slope form, that passes through the 2 given points. points: (-9,4) , (13, -7)

answer

__________________

question

What is an equation of the line, in point-slope form, that passes through the given point and has the given slope? point: (9,6) ; slope: 1/3

answer

__________________

Algebra
Algebra 1
Algebra 2
Equations

Algebra 2/Trigonometry Regents Review – Flashcards 56 terms
Alexandra Robertson

56 terms
Preview

Algebra 2/Trigonometry Regents Review – Flashcards

question

When raising a negative number to a power always put the negative number in a parenthesis.

answer

Raising a negative number to a power

question

answer

Factoring ax²+bx+c

question

answer

Factoring by grouping

question

If both terms are opposite signs they can be crossed out and replaced by a negative 1.

answer

Canceling out opposites

question

To factor out a -1, remove the negative and change the signs of the terms

answer

Factoring out a -1

question

answer

Operations with fractions

question

answer

Complex fractions

question

To solve equations with fraction, find a common denominator. Drop the denominators Solve the resulting equation. Check the answer(s) in the denominators for extraneous roots.

answer

Equations with fractions

question

the quadratic formula is x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a.

answer

Quadratic formula (Find the Roots)

question

answer

Completing the square

question

if the discriminant is 0, the roots are real, rational and equal. if the discriminant is negative, the roots are complex or imaginary. if the discriminant is a perfect square, the roots are real, rational, and unequal. if the discriminant is not a perfect square, the roots are real, irrational, and unequal

answer

Discriminant (describe the roots)

question

The sum of the roots is negative b divided by a. The product of the roots is c divided by a. The equation for sum and product of the roots is x squared minus the sum times x plus the product equals 0.

answer

Sum and product of roots

question

To solve absolute value inequalities Isolate the absolute value on one side of the equation. Change the inequality sign and the sign(s) of the terms on the right to the opposite signs. If the original inequality has a greater than or greater than or equal to (≥ or >) sign use or between your solutions. Solution is (≥) solution. If the original inequality has a less than or less than or equal to (≤ or <) write as an interval. Solution <(≤) x <(≤) solution. You have to divide by a negative, do not forget to flip the inequality sign.

answer

Absolute value inequalities

question

To solve an absolute value equation Isolate the absolute value on one side of the equation. Change the sign(s) of the terms on the right to the opposite sign(s). check your answer(s) for extraneous roots.

answer

Absolute value equations

question

The inverse variation formula is x one times x two equals y one times y two. Inverse variation creates a corner hyperbola.

answer

Inverse variation

question

To find the conjugate The first term stays the same. Change the sign of the second term.

answer

Conjugate

question

The domain is the x coordinates. The range is the y coordinates. To find the inverse switch the x and y coordinates.

answer

Domain, range, inverse

question

To be a function It must pass the vertical line test. No x coordinate can repeat. An equation must have a y, but the y cannot be squared.

answer

Function

question

A one to one function must pass the vertical and horizontal line test. No x or y coordinate can repeat.

answer

One to one function

question

answer

Logarithms

question

To convert from degrees to radians multiply the degrees by pi and divide by 180.

answer

Convert degrees to radians

question

To convert from radians to degrees, multiply the radians by 180 and divide by pi.

answer

Convert radians to degrees

question

Once around a circle is 2 pi radians or 360 degrees. ½ of the way around a circle is pi radians or 180 degrees. ¼ of the way around a circle is pi divided by 2 or 90 degrees.

answer

Degrees and radians

question

In a circle the central angle in radians equals the arc length divided by radius.

answer

Arc length - radius formula

question

The circle formula is x minus h squared plus y minus k squared equals the radius squared.

answer

Circle formula

question

Secant equals 1 divided by cosine.

answer

Secant

question

Cosecant equals 1 divided by sine.

answer

Cosecant

question

cotangent equals 1 divided by tangent or cosine divided by sine.

answer

Cotangent

question

Tangent equals sine divided by cosine.

answer

Tangent

question

Cosine squared plus sine squared equals 1.

answer

Trigonometric identity

question

answer

Exact values of trigonometric functions

question

An arithmetic sequence is created by adding or subtracting a common difference.

answer

Arithmetic sequence

question

A geometric sequence is created by multiplying or dividing a common ratio. If the terms alternate between positive and negative, the common ratio is negative.

answer

Geometric sequence

question

a to the n minus 1 - look to the term behind. a to the n plus 1 - loot to the term in front.

answer

Recursive sequences

question

To rationalize a denominator multiply the numerator (top) and denominator (bottom) by the conjugate of the denominator (bottom).

answer

Rationalizing the denominator

question

Survey - ask Observation study - watch Experiment - change

answer

Survey, observational study, experiment

question

All students take classes. Sine and cosecant are positive in quadrants 1 and 2. Cosine and secant are positive in quadrants 1 and 4. Tangent and cotangent are positive in quadrants 1 and 3.

answer

Quadrants

question

answer

Sine, Cosine, Tangent on the unit circle

question

Multiply by 180 and then divide by pi. The part before the decimal is the degrees. Multiply the decimal by 60 to find the minutes.

answer

Converting radians to degrees and minutes

question

Coterminal angles are just different ways of naming the same angle.

answer

Conterminal Angles

question

answer

Arc functions

question

Need side angle side (S.A.S) to find area. The area of a triangle equals ½ times a times b times sine of C.

answer

Area of a triangle (need S.A.S.)

question

A parallelogram is made up of 2 congruent triangles.

answer

Area of a parallelogram

question

The law of sines is a divided by sine of A equals b divided by sine of B equals c divided by sine of C.

answer

Law of Sines

question

The law of cosines is b squared plus c squared minus 2 times b times c times the cosine of A. Take the square root of the answer to find the missing side.

answer

Law of cosines given (S.A.S.)

question

The law of cosines a squared(the side across from the angle) equals b squared plus c squared minus 2 times b times c times the cosine of x (A). Use numerical solve to find the measure of angle A.

answer

Law of cosines given (S.S.S.)

question

To solve vector problems remember that The opposite sides in a parallelogram are congruent. The consecutive angles in a parallelogram are supplemental (add up to 180 degrees). Use law of Cosines to find the resultant and the angle between the 2 forces. Use law of Sines to find the angle between a force and the resultant.

answer

Vector problems

question

answer

Ambiguous Case (0,1,2 triangles?

question

answer

Permutations with repetition

question

answer

Binomial Expansion

question

answer

∑ (Sigma)

question

To solve square root equations Isolate the square root on one side of the equation. Square both sides of the equation Check the answer(s) in the original equation for extraneous roots.

answer

Square root equations

question

To convert from logarithmic form to exponent form the base remains the base and the rest of the stuff crosses. the b and the n can never be negative.

answer

Converting between logarithm and exponent form

question

answer

Common Logarithms

question

answer

Natural Logarithms

question

...

answer

Inverses of exponential and logarithmic equations

Algebra 1
Algebra 2

Algebra II Final – Flashcards 281 terms
Ray Collins

281 terms
Preview

Algebra II Final – Flashcards

question

Hans pays $205 in advance on his account at the athletic club. Each time he uses the club, $10 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 11 visits.

answer

V = 205 - 10x; $95

question

Solve the proportion (x−8)/8 = 4/5

answer

x=14 or 72/5

question

Solve for x. x-7=1

answer

x=8

question

Solve the equation or formula for the variable specified. B = 7a²b, for b.

answer

b = B/(7a²)

question

Which equation best describes the graph below? (Evernote)

answer

y = -2x + 5

question

solve for x. 3x - 3 = x - 9

answer

x = -3

question

Which inequality has the solution shown in the graph? (Evernote)

answer

m + 7 ≥ 9

question

What inequality describes the graph? (Evernote)

answer

x ≤ -5

question

For the data given, find the equation of the line of best fit. (Evernote)

answer

Incorrect: None of the listed answers are correct Correct: y = 0.63x + 1.90

question

Write a proportion that models the statement 10 is to 5 as 16 is to 8.

answer

10/5 = 16/8

question

Write an equation in slope-intercept form for a line that passes through the given pair of points. (4,-7), (-2,-10)

answer

y = 1/2x - 9 Solution Slope Formula: slope(m) = (y2 - y1) / (x2 - x1) Substitute and Solve m = (-10 +7) / (-2 - 4) m = (-3) / (-6) m = 1/2 or 0.5 Slope intercept form: y = mx + b Pick one of the two points (4,-7) or (-2,-10), substitute and solve -7 = 1/2(4) + b -7 = 2 + b -7 - 2 = b -9 = b Final Answer y = 1/2x - 9

question

Write an equation in slope-intercept form for a line that passes through the given pair of points. (-6,5), (-9,0)

answer

y = 5x/3 + 15

question

Write an equation in slope-intercept form of the line that passes through (- 5, 4) and is parallel to the graph of y = -4x + 1.

answer

y = -4x -16

question

When Spheres-R-Us ships bags of golf balls, each bag must be within 5 balls of 370. Identify the inequality which results in an acceptable number of golf balls in each bag.

answer

365 ≥ 375

question

Abbiville is a small town that has been steadily growing since 1960. Use the table below to create a linear equation that estimates Abbiville's population over time. What will the population be in 2014 if the growth remains constant? (Evernote)

answer

364 people

question

Which is the equation of the line with slope -4 and y-intercept 5?

answer

4x + y -5 = 0 y = -4x + 5

question

A server at a restaurant kept track of the number of requests for the daily special, and the time of day the request was made. The data is displayed below. (Evernote)

answer

Incorrect: It is a linear model with a positive correlation.

question

Write the equation of the line, in slope-intercept form, that contains the point (-1, - 5) and is perpendicular to the line -8x - 4y = 3.

answer

y = -2x -7

question

Write the slope-intercept form of an equation of the line that passes through the point (3, - 6) and has the slope m = -4.

answer

y = -4x + 6

question

If x = 78 when y = 130 and x varies directly as y, then find x when y = 190.

answer

x = 114 when y = 190 Formula: y = ky(solving for y) or x = ky(solving for x) Substitute 78 = k(130) Divide by 130 on both sides k = 0.6 x = 0.6(190) x = 114

question

Describe how the graph of the function y = f(x-3) can be obtained from the graph of y = f(x).

answer

move it 3 to the right

question

Evaluate the expression. (2/5)⁵

answer

32/3125

question

Which of the following is an example of the Commutative Property of Addition?

answer

5 + 2 = 2 + 5

question

Evaluate the expression. 64 × 4² - 2 × 2²

answer

1016

question

Ivan Bogdanovich plans to decorate stuffed animals to sell at a crafts fair. The decorations cost $44.00 and the stuffed animals cost $5.25 each. a. Write a function expressing the cost, C(x), of the project in terms of the number of stuffed animals decorated, x. b. Determine the cost of decorating 25 stuffed animals. c. How many stuffed animals can be decorated with a budget of $227.75?

answer

a. C(x) = 5.25x + 44.00 b. $175.25 c. 35

question

For the pair of functions, f and g, find (g o f)(x) and (f o g)(x). f(x) = 6 - x, g(x) = x² - 2

answer

(g o f)(x) = x² - 12x + 34 Solution (6-x)² - 2 36 - 6x - 6x + x² - 2 x² - 6x - 6x + 36 - 2 x² - 12x + 34 (f o g)(x) = -x² + 8 Solution -x(x² - 2) + 6 -(x² - 2) + 6 -x² + 2 + 6 -x² + 8

question

Evaluate the expression. (3/8)⁻²

answer

64/9

question

Describe how the graph of the function y = 15(x + 2) + 4 can be obtained from the graph of y = 3(x + 2).

answer

shift up 4 units, and vertically stretch by a factor of 5

question

Simplify the expression. ((-u)³(-u⁹)⁸)/(u⁵)³

answer

-u⁶⁰ Solution (-u³ × u⁷²)/u¹⁵ -u⁷⁵/u¹⁵ = -u⁶⁰

question

Evaluate the expression. (-3/8)²

answer

9/64

question

The graph of f(x) = x² is stretched vertically by a factor of 3, translated 4 units to the right, and translated 8 units downward. Determine the equation of the transformed function, g(x).

answer

g(x) = 3(x - 4)² - 8

question

A T-shirt company estimates that the average cost per shirt can be approximated by the function A(x) = (3.75x + 200)/x, where x is the number of T-shirts made. Find the average cost per T-shirt when the company makes 10 shirts.

answer

$23.75

question

Find the inverse of the function and determine whether the inverse is a function. y = 7x²

answer

y = ±√(x/7), y is not a function.

question

Find the inverse of the function and determine whether the inverse is a function. f(x) = 19x²

answer

f⁻¹(x) = ±√(x/19), f⁻¹(x) is not a function.

question

Since 1993, Daphne Hamilton has owned a franchise of take-out restaurants called The Burger Barn. The number of customers, C, in thousands, that The Burger Barn has served each year can be modeled by the function C(t) = t² + 38t + 600, where t is the number of years from 1993. Using this model, estimate the number of customers served in 1999.

answer

864,000

question

If f(x) = 9 - x² and g(x) = 3 - x, which is the rule of function (f × g)(x)?

answer

x³ - 3x² - 9x + 27

question

Evaluate the expression. 3 - 14 × 6 ÷ 7 + 3

answer

-6

question

If f(x) = 3x + 4 and g(x) = 2 + x, which is the rule of function 3g(x) - 3f(x)?

answer

-6x - 6

question

Which property is shown by the following statement? (13 + 3)+ 8 = 13 + (3 + 8)

answer

The Associative Property of Addition

question

Given the graph of y = 3(x + 1), what function would be obtained by moving the graph up 4 and moving it 6 to the right?

answer

f(x) = 3(x - 5) + 4

question

Use elimination to solve the system of equations. {7x - 3y = -43 {5x + 6y = -47

answer

(-7, -2)

question

Write the pair of parametric equations as a single equation in x and y. {x = 8t - 4 {y = 6t² - 2

answer

y = 6((x+4)/8)² - 2 Solution x = 8t - 4 Add 4 to both sides x + 4 = 8t Divide by 8 on both sides t = (x + 4)/8 Substitute y = 6((x+4)/8)² - 2

question

Mr. Reaich, the ticket agent for a small commuter airline, has developed a model to forecast the total monthly revenue from the airline's passenger service. Under this model, the total revenue, R, is equal to $368 times the number of first-class, F, plus $324 times the number of coach passengers, C. Their flight schedule and overall aircraft capacity limit the total number of passengers carried during a single month to a maximum of 30,775. The number of coach class passengers is at least seven times the number of first-class passengers, and logically, the number of airline passengers in either class cannot be negative. Express the model in mathematical form.

answer

$368F + $324C = R F + C ≤ 30,775 C ≥ 7F F ≥ 0; C ≥ 0

question

Solve the system of equations by substitution. {3x + 4y = 32 {3x + y = 17

answer

(4, 5)

question

Use a graph to solve the system of equations. {x + y = -1 {y = 3x + 19

answer

(-5, 4)

question

Graph and classify the system of equations as independent, inconsistent, or dependent. If the system is independent, find the solution from the graph. {3x + 3y = 2 {3x - y = 8

answer

Independent (2, -2)

question

Use elimination to solve the system of equations. {2x - 5y = 1 {5x -2y = -4

answer

(-22/21, -13/21)

question

Use elimination to solve the system of equations. {-16x - 6y = 170 {8x + 3y = -85

answer

Incorrect: no solutions Correct: Infinitely Many Solutions

question

Use a graph to solve the system of equations. {x + y = -4 {y = 3x - 8

answer

(1, -5)

question

Which of the given ordered pairs are NOT solutions to the system of inequalities? {2x + 3y 2 (3, 1), (-3, -2), (5, -5), (-2, 4), (-4, 5)

answer

(-4, 5), (3, 1), (-2, 4)

question

Write the system of inequalities whose solution is graphed as the shaded region.

answer

Incorrect: y -2x + 5 Use mathway; Graph the intersection (and)

question

Use the graph of the feasible region for the set of constraints to find the maximum and minimum values of the objective function C = 3x + 5y. Constraints: {x + y ≥ 1 {4x - 2y ≤ 4 {3y ≤ 3x + 3

answer

The maximum value of C is 29 at (3, 4) and the minimum value is 3 at (1, 0) .

question

Determine which ordered pair (x, y) is a solution of 3x - y ≤ 15.

answer

(5, 4) Solution Substitute 3(5) - 4 ≤ 15 11 ≤ 15 True

question

Which inequality has (1, 7) as a solution?

answer

Incorrect: -2x - 5y ≥ -32 Solution Substitute -2(1) - 5(7) ≥ -32 -2 - 35 ≥ -32 -37 ≥ -32 False, not a solution of the inequality

question

Use elimination to solve the system of equations. {4x + 2y = -12 {3x - 2y = 5

answer

(-1, -4)

question

An airplane, flying at an altitude of 3.21 miles above the ground, has a horizontal speed of 350 miles per hour and is descending at a rate of 14 miles per hour. Use parametric equations to find the airplane's altitude above ground after it has traveled 11 miles, as measured along the ground.

answer

2.77 mi Solution x(t)=350t y(t)=3.21-14t Solve either equation for "t" x=350t t=x/350 Substitute y=3.21-14(x/350) Substitute for "x", x=11 y=3.21-14(11/350) y=2.77

question

Use the set of constraints to find the maximum and minimum values of the objective function C = 5x + 11y Constraints: {x + y ≥ 2 {6x - 6y ≤ 12 {8y ≤ 4x + 16

answer

Incorrect: The maximum value of C is 139 at (8, 9) and the minimum value is 10 at (0, 2). Correct: The maximum value of C is 106 at (8,6) and the minimum value is 10 at (2,0).

question

Ms. Kim, an analyst at Multi-Fastener Corp, has developed a model to forecast the company's total production of metal fasteners. Under this model, production, P, is equal to 4500 times the man-hours spent producing machine screws (S) plus 2900 times the man-hours spent producing nuts and bolts (P). Manpower constraints mean that total number of man-hours per year cannot exceed 44,000; logically, the number of man-hours assigned to either task cannot be negative. Express the model in mathematical form.

answer

P = 4500S + 2900B {S + B ≤ 44,000 {S ≥ 0 {B ≥ 0

question

Solve the system of equations by substitution. {4y = 4 {x + 2y + z = 10 {y - 2z = -5

answer

Incorrect: None of the listed answers are correct Correct: x=5 y=1 z=3

question

Write the pair of parametric equations as a single equation in x and y. {x = 8t² -3 [y = 6t - 7

answer

x = 8((y + 7)/6)² - 3

question

Find [1 17 14][11 3] [19 7] [9 5]

answer

[460 192]

question

Which system of equations can be classified as independent?

answer

none of these

question

Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {4x + y = -24 {2x + 2y = -18

answer

(-5, -4) You can just solve by using Elimination or Substitution

question

Find the determinant, and tell whether the matrix has an inverse. det [10 -7] [-5 -6 ]

answer

-95; Yes

question

Write the augmented matrix for the system of equations. {x - y = -9 {5x = 0

answer

[1 -1| -9] [5 0| 0] Solution x=1, y=-1 5x=5

question

The band and the cheerleading squad at a local school are ordering supplies. The supplies they need are listed in the table. (Evernote)

answer

[10 13 5] [ 5 ] [10 16 8] [12] [ 2 ] = [216] [258]

question

Perform the indicated operations on the given matrices. [3 -6 -7] [-2 -1 7] [-3 -2 4] + [ 3 5 -7] [-4 -1 7] [4 -9 -3]

answer

[ 1 -7 0 ] [ 0 3 -3 ] [0 -10 4]

question

Write the augmented matrix for the system of equations. {8x + 2y + 6z = -3 {3x - y + 10z = 3 {-9x -2y -4z = -7

answer

[8 2 6| -3 ] [3 -1 10| 3 ] [-9 -2 -4 |-7 ]

question

The Student Government secretary, and two teacher's aides are ordering supplies. The supplies they need are listed in the table. (Evernote)

answer

(Evernote)

question

Kozinski played in 16 basketball games this season, Hussein played in 32 games, and Johnson played in 55 games. Kozinski averaged 6 points and 2 rebounds per game, Hussein averaged 8 points and 11 rebounds, and Johnson averaged 18 points and 16 rebounds. Multiply the following matrices to get the total number of points scored and the total number of rebounds made, by all three players combined. [ 6 2 ] [16 32 55] [ 8 11] [18 16]

answer

1342 points, 1264 rebounds

question

Solve: (Evernote) det[x+3 2] [3 x-2] =0

answer

Incorrect: x =-4 Correct: x = 0 Mathway: Find the Determinant

question

Classify the following system of equations as inconsistent, dependent, or independent: {-3x -7y -2z = -25 {-6x +21y -6z = 57 {-3x +14y -4z = 40

answer

independent, because there is an intersection

question

Find the reduced row-echelon form of the augmented matrix that represents the following system of equations: (Evernote) {-6x + 9y = -5 {-8x - 4y = 0

answer

Incorrect: [1 0| 5/24 ] [0 1|-5/12] Correct: [1 0| -5/24] [0 1| 5/12

question

Perform the indicated operations on the given matrices. (Evernote) [-8 -8] + [-2 3] [-6 4] + [3 -1] (2×2 matrice + 2×2 matrice)

answer

[-10 -5] [-3 3]

question

Find AC - CB (Evernote)

answer

[-13 19] [-12 -44]

question

Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {3x + 2y + z = -2 {3x -2y -z = -22 {3x + 2y -z = -10

answer

[3 2 1] [x] [ -2 ] [3 -2 -1] [y] = [-22] [3 2 -1] [z] [-10] ;(-4, 3, 4)

question

Find the inverse of the following matrix (if it exists): [2 -13 -6] [0 5 0] [0 -24 0]

answer

The matrix has no inverse.

question

Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. {x + 2y + z = -17 {3x + 7y + 2z = -56 {x - y + 2z = 0

answer

x = -4, y = -6, z = -1

question

In May, Victor bought 24 styrofoam balls and decorated them as toy figurines. In June, he sold 17 figurines. In May, Wanda bought 28 styrofoam balls to decorate and in June, she sold 12 figurines. Which matrix represents all of their May purchases and their June sales?

answer

May June Victor [24 -17] Wanda [28 -12]

question

Which matrix represents the graph of polygon PQRS? (Evernote)

answer

P Q R S [2 -3 -3 2] [6 2 -7 3]

question

Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if necessary. 4x² = 8

answer

±√2; ±1.41

question

Use factoring and the Zero-Product Property to solve the quadratic equation 2x² + 5x -3 = 0

answer

1/2, -3 Use Quadratic equation: (-b ± √((b² - 4ac))/2a

question

Find a quadratic function that fits the set of data points exactly, in the form y = ax² + bx + c with values of a, b, and c to two decimal places. (1, 4.1), (5, 2.3), (11, 4.9)

answer

y = 0.09x² - 0.98x + 4.99 Mathway: Find the Equation of the Parabola

question

Which function is the correct match with the the given graph and vertex (Evernote)

answer

f(x) = -3(x + 1)²

question

Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = -6x² - 24x - 31

answer

Incorrect: y = 6(x + 2)² - 7 x = -2; (2,-7) Correct: y = -6(x + 2)² - 7 x = -2; (-2, -7) Mathway: Find the Vertex Form Find the Axis of Symmetry Find the Vertex (Coordinates)

question

Use the quadratic formula to solve the equation. 6x² - 24x - 30 = 0

answer

5, -1

question

Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if necessary. 2(x + 4)² - 48 = 0

answer

Incorrect: 4 ± 2√6; 5.8 or -13.9 Correct: -4 ± 2√6; 0.9 or -8.9

question

Simplify: (2 + 5i)/(5 + 4i)

answer

(30/41) + (17/41)i

question

Solve the quadratic inequality, and graph the solution on a number line. x² - 2x ≥ 24

answer

x ≤ -4 or x ≥ 6

question

Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = x² + 14x + 4

answer

Incorrect: None of the listed answers are correct Correct: y = (x+7)² - 45 x = -7; (-7, -45)

question

Which inequality is best represented by the graph shown: (Evernote)

answer

y ≤ -x² + 5x

question

Use factoring and the Zero-Product Property to find the zeros of the quadratic function. f(x) = x² -7x - 8

answer

8, -1

question

Which of the following is a quadratic function?

answer

f(x) = -1 + 9x² + 7x

question

Find the value of x to the nearest hundredth.

answer

17.2

question

Solve the quadratic inequality, and graph the solution on a number line. (Evernote) x² - 4x + 3 < 0

answer

1 < x < 3

question

Factor the quadratic expression. x² - 11x + 30

answer

(x - 5) (x - 6)

question

Gupta threw a baseball off a cliff into an open field 50 feet below. The chart gives the horizontal distance, x (in feet), the baseball traveled from Gupta and the height, y (in feet), of the baseball above the field. (Evernote) distance, x | 8 | 18 | 33 | 43 | height, y | 65 | 76 | 79 | 71 | Choose the quadratic equation that best fits the baseball's trajectory from Gupta to the open field below.

answer

y = -0.0383x² + 2.143x + 50

question

Show that the function is a quadratic function by writing it in the form f(x) = ax² + bx + c and indentifying a, b and c. f(x) = (5x - 4) (5x + 3)

answer

f(x) = 25x² - 5x - 12 a = 25, b =5, c = -12

question

The turnstiles at the entrance to the State Fair kept track of the number of people entering the fairgrounds, for the first seven hours following the openning of the fair. Find a quadratic equation that models the data shown. (Evernote)

answer

0.083x² - 0.197x + 7.62 Graphing Calculator STAT→Edit Put x values into L1 and y values into L2. 2ND→MODE→STAT→CALC →5:QuadReg

question

Solve the equation by completing the square. Give exact solutions. x² - 2x - 24 = 0

answer

-4, 6

question

Solve the equation for x. Write the exact solution and the approximate solution to the nearest hundredth, when appropriate. In(8x - 6) = 3

answer

x = (3/4) + (e³/8) x ≈ 3.26 Exponential form e³= 8x - 6

question

Solve the equation for x: 10^x = 18

answer

1.26

question

Evaluate 8^log₈ 9

answer

9

question

Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined: In 10

answer

2.303

question

Solve log₇ 8 - log₇ (x + 3) = log₇ 3, for x

answer

Incorrect: None of the listed answers are correct Correct: x=-1/3 Solution log(x) - log(y) = log(x/y) log₇ 8 - log₇ (x+3) = log₇ (8/(x+3)) log₇ (8/(x+3)) = log₇ 3 (Mathway can solve once the left terms are combined)

question

If a principal of $1250 is invested at an annual interest rate of 4% compounded annually, what is the account balance at the end of 6 years?

answer

$1581.648

question

Solve the equation 3^4x = 27^x+3

answer

x = 9

question

The magnitude of an earthquake is found by the equation M = 2/3 log E/10^11.8 , where M is the magnitude and E is the energy released. Find the magnitude of an earthquake that released 10^24.4 ergs of energy.

answer

Incorrect: None of the listed answers are correct Correct: M = 8.4 Solution M = 2/3 log₁₀ (10^24.4/10^11.8)

question

The formula for estimating the number, N, of a certain product sold is N = 7400 In(7t + 3), where t is the number of years after the product is introduced. What is the expected number of sales 7 years after the product is introduced? Round to the nearest whole number.

answer

29,239

question

Solve the equation. Round your answers to the nearest hundredth. 5^x-1 = 25

answer

3

question

Find the final amount of the investment: $3000 at 8% interest compounded quarterly for 4 years.

answer

$4118.36

question

Describe the value of b for the function y(x) = 1/3(1/b)^x to represent exponential growth.

answer

Incorrect: None of the listed answers are correct Correct: "b" has to be greater than 0 and less than 1. (0 < b < 1)

question

Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined: e^¼

answer

1.284

question

Solve log₃(x+4) - log₃(x-4) = log₃5 for x

answer

6

question

The inflation rate of the U.S. dollar is 3.1 percent. What this means is that every year, prices increase by 3.1 percent. If a pound of meat cost $2.37 nine years ago, what does it cost now?

answer

$3.12 Solution 2.37(1+0.031)⁹

question

Erosion gradually reduces the size of a small Pacific island that has a current area of just 460 acres. If the island's area decreases at an annual rate of 0.05%. Find the multiplier for the rate of exponential decay.

answer

Incorrect: 0.95 Correct: 0.9995 Solution 100 - 0.05 = 99.95 99.95/100 = 0.9995

question

Write the equation in logarithmic form. 6^-4 = 1/1296

answer

log₆ 1/1296 = -4

question

Which function represents exponential decay?

answer

y(x) = 5(0.44)^x

question

Evaluate the logarithmic expression to the nearest thousandth. log₈ 1/2

answer

-0.333

question

If $1500 is invested at an interest rate of 10%, compounded continuously, determine the balance in the account after 2 years. Use the formula A = Pe^rt.

answer

$1832.10

question

Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x⁴ - 9x³ + 10x² + 90x - 200

answer

4, 5, ±3.16

question

Divide x³ + 5x² + 9x + 9 ÷ x + 3

answer

x² + 2x + 3

question

Use a graph, synthetic division, substitution, and factoring to solve the equation. x³ - 7x² + 14x - 8 = 0

answer

2, 1, 4

question

Find all the zeros of the polynomial function. f(x) = x² - 10x + 34

answer

Incorrect: 5 ± 6i Correct: 5 ± 3i

question

The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998. (Evernote)

answer

T(x) = 0.2x³ + 0.3x² + 0.2x + 0.1; 304.8 thousand

question

Use a graph, synthetic division, substitution, and factoring to solve the equation. x³ - x² - 14x + 24 = 0

answer

-4, 2, 3

question

Find all the zeros of the polynomial function. f(x) = x³ + 4x² + 6x + 9

answer

-3, (-1 ±i√11)/2

question

Write the product as a polynomial in standard form. (5x² - 2x + 5)(x² - 8x - 2)

answer

5x⁴ - 42x³ + 11x² - 36x - 10

question

Write a polynomial equation in standard form by using the given information. P is of degree 3; P(0) = 24; zeros: 3, -4, 2

answer

P(x) = x³ - x² - 14x + 24

question

Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x³ - 4x² + 7x - 12

answer

None of the listed answers are correct

question

Simplify 3x² - 4x - 5 + 4x² + 8x - 7

answer

7x² + 4x - 12

question

Classify the polynomial by degree and number of terms. Describe the shape of its graph. 3x³

answer

cubic monomial; 'S' shaped with 2 turns

question

Evaluate 2x² + 3x + 4 when x=2

answer

18

question

For the function, use synthetic division and substitution to determine whether the given value is a zero of the function. P(x) = 3x⁴ - 10x³ - 41x² + 68x + 60

answer

Zeroes are 5, 2, -2/3, -3

question

Evaluate x⁴ - 10x² + 24 when x=3

answer

15

question

Write the product as a polynomial in standard form. (x - 6)(x + 5)(x - 4)

answer

x³ - 5x² - 26x + 120

question

Use substitution to determine which of the given linear expressions is a not a factor of 3x⁴ - 16x³ - 15x² + 88x + 60

answer

x + 5 Mathway (Algebra) Factor

question

Determine the end behavior of the graph of the function f(x) = 3x⁴ - 2x³ + 2x + 2

answer

rises to the left; rises to the right

question

Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary. f(x) = x⁴ - x³ - 16x² + 10x + 60

answer

3, -2, ±3.16

question

Classify the polynomial by degree and number of terms. Describe the shape of its graph. 7x² + 7x + 7

answer

quadratic trinomial; parabola

question

Determine whether the function is a rational function. If so, find the domain and identify the horizontal and vertical asymptotes, and any holes in the graph. If the function is not rational, state why not. f(x) = (x - 1)/((x - 7)(x + 3))

answer

Incorrect: rational; x≠1, 7 or -3; asymptotes at y=0, x=1, x=7 and x=-3 Correct: rational; x≠-3,7 asymptotes at y=0, x=-3, and x=7

question

Simplify the rational expression. (Evernote) ( 3/(x² + 7x + 12) + 1/(x² + 11x + 28) ) ÷ ( 2/(x² + 10x + 21) + 1/x² + 13x + 36) )

answer

( 4(x + 9)(x + 6) ) / ( 3(x² + 12x + 31) )

question

Simplify. ( (x - 2)/(2x²) ) - ( (2x + 1)/(9x) ) + ( (7x)/(12) )

answer

( 21x³ - 8x² + 14x - 36 ) / 36x²

question

Solve the radical inequality. ³√(3x-6) + 6 ≥ 7

answer

x ≥ 7/3

question

Simplify the rational expression. ( (x² + 14x + 49)/8x ) ÷ ( (x+7)/4x )

answer

(x+7)/2

question

Evaluate the radical expression: (-1/7)(³√-64)⁴

answer

-256/7

question

Rationalize the denominator. 2 ÷ √5

answer

(2√5)/5

question

Rationalize the denominator. (√11) ÷ (9 + √5)

answer

( 9√11 - √55) / 76

question

Simplify. (-3x + 8)/(x² - 49) - (-2x + 1)/(x² - 49)

answer

-1/(x+7)

question

Use the information to write the appropriate variation equation, and find y for the given values. y varies jointly as x and the inverse of z. y=-99.4 when x=-11 and z=4. Find y when x=2 and z=-8.

answer

y = 9x/z; -9/4

question

Simplify the sum, difference, product, or quotient. Assume that the value of any variable is positive ³√(-27x) - 4 ³√(x⁴) + 9 ³√(x) + 9x ³√(x)

answer

6 ³√(x) + 5x ³√(x)

question

Evaluate the radical expression: 8(⁴√(81)²

answer

72

question

Solve the equation or inequality. 4/(x-3) - 2/(x+4) = 0

answer

x=-11

question

Find the domain of the radical function. f(x) - √(9-x)

answer

x ≤ 9 Solution f(x) - √(9-x) = 0 Add √(9-x) to both sides f(x) = √(9-x) Mathway: Find the Domain

question

Use the information to write the appropriate variation equation, and find y for the given values. y varies jointly as x and z. y=98/3 when x=2 and z=7. Find y when x=8 and z=3

answer

y = 7/3(x)(z); 56

question

Designer Dolls, Inc. found that the number of dolls sold, N, varies directly as their advertising budget, A, and inversely as the price of each doll, P. Designer Dolls, Inc. sold 8400 dolls when $84,000 was spent on advertising and the price of a doll was set at $70. Determine the number of dolls sold when the amount spent on advertising is increased to $98,000.

answer

9800

question

Write an equation that can be used to solve the problem. Then answer the question asked. A group of college students are volunteering for Habitat for Humanity during their spring break. They are putting the finishing touches on a house they built. Working alone, Dale Horton can paint a certain room in 3 hours. Kathy Garcia can paint the same room in 9 hours. How long will it take them working together to paint the room?

answer

x/3 + x/9 = 1; 2.25 hr

question

The wattage rating of an appliance is given as "W", in watts, and varies jointly as the resistance, "R", in ohms, and as the square of the current, "I", in amperes. If the wattage is 2 watts when the resistance is 200 ohms and the current is 0.1 amperes, find the wattage when the resistance is 150 ohms and the current is 0.4 amperes.

answer

Incorrect: None of the listed answers are correct Correct: W (wattage) = 24

question

Solve the equation or inequality. (2x-2)/(x²-36) ≥ 1/(x+6)

answer

-6 ≤ x ≤ -4 or x ≥ 6

question

Solve the radical inequality. √(x + 14) ≤ x - 16

answer

x ≥ 22

question

Find the standard equation for the hyperbola with the given characteristics. vertices: (2, 0) and (-2, 0) asymptote: y=1/2x

answer

x²/4 - y² = 1 Put in each answer using Mathway: Find the Vertex Form, till the verices and asymptote matches up

question

Which equation describes a parabola?

answer

6y² + 11x - 13y = -1

question

Find the center and the radius of the circle that has a diameter with the given endpoints. Diameter CD, C(-1, -4), D(5, 4)

answer

center: (2, 0) radius: 5

question

Find the standard equation for the ellipse, using the given characteristics taken from the graph. (Evernote)

answer

(x+4)²/16 + (y+3)²/9 = 1

question

Write the equation in standard form and classify the conic section it defines. 2x² + 2y² - 28x + 24y + 162 = 0

answer

(x-7)² + (y+6)² = 4; circle

question

Find the center and the radius of the circle that has a diameter with the given endpoints. Diameter CD, with endpoints C(- 1, 5), D(5, 9)

answer

center: (2, 7) radius: √13; 3.61 Mathway: Find the Midpoint

question

Find the standard equation of a circle with the given radius and center. radius: 7 center: (1, 1)

answer

(x - 1)² + (y - 1)² = 49

question

Solve the nonlinear system of equations. {x² + y² = 144 {x² - 4y² = 64

answer

four solutions: (±8√2, ±4)

question

Which set of characteristics matches the given standard equation and parabola graph? (Evernote) x = 1/24 y²

answer

vertex: (0, 0) directrix: x=-6

question

Solve the nonlinear system of equations. {x² + y² = 256 {x + y = 16

answer

two solutions: (0, 16) and (16, 0)

question

Which set of characteristics matches the given parabola graph and standard equation? (Evernote) x = -1/4 y²

answer

axis of symmetry: y=0 focus: (-1, 0) vertex: (0, 0) Mathway: Graph

question

Find the standard equation for the hyperbola with the given characteristics. center: (5, 4) one focus: (-25, 4) one vertex: (23, 4)

answer

(x-5)²/324 - (y-4)²/576 = 1

question

The two hyperbolas in the graph are conjugates, meaning they share the same asymptotes. Given the following equation of the hyperbola represented by the thin curve, find the equation of its conjugate, which is represented by the thick curve. (Evernote) x²/9 - y²/25 = 1

answer

y²/25 - x²/9 = 1

question

Identify the conic section produced by the following diagram. (Evernote)

answer

hyperbola

question

Find the standard equation for the hyperbola with the given characteristics. vertices: (2, 0) and (−2, 0) asymptote: y = 3x

answer

x²/4 - y²/36 = 1

question

Which set of characteristics matches the given standard equation and parabola graph? (Evernote)

answer

focus: (-1, -4) vertex: (-1, 2)

question

Identify the conic section produced by the intersection of the plane and the cones in the following diagram.

answer

circle

question

Find the standard equation of a circle with the given radius and center. radius: 4 center: (3, - 5)

answer

(x - 3)² + (y + 5)² = 16 Mathway: Find the Equation (put coordinate points comma r=4)

question

Find the distance between points B(5, 7) and F(1, 2), and the coordinates of the midpoint of BF.

answer

distance = √41; 6.4 midpoint = (3, 9/2) Mathway

question

Find the standard equation for the ellipse, using the given characteristics. vertices: (0, ±8) foci: (0, ±√55)

answer

x²/9 + y²/64 = 1

question

Find: ₇P₄

answer

840

question

A hat contains 22 names, 10 of which are female. If five names are randomly drawn from the hat, what is the probability that at least four female names are drawn?

answer

0.105 ((₁₀C₄ × ₁₂C₁)+(₁₀C₅ × ₁₂C₀))÷(₂₂C₅) ((210 × 12)+(252 × 1))÷(26334) 2772÷26334 = 0.105

question

Teesha is in the bowling club. There are 33 students in the club. Five of them will be picked at random to attend an awards banquet. What is the probability that Teesha will not be randomly chosen to attend the banquet?

answer

28/33 Solution Probability of getting chosen is 5/33, so the the probability of not getting chosen is 33 - 5 = 28

question

How many different arrangements can be made using all of the letters in the word GAME?

answer

24 Solution ₄P₄

question

A spinner is evenly divided into 8 equal areas and numbered from 1 through 8. What is the probability of spinning a number less than 4 in a single spin?

answer

3/8

question

A lunch menu consists of 4 different kinds of sandwiches, 2 different kinds of soup, and 5 different drinks. How many choices are there for ordering a sandwich, a bowl of soup, and a drink?

answer

40 4 × 2 × 5 = 40

question

Two cards are randomly drawn in succession from a deck of 52 playing cards. Find the probability that the king of spades and any ace are drawn, in that order, without replacement.

answer

1/663 or 0.0015082 Solution 1/52 × 4/51 = 0.0015082

question

Evaluate: (₁₂C₇ × ₁₄C₁₀)/₁₃C₅

answer

616 Solution ₁₂C₇ = 792 ₁₄C₁₀ = 1001 ₁₃C₅ = 1287 (792 × 1001)/1287 = 616

question

If 2 blocks are randomly taken from a bag containing 10 blue blocks, 10 red blocks, and 7 yellow blocks, what is the probability of drawing a blue block and a red block?

answer

50/351 or 0.1424501 Solution 10/27 × 10/26 = 0.1424501

question

Determine the probability that you will roll a number greater than 1 on a number cube.

answer

5/6

question

Evaluate: ₇C₄

answer

35

question

A circular, rotating, serving tray has 5 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the circular tray?

answer

24 Solution (n-1)! (5-1)! 4! = 4 × 3 × 2 × 1 = 24

question

How many different ways can 6 people be seated around a circular table?

answer

120 Solution (n-1)! (6-1)! 5! = 5 × 4 × 3 × 2 × 1 = 120

question

Three cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of three cards are possible?

answer

22,100 Solution 52 choose 3 ₅₂C₃ = 22,100

question

How many distinct committees of 14 people can be formed if the people are drawn from a pool of 23 people? Use factorials to express the answer.

answer

₂₃C₁₄ = 23!/(9! 14!) Solution nCr = n!/(r!(n-r)!) 23!/(14!(23-14)!) 23!/(14!(9)!) 23!/ (9! 14!)

question

Jamila spins a spinner with 3 sections of equal area, like the one below, 25 times. It lands on the 1eight times. What is the experimental probability of spinning a 1?

answer

8/25

question

In a bag there are 3 green jelly beans, 2 black jelly beans, and 8 yellow jelly beans. Once a jelly bean is drawn, it is not replaced. Find the probability of randomly drawing a green jelly bean and then a black jelly bean in two consecutive draws.

answer

1/26

question

Suppose you mix-up the cards below and choose one without looking. What is the probability of selecting neither "E" nor "G"? H E H E G W I

answer

4/7 Solution Probability of selecting "E" or "G" is 3/7. 7/7 - 3/7 = 4/7

question

Two cards are randomly selected from a standard 52-card deck. What is the probability of getting 2 diamonds or 2 face cards?

answer

Incorrect: 0.108 Correct: 0.106 or 47/442 Solution (13/52 × 12/51) + (12/52 × 11/51) - (3/52 × 2/51)

question

A box contains 2 green, 6 yellow, and 3 purple balls. Find the probability of obtaining a purple ball in a single random draw.

answer

3/11

question

Find the four arithmetic means between -3 and 102.

answer

18, 39, 60, 81 Solution t(n) = t(1) + (n - 1)d 102 = -3 + (6 -1)d 102 = -3 + 5d 105 = 5d d = 21 Substitute t(2) = -3 + (2 - 1)21 -3 + (1)21 -3 + 21 18 t(3) = -3 + (3 - 1)21 -3 + (2)21 -3 + 42 39 And so on

question

Use Pascal's Triangle to determine the probability that you will get three green lights in a row of five lights. Assume red and green are equally likely occurrences.

answer

Incorrect: 7/32 Correct: 5/16 (10/32) Solution (n C k)(p∧k)(1 - p)∧(n-k) (₅C₃)(½)³(1 - ½)⁵⁻³ (₅C₃)(½)³(1 - ½)² 10 × 1/8 × 1/4 = 5/16

question

Write the first five terms of the sequence defined by the given recursive or explicit formula. (Evernote)

answer

4, -3, 31, -167, 959

question

Expand the binomial raised to a power. (3a - b)⁵

answer

243a⁵ - 405a⁴b + 270a³b² - 90a²b³ + 15ab⁴ - b⁵ Mathway: Expand Using the Binomial Theorem

question

Express 0.7312 as a geometric series, and write its sum as the ratio of two integers.

answer

(Evernote)

question

Evaluate the sum. (Evernote)

answer

-3003

question

Find the sum of the geometric series 0.2 + 0.02 + 0.002 + . . . given the formula S=a/(1 - r), where "a" is the first term, "r" is the common ratio, and "S" is the sum.

answer

2/9 Solution S = 0.2/(1 - 0.1) S = 0.222... or 2/9

question

Find the 6th and 8th entries in the row 12 of Pascal's triangle.

answer

792;792 Solution Use nCk-₁ to love for nth entry ₁₂C₆-₁ = ₁₂C₅ = 792 ₁₂C₈-₁ = ₁₂C₇ = 792

question

Use Pascal's triangle to find the number of ways to choose 3 boxes from 7 boxes.

answer

Incorrect: 21 Correct: 35 Solution ₇C₃ = 35

question

Find the three positive geometric means between 6 and 1875/8.

answer

15, 75/2, 375/4 Solution t₁=6 and t₅=1875/8 t(n) = t₁r^(n-1) t₅ = 6r⁴ 1875/8 = 6r⁴ r = 2.5 t₂ = 6(2.5)¹ 15 t₃ = 6(2.5)² 37.5 or 75/2 t₄ = 6(2.5)³ 9375 or 375/4

question

A 50-row theater has 30 seats in the front row. The second row has 31 seats. If each row has one more than the row in front of it, how many seats are there in the theater?

answer

2725 Solution t₁ = 30 and d = 1 t(n) = t₁ + (n-1)d t₅₀ = 30 + (49)1 t₅₀ = 79 S = n/2[2t₁ + (n - 1)d] S = 50/2[2(30) + 49] S = 25(60 + 49) S = 25(109) S = 2725

question

Find the sum of the infinite geometric series, if it exists. 3 - 9/5 + 27/25 - 81/125 + 243/625 - ...

answer

15/8 Solution (9/5) ÷ 3 = 0.6 r = 0.6 (common ration) t₁ = 3 S = t₁ ÷ (1 - r) S = 3 ÷ (1 - 0.6) S = 3 ÷ 0.4 S = 7.5 or 15/8

question

Use the given formula to find the first four terms of the arithmetic sequence. t(n) = 12 - 3n

answer

9, 6, 3, 0 Solution t(1) = 12 - 3(1) 9 t(2) = 12 - 3(2) 6 ...

question

There are 8 cars in a parking lot on a very cold day. Suppose the probability of any one of them not starting is 0.14. What is the probability that exactly 3 of the cars will not start?

answer

Incorrect: ≈ 0.003 Correct: ≈ 0.072 Solution (nCk) × (p)^n × (1 - p)^(n - k) (₈C₃) × (0.14)³ × (1 - 0.14)⁵ = 0.072

question

Write an explicit formula for the nth term of the geometric sequence. 7/4, 49/24, 343/144, 2401/864, ...

answer

(Evernote) Solution explicit formula for nth term in a geometric sequence is t(n) = t₁r^(n-1) t₁ = 7/4 and r = 7/6 t(n) = 7/4(7/6)^(n-1)

question

Find the sum of the infinite geometric series, if it exists. (Evernote) ∑3(-½)^(k-1)

answer

2 Solution ∑3(-½)^(k-1) t₁ = 3(-½)⁰ 3 t₂ = 3(-½)¹ -1.5 r = t₂/t₁ r = -1.5 ÷ 3 r = -½ S = t₁/(1 - r) S = 3/(1 - (-½)) S = 3/1.5 S = 2

question

Find the sum of the first 7 terms of the geometric series 8 + 8/3 + 8/9 + 8/27 + ...

answer

11.99 Solution r ≠ 1 r = 8/3 ÷ 8 r = 1/3 & t₁ = 8 S(n) = t₁[(1 - r^n) ÷ (1 - r)] S₇ = 8[(1 - (1/3)⁷) ÷ (1 - 1/3)] S₇ = 11.99

question

Use Pascal's triangle to solve for the value of n: 2(n C 3) = n+4 C ₇ (Evernote)

answer

Incorrect: 2 Correct: 4

question

Make a conjecture about the pattern of the given data. Find the sum of the 7th row. 3 3 + 6 + 3 3 + 6 + 9 + 6 + 3 3 + 6 + . . . + ( 3n − 3) + ( 3n ) + ( 3n − 3) + . . . + 3

answer

Incorrect: The sums of the rows are 3, 12, 27, . . . . The sum of the nth row is n(2n +3). The sum of the 7th row is 119. Correct: The sum of the rows are 3, 12, 27, . . . . The sum of the nth row is 3(n²). The sum of the 7th row is 147.

question

Find the two geometric means between 7 and 3584.

answer

Incorrect: 63, 567 Correct: 56, 448 Solution t₁=7 and t₄=3584 Formula t(n) = t₁r^(n - 1) Substitute t(4) = 7r⁴⁻¹ 3584 = 7r³ divide both sides by 7 r³ = 512 Take cube root of both sides r = 8 t(2)=7 × 8 56 t(3)=7 × 8² 448 7, 56, 448, 3584

question

Find the mean, the median, and mode of the data set: 14, 6, 21, 16, 16, 7, 20, 19, 7

answer

Mean: 14 Median: 16 Mode: 7, 16

question

Using the given information, which data set is the correct choice? (Evernote)

answer

20, 12, 27, 14, 16, 13, 12, 13, 26, 27, 21, 28, 20, 22, 20

question

Find the minimum and maximum values, quartiles, range, and interquartile range for the data set. 29, 14, 40, 12, 16, 46, 22, 23, 19, 31, 7, 9

answer

Minimum = 7 Maximum = 46 Q₁=13; Q₂=20.5; Q₃=30 Range = 39 IQR = 17 Q₂ = mean

question

Last year, the personal best high jumps of track athletes in a nearby state were normally distributed with a mean of 205 cm and a standard deviation of 13 cm. What is the probability that a randomly selected high jumper has a personal best between 218 and 244 cm? (Evernote)

answer

0.1574 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(→Enter→75, 90, 85, 7) Between, mean, then standard deviation

question

The bowling scores of all of the bowlers in 12 bowling leagues are normally distributed. Their mean score is 201 points, with a standard deviation of 33 points. If one league has 120 bowlers, how many of them are likely to score more than 168 points?

answer

101 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(168, 10⁹⁹, 201, 33)→Enter = 0.84 .84 or 84% 84% of 120 is 100.8 rounded to the nearest whole number equals 101

question

Find the variance and the standard deviation for the following data. 7, 20, 7, 15, 21, 4, 22, 17, 13

answer

variance ≈ 39.78; standard deviation ≈ 6.31 https://www.easycalculation.com/statistics/standard-deviation.php Take the Variance (Population Standard deviation) and Population Standard deviation

question

Find the minimum and maximum values, quartiles, range, and interquartile range for the data set. 27, 8, 9, 48, 19, 10, 29, 42, 2, 50, 44

answer

Minimum = 2 Maximum = 50 Q₁=9; Q₂=27; Q₃=44 Range = 48 IQR = 35 Mathway Find the Five Number Summary, range, and Find the Interquartile Range (H-Spread)

question

Using the given stem and leaf plot and and it's median and mode, select the data set on which it was created. (Evernote)

answer

7, 6.9, 8.2, 7.6, 6, 7.2, 8.4, 7.6, 7.3, 7.8, 6.2, 9.5, 8.9, 6.5, 9

question

An English class was taken by 28 students. Their final scores were: three As, five Bs, nine Cs, six Ds, and five Fs. Using the given frequency table, find the mean grade point score, using A = 4, for the entire group of 28 students. Give the answer to the nearest hundredth, if necessary. (Evernote)

answer

Incorrect: [none] Correct: 1.82 (Close to a "C")

question

NCUse the frequency table below, with the a total of 18 catalog items sold at four different prices, to find the average price per item. (Evernote)

answer

$16.50

question

The relative frequency histogram below represents the age in years of the first 100 children to have their portraits taken at the "See What Develops" photography studio. What is the probability that the next child to have portraits taken will be between 1 and 2 years old?

answer

Incorrect: None of the listed answers are correct Correct: 31/100 or 31% (maybe 0.315 or 32%) Solution .11 + .20 + .31 + 30 + .15 + 24 = 1 (or 100%) Age 1= .20 Age 2= .11 .20 + .11 = .31 (or 31%) 31/100 or 31% Probability

question

A number cube is tossed 10 times with the following results. 5, 6, 1, 5, 5, 2, 6, 1, 2, 2 Find the range and the mean deviation of the data.

answer

None of the listed answers are correct To find mean deviation minus the mean from each data value, add everything up, then divide by the number of data values. Example: 54, 49, 47, 48, 52 mean of data = 50 54 - 50 = | 4 | = 4 49 - 50 = |-1| = 1 47 - 50 = |-3| = 3 48 - 50 = |-2| = 2 52 - 50 = | 2 | = 2 4 + 1 + 3 + 2 + 2 = 12 12 ÷ 5 = 2.4 Mean deviation = 2.4

question

A company guarantees customer satisfaction on the purchase of a product, or the company will refund the purchase price of the product. Previous experience has shown that 6% of the purchases are returned. What is the probability that no more than 1 of the next 6 purchases will be returned?

answer

0.954 Solution ((₆C₁)(0.06)¹(1 - 0.06)⁵) + ((₆C₀)(0.06)⁰(1 - 0.06)⁶) = 0.954

question

In Sean's school there are 96 families which have 4 children. The circle graph shows the probability of each combination of girls and boys in a family with four children. Use the circle graph to predict the probability that one of these 96 families, chosen at random, will only have children of the same sex. (Evernote)

answer

12.5%

question

A biologist is collecting insects in a field. Beetles represent 67 percent of all the insects that have been collected so far. What is the probability that exactly half of the next 6 insects collected will be beetles?

answer

0.21617 Solution (₆C₃)(0.67)³(1-0.67)³ = 0.21617

question

The depth of snow at seven different mountain lodges is 13 in., 15 in., 21 in., 17 in., 90 in., 13 in., and 19 in. Find the mean, median, and mode. Tell which measure is the most useful for predicting how deep the snow will be at an eighth lodge.

answer

Mean = 26.9 in Median = 17 in Mode = 13 The median is the most useful.

question

The personal savings of the Young Saver Club were normally distributed with a mean of $525 and a standard deviation of $64. What is the probability that a randomly selected saver has an account total between $525 and $589?

answer

0.3413 Solution (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(525, 589, 525, 64)→Enter = 0.3413

question

A company guarantees customer satisfaction on the purchase of a product, or the company will refund the purchase price of the product. Previous experience has shown that 6% of all purchases are returned. What is the probability that no more than 1 of the next 7 purchases will be returned?

answer

≈ 0.938 ((₇C₁)(0.06)¹(1 - 0.06)⁶) + ((₇C₀)(0.06)⁰(1 - 0.06)⁷) ≈ 0.938

question

The class average on a math test was 77.5 and the standard deviation was 5.8. Find the z-score for a test score of 83, and the percentage of the class who scored below 83.

answer

≈ 0.95; 82.89% Solution z-score z = (x - x̅) ÷ σ z = (83 - 77.5) ÷ 5.8 = 0.948 → 0.95 (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(-10⁹⁹, 83, 77.5, 5.8)→Enter = 0.83 or 83%

question

In a certain normal distribution of scores, the mean is 30 and the standard deviation is 5.5. Find the z-score corresponding to a score of 37 and find the percentage of the scores that are below 37.

answer

1.27; 89.80% Solution z-score z = (x - x̅) ÷ σ z = (37 - 30) ÷ 5.5 = 1.27 (Graphing calculator) 2nd→VARS→DRAW→1:ShadeNorm(-10⁹⁹, 37, 30, 5.5)→Enter = 0.8984 or 89.80%

question

Refer to ∆ ABC below to find the indicated value listed. Find the exact value and the value rounded to the nearest ten-thousandth, if necessary. Find tan x (Evernote)

answer

3/4 or 0.75 Solution tan x = opp./adj. 24/32 = 0.75

question

Evaluate the trigonometric expression. Sin⁻¹(-½)

answer

-30° Solution π = 180° -π/6 -180°/6 = 30° Mathway Evaluate (Do not use Find the Exact Value)

question

Refer to ∆ ABC below to find the indicated value listed. Find the exact value and the value rounded to the nearest ten-thousandth, if necessary. (Evernote)

answer

8/17 or 0.4706 sinθ = opp./hyp.

question

Use the following information to find the unknown sides and angles. m∠B = 28°; c=18

answer

b = 8.5; a = 15.9; m∠A = 62°; m∠C = 90° Solution We have two angles m∠A + m∠B + m∠C = 180 m∠A + 28° + 90° = 180° m∠A = 62° Use Law of Sines to solve for side "a" or "b' a/sin A = c/sin C a/sin(62°) = 18/sin(90°) a = 18sin(62°)/sin(90°) a = 15.89 → 15.9 b/sin B = a/sin A b/sin(28°) = 15.9/sin(62°) b = 15.9sin(28°)/sin(62°) b = 8.45 → 8.5

question

What is the reference angle for 516° ?

answer

24° Mathway (Trigonometry) Find the Reference Angle

question

Find tan 421°.

answer

1.804 Mathway (Trigonometry) Find the Exact Value

question

For ∆ ABC, find the measure of ∠A to the nearest degree. (Evernote)

answer

19° Solution Use Law of Cosines for "c" c = √(a² + b² - 2ab cos C) c = 37 a = 12, b = 35, and c = 37 Use Law of Sines sin A/a = sin C/c sin A/12 = sin(90°)/37 sin A = 12sin(90°)/37 sin A ≈ 12/37 Convert from radians to degrees ∠A = 18.58° → 19°

question

Evaluate the trigonometric expression. cos(Cot⁻¹1)

answer

√2/2 Mathway (Trigonometry) Find the Exact Value

question

Given the quadrant of θ in standard position and a trigonometric function value of θ, find exact values for the remaining functions. Quadrant II, sinθ = 2/7

answer

cosθ = -3√5/7 tanθ = -2√5/15 cotθ = -3√5/2 secθ = -7√5/15 cscθ = 7/2 Mathway (Trigonometry) Find the Other Trig Values in Quadrant II

question

Find tan 382°.

answer

0.404 Mathway (Trigonometry) Find the Exact Value

question

Convert 279° to radians.

answer

(31/20)π Mathway (Trigonometry) Convert from Degrees to Radians

question

Find the reference angle for 525°.

answer

15° Mathway (Trigonometry) Find the Reference Angle

question

Point P is located at the intersection of a circle with a radius of r and the terminal side of an angle θ. Find the coordinates of P to the nearest hundredth. θ = 120° , r = 13

answer

P(- 6.5, 11.26) Solution 120° is in Quadrant II Coordinates: (cos θ = x/r, sin θ = y/r) θ = 120° and r = 13 cos(120°) = x/13 -½ = x/13 x = -13/2 or -6.5 sin(120°) = y/13 √3/2 = y/13 y = 13√3/2 or 11.26 P(-6.5, 11.26)

question

The function d = - 6 cos 3t describes a simple harmonic motion, where d is the distance (in meters) an object travels in t seconds. What is the frequency?

answer

Incorrect: 3π/2 cycles/seconds Correct: 3/2π Solution d = A cos wt d = -6 cos 3t w = 3 f (frequency) = w/2π f = 3/2π

question

For a circle of radius 4 feet, find the arc length "s" subtended by a central angle of π/30 radians. Round to the nearest hundredth.

answer

None of the listed answers are correct Solution r = 4 and θ = π/30 s = rθ s = 4(π/30) s = 2π/15

question

The function d = 9 cos 2t describes a simple harmonic motion, where d is the distance (in meters) an object travels in t seconds. What is the maximum displacement of the object from its resting position?

answer

9 m Solution A = displacement d = A cos wt d = 9 cos 2t A = 9 or 9m

question

Find cot (-290°).

answer

0.364 Mathway (Trigonometry) Find the Exact Value

question

For a circle of radius 8 feet, find the arc length of a central angle of 30°.

answer

(4/3)π feet Solution r = 8 and θ = π/6 (change 30° to radians) s = rθ s = 8(π/6) s = (4/3)π or 4π/3

question

Find the amplitude, the period, and the frequency of the graph. Then write an equation for the sine function for the graph.

answer

3/4, 180°, 2, y = 3/4 sin 2x Graph all multiple choices and pick the one that fits

question

Find the exact value of the sine, cosine, and tangent of -210°.

answer

sin = 1/2 cos = -√3/2 tan = -√3/3 Mathway (Trigonometry) Find the Exact Value

question

Suppose the depth of the tide in a certain harbor can be modeled by y = 25 - 4 cos(π/6t), where "y" is the water depth in feet and "t" is the time in hours. Consider a day in which t = 0 represents 12:00 midnight. For that day, when are high tide and low tide and what is the depth of each?

answer

Incorrect: high tide at 12:00 noon and 12:00 midnight, depth 29 ft low tide at 6:00 a.m. and 6:00 p.m., depth 21 ft Correct: high tide at 12:00 noon and 12:00 midnight, depth 21 ft low tide at 6:00 a.m. and 6:00 p.m., depth 29 ft

question

Use either the Law of Sines or the Law of Cosines to solve for "a" to the nearest tenth. (Evernote)

answer

28.8 Solution ∠A + 61° + 76° = 180° ∠A = 43° Use Law of Sines a/sin(43°) = 41/sin(76°) a = 41sin(43°)/sin(76°) a = 28.8

question

Find cos((1/2)A) and sin((1/2)A) if sin(A)=4/5 and Ais a first-quadrant angle. (Evernote)

answer

Incorrect: cos(A/2) = √3/5 sin(A/2) = 2/5 Correct: cos(A/2) = (2√5)/5 sin(A/2) = √5/5 Solution Pathagorean Identities sin A = 4/5 cos²A = 1 - sin²A cos A = 1 - (4/5)² cos A = 3/5 Use Half-Angle Identities sin(A/2) = √((1 - cos A)/2) sin(A/2) = √((1 - 3/5)/2) sin(A/2) = √5/5 cos(A/2) = √((1 + cos A)/2) cos(A/2) = √((1 + 3/5)/2) cos(A/2) = (2√5)/5 A = θ and the cos((1/2)A) is the same as cos(A/2)

question

Find all solutions of cos(x) - √(1 - 3cos²(x)) = 0

answer

Incorrect: None of the listed answers are correct Correct: No Solution

question

Use the Law of Sines to solve for m∠A to the nearest tenth. (Evernote)

answer

29.8 Solution sin B/b = sin C/c sin B/43 = sin(80°)/45 sin B = 43sin(80°)/45 sin B = 0.94103 sin⁻¹(sin B) = ∠B sin⁻¹((43sin¹(80°)/45)) sin⁻¹(0.94103) = 70.2° (rounded to the nearest tenth) ∠B = 70.2° ∠A + 70.2° + 80° = 180° ∠A = 29.8° Use graphing calculator on degree mode or use Mathway and change answer to degrees.

question

Write the expression csc(2x) + cot(2x) in terms of tan x or cot x.

answer

Incorrect: None of the listed answers are correct Correct: cot(x)

question

Use the Law of Cosines to solve for "A" to the nearest tenth of a degree. (Evernote)

answer

35.3° Law of Cosines cos A = (b² + c² - a²)/(2bc) cos A = (43² + 50² - 29²)/(2 × 43 × 50) cos A = 0.8158 cos⁻¹(0.8158) = 35.3° Just do this ↓ ∠A = cos⁻¹((b² + c² - a²)/(2 × 43 × 50)) ∠A = 35.3°

question

Find the exact value of sin(- 450° + 300°).

answer

-1/2 Solution Use Sum and Diffrence Identities: sin(A + B) = sinAcosB + cosAsinB sin(450°)cos(300°) + cos(450°)sin(300°) = -1/2 Mathway (Trigonometry) Find the Exact Value

question

Solve sin(x) - √(1 - 3sin²(x)) = 0 given that 0° ≤ x ≤ 360°.

answer

Incorrect: 90°, 270° Incorrect: None of the listed answers are correct Correct: 30°, 150°, 210°, 330° Solution sin(x) = √(1 - 3sin²(x)) sin²(x) = 1 - 3sin²(x) sin²(x) + 3sin²(x) - 1 4sin²(x) - 1 (2sin(x) + 1)(2sin(x) - 1) sin(x) = -1/2 and 1/2 x = -30°, 30°, 150°, 210° Add 360° to -30° -30° + 360° = 330° x = 30°, 150°, 210°, 330° Or graph y = sin²(x) y = 1 - 3sin²(x) Intersections: 30°, 150°, 210°, 330°

question

Find the image of (5, -6) after a counterclockwise rotation of 270° about the origin. (Evernote)

answer

(-6, -5)

question

Wilfred is checking his bicycle's wheel. The wheel has a radius of 25 cm, and its center is 54 cm above the ground. Wilfred is rotating the wheel at a constant speed of 230° /s. The height of a point on the tire as a function of time is given by h = 54 + 25 sin(230t), where h is the height in centimeters and t is the time in seconds. Find h when t = 5.5 s. Round your answer to the nearest tenth of a centimeter.

answer

Incorrect: None of the listed answers are correct Correct: 51.8 Solution h = 54 + 25 sin(230t) h = 54 + 25 sin(230 × 5.5) h = 51.8

question

Solve sin(x) - √(1 - 3sin²(x)) = 0 given that 0° ≤ x ≤ 360°

answer

Incorrect: 90°, 270° Incorrect: None of the listed answers are correct Correct: 30°, 150°, 210°, 330° Solution sin(x) = √(1 - 3sin²(x)) sin²(x) = 1 - 3sin²(x) sin²(x) + 3sin²(x) - 1 4sin²(x) - 1 (2sin(x) + 1)(2sin(x) - 1) sin(x) = -1/2 and 1/2 x = -30°, 30°, 150°, 210° Add 360° to -30° -30° + 360° = 330° x = 30°, 150°, 210°, 330° Or graph y = sin²(x) y = 1 - 3sin²(x) Intersections: 30°, 150°, 210°, 330°

question

Given that F = 32°, G = 55°, and f = 10, solve the triangle. If no such triangles exist, write none. Round to the nearest tenth. (Evernote)

answer

E = 93° , g = 15.5, e = 18.8 Solution F = 32°, G = 55° , E = ?° f = 10, g = ?, e = ? 32° + 55° + ∠E = 180° ∠E = 93° Use Law of Sines 10/sin(32) = g/sin(55) g = 10sin(55)/sin(32) g = 15.5 10/sin(32) = e/sin(93) e = 10sin(93)/sin(32) e = 18.8

question

Given sinθ = 5/9, where π/2 < θ < π, find the exact values of sin 2θ and cos 2θ.

answer

Incorrect: -31/81, (20√14)/81 Correct: 10/9, -(4√14)/9

question

Which of the following is equal to sin²(x)/(1 - cos(x))

answer

Incorrect: None of the listed answers are correct Correct: 1 + cos(x) or 1 + cosθ Mathway Rationalize the Denominator Mathway Verify the Identity+

question

Find the exact value of cos(345°).

answer

(√6 + √2)/4 Mathway (Trigonometry) Find the Exact Value

question

Whitney starts the engine on her small private airplane. The engine drives a propeller with a radius of 7.5 feet and its centerline 12.5 feet above the ground. At idle, the propeller rotates at a constant speed of approximately 850 revolutions per minute. The height of one propeller tip as a function of time is given by h = 12.5 + 7.5 sin(850t), where h is the height in feet and t is the time in minutes. Find h when t = 2.5

answer

8.2 ft Solution h = 12.5 + 7.5 sin(850t) h = 12.5 + 7.5 sin(850 × 2.5) h = 8.2

question

Solve triangle ABC given that a = 11, b = 13, and c = 15.

answer

A = 45.6° , B = 57.6° , C = 76.9° Solution Use Law of Cosines cos A = (b² + c² - a²)/2bc cos A = (13² + 15² - 11²)/(2 × 13 ×15) cos A = 7/10 cos⁻¹(7/10) = 45.6° cos B = (c² + a² - b²)/2ca cos B = (15² + 11² - 13²)/(2 × 15 × 11) cos B = 59/110 cos⁻¹(59/110) = 57.6° cos C = (a² + b² - c²)/2ab cos C = (11² + 13² - 15²)/(2 × 11 × 13) cos C = 5/22 cos⁻¹(5/22) = 76.9°

question

csc(2x) + cot(2x) forms an identity with which of the following?

answer

cot x Use Mathway to "Verify the Identity" csc(2x) + cot(2x) = cot(x)

question

Which of the following is an identity?

answer

(cos(x))/(1 + sin(x)) = (1 - sin(x))/(cos(x)) Mathway Verify the Identity

question

√((6x + 2)² - 4(9)(x²+1))/(2(9)) I got √(12x - 16)/9 → √(4(3x - 4))/9 But the book has √(6x - 8)/9 → √(2(3x -4))/9

answer

Algebra 2
Data
Measure Of Central Tendency
Statistics

Validity and Reliability Assessments-Epidemiology – Flashcards 35 terms
Henry Smith

35 terms
Preview

Validity and Reliability Assessments-Epidemiology – Flashcards

question

What are the three indices of central tendency?

answer

1. mode 2. median 3. mean

question

the most frequently occurring observation

answer

mode

question

the measurement level below which half the observations fall, the 50th percentile

answer

median

question

the sum of the observed measurements divided by the number of observations

answer

mean

question

ability to distinguish between who has a disease and who does not

answer

validity

question

What are two ways to measures validity?

answer

1. specificity 2. sensitivity

question

ability of the test to determine correctly those who have the disease

answer

sensitivity

question

ability of the test to determine correctly those who do not have the disease

answer

specificity

question

true positive/true positive + false negative

answer

sensitivity

question

true negative/true negative + false positive

answer

specificity

question

the degree to which the study accurately answers the question it is intended to answer

answer

internal validity (study)

question

What are threats to internal validity?

answer

1. selection bias 2. information bias 3. uncontrolled confounding 4. small study sample

question

the extent to which we can generalize the results of a study to a broader population beyond the study population

answer

external validity (generalizability)

question

What is the threats to external validity?

answer

1. small study sample 2. improper selection of sample

question

the degree to which a test actually measures what it is designed to measure

answer

measurement validity (variable)

question

What are the threats to measurement validity?

answer

1. observer bias 2. instrument bias

question

restrict the study population to individuals who are comparable in other respects for the outcome under study

answer

increasing validity

question

restrict the study population to individuals whom complete and accurate information can be obtained

answer

increasing validity

question

provides information about the proportion of people who have the disease and those who do not have the disease

answer

predictive value

question

found by dividing the number of true positives by the total number who tested positive (true positives + false positives)

answer

positive predictive value

question

found by dividing the number of true negatives by the total number who tested negative (true negatives + false negatives)

answer

negative predictive value

question

What are the factors that affect the predictive value?

answer

1. prevalence of disease 2. specificity of the test

question

the degree to which a measurement procedure can be reproduced

answer

reliability

question

What are the threats to reliability?

answer

1. differences in observations 2. differences in instruments of measurements 3. instability of the attribute being measured

question

What affects reliability?

answer

1. intrasubject variation 2. intraobserver variation 3. interobserver variation

question

variation within individual subjects

answer

intrasubject variation

question

intrinsic biologic variability in the study subjects due to such things as fluctuations in mood or circadian rhythms

answer

intrasubject variation

question

variation in the reading of test results by the same reader

answer

intraobserver variation

question

variability in measurement that is due to the observer and includes such things as choice of words in an interview.

answer

intraobserver variation

question

variation between those reading the test results

answer

interobserver variation

question

variation between observers

answer

interobserver variation

question

What is used to evaluate interobserver variation?

answer

1. Percent agreement 2. Kappa Statistic

question

total agreed observations/total observations x 100

answer

percent agreement

question

quantifies the agreement that exceeds that which would be expected by chance alone

answer

kappa statistic

question

What are ways to increase reliability?

answer

1. standardizing the study procedures 2. standardizing the measurement methods 3. using the most up to date equipment 4. using similar testing conditions 5. repeat testing of samples

Algebra
Algebra 2
Greater Than Zero
Multiplication

6th Grade Math – 100 things to know – Flashcards 100 terms
Kevin Stewart

100 terms
Preview

6th Grade Math – 100 things to know – Flashcards

question

1. Addition, subtraction, multiplication and division are called the

answer

operations.

question

2. A pneumonic device to help you remember the order of operations is

answer

PEMDAS.

question

3. If an equation contains both addition and subtraction with neither in parenthesis, you do the first one

answer

first.

question

4. If an equation contains both multiplication and division with neither in parenthesis, you do the first one

answer

first.

question

5. The answer to an addition problem is a

answer

sum.

question

6. The answer to a subtraction problem is the

answer

difference.

question

7. The answer to a division problem is a

answer

quotient.

question

8. The answer to a multiplication problem is a

answer

product.

question

9. A lower case letter that stands for an unknown number is a

answer

variable.

question

10. A complete number sentence with an equal sign is called an

answer

equation.

question

11. A combination of numbers and algebraic terms which does not include an equal sign is an

answer

expression.

question

12. An expression does not contain an

answer

equal sign.

question

13. To multiply by 10, move the decimal one place to the

answer

right.

question

14. To multiply by 100, move the decimal two places to the

answer

right.

question

15. To divide by 10, move the decimal one place to the

answer

left.

question

16. To divide by 100, move the decimal two places to the

answer

left.

question

17. Fractions and decimals can be multiplied and divided, but percents

answer

cannot.

question

18. By dividing the numerator by the denominator, a fraction is changed to a

answer

decimal.

question

19. Moving the decimal two places to the right changes a decimal number to a

answer

percent.

question

20. A percent can be changed to a fraction by putting the number over 100 and

answer

reducing to lowest terms.

question

21. When dividing a fraction to change it to a decimal, the top number goes in the

answer

"house".

question

22. To change a percent to a decimal, remove the percent sign and

answer

move the decimal two places to the left.

question

23. To add or subtract fractions, you must first find a common denominator and

answer

change both fractions.

question

24. To add or subtract decimals, you must first

answer

align the decimals.

question

25. To multiply decimals, you multiply the problem first and then put the decimal in the answer,

answer

counting the same number of decimal places from the right as found in the problem.

question

26. To divide by a decimal, change the divisor to a whole number and move the decimal in the dividend

answer

the same number of places to the right.

question

27. To multiply fractions, multiply the numerators and denominators

answer

straight across and simplify.

question

28. To divide fractions,

answer

flip the second fraction and multiply.

question

29. A triangle with all sides congruent is

answer

equilateral.

question

30. A triangle with two congruent sides is

answer

isosceles.

question

31. A triangle with no congruent sides is

answer

scalene.

question

32. Every triangle can be classified by its

answer

sides or angles.

question

33. A triangle with two congruent angles and two congruent sides is

answer

isosceles.

question

34. A triangle with 2 acute angles and one obtuse angle is

answer

obtuse.

question

35. A triangle with 3 angles which measure less than 90° is

answer

acute.

question

36. A triangle with one angle which measures exactly 90° is

answer

right.

question

37. Two values that are the same are

answer

equal.

question

38. Two shapes that are exactly the same are

answer

congruent.

question

39. Two shapes that are the same shape but different sizes are

answer

similar.

question

40. A number can be divided evenly by 2 if it is

answer

even.

question

41. A number can be divided evenly by 5 if it ends

answer

in 5 or 0.

question

42. A number can be divided evenly by 3 if the sum of its digits can be divided evenly by

answer

3

question

43. A number can be divided evenly by 9 if the sum of its digits can be divided evenly by .

answer

9

question

44. A number can be divided evenly by 6 if it is even and can be divided by

answer

3

question

45. A closed figure made of straight lines is a

answer

polygon.

question

46. A polygon with 5 sides is a

answer

pentagon.

question

47. A polygon with 6 sides is a

answer

hexagon.

question

48. A polygon with 7 sides is a

answer

heptagon.

question

49. A polygon with 8 sides is an

answer

octagon.

question

50. A polygon with 10 sides is a

answer

decagon.

question

51. A polygon with 4 sides is a

answer

quadrilateral.

question

52. The symbol for "is less than" is

answer

<.

question

53. When placing numbers on a number line, negative numbers always go the

answer

left of zero.

question

54. When comparing two numbers, the largest is always the one to the

answer

right on a number line.

question

55. When comparing two fractions with different denominators, use the

answer

bottoms-up method.

question

56. When comparing 3 or more fractions with different denominators, you must find a

answer

common denominator.

question

57. When comparing decimals, write the decimals in a list,

answer

align the decimals, annex zeros, and compare.

question

58. An angle measuring exactly 90°is a

answer

right angle.

question

59. An angle measuring less that 90°is called

answer

acute.

question

60. An angle measuring more than 90°is called

answer

obtuse.

question

61. An angle measuring exactly 180°is called a

answer

straight angle.

question

62. Two angles which are next to each other and share a leg are said to be

answer

adjacent.

question

63. Two angles whose measurement totals 90°are

answer

complementary.

question

64. Two angles whose measurement totals 180° are

answer

supplementary.

question

65. When two lines cross, the two angles directly across from each other look like kissing foxes and are classified as

answer

vertical angles.

question

66. Lines that cross are

answer

intersecting lines.

question

67. Lines that cross at a 90° angle are

answer

perpendicular lines.

question

68. Two lines that are in the same plane and stay the same distance apart are

answer

parallel lines.

question

69. Two lines that are not in the same plane and never touch are

answer

skew lines.

question

70. Numbers that only have themselves and one as factors are

answer

prime numbers.

question

71. Numbers that are not prime are

answer

composite.

question

72. Little numbers that are multiplied to make a product are called

answer

factors.

question

73. Two numbers equal distance from zero are called

answer

opposites.

question

74. The distance a number is from zero is called its

answer

absolute value.

question

75. The smallest number in a set of data is called the

answer

minimum.

question

76. The highest number in a set of data is called the

answer

maximum.

question

77. The middle number in a set of data is called the

answer

median.

question

78. The average is also called the

answer

mean.

question

79. To solve for the variable in a one-step equation, you must do the

answer

inverse operation.

question

80. On a coordinate plane, the horizontal number line is called the

answer

x-axis.

question

81. On a coordinate plane, the vertical number line is called the

answer

y-axis.

question

82. The place where the x- and y-axis cross is called the

answer

origin.

question

83. The points on a coordinate plane are designated by two numbers in parenthesis called the

answer

ordered pair.

question

84. In an ordered pair, the first number tells you to go left or right from the

answer

origin.

question

85. In an ordered pair, the second number tells you to go up or down from the

answer

x-axis.

question

86. Compound probability can be displayed by making a

answer

list or drawing trees.

question

87. The list of all possible outcomes when figuring probability is known as a

answer

sample space.

question

88. The result of an experiment or even is an

answer

outcome

question

89. An outcome is always shown as a

answer

whole number.

question

90. Probability is shown as a

answer

decimal or a fraction.

question

91. Sliding a point or one dimensional figure on a coordinate plane is called

answer

translation.

question

92. Flipping a point over an axis on a coordinate plane is called

answer

reflection.

question

93. Turning a figure around a point on a coordinate plane is called

answer

rotation.

question

94. To convert a metric measurement to a smaller unit, move the decimal to the

answer

right.

question

95. To convert a metric measurement to a larger unit, move the decimal to the

answer

left.

question

96. The formula for perimeter of a polygon is

answer

add all sides.

question

97. The formula for area of a square is

answer

side squared. (length x width)

question

98. The formula for area of a rectangle is length times

answer

width.

question

99. The formula for area of a triangle is base times height divided by

answer

two.

question

100. The area of a polygon is always labeled in

answer

square units.

Algebra
Algebra 2
Completing The Square

Quadratic Functions – Vocabulary – Flashcards 20 terms
Martha Hill

20 terms
Preview

Quadratic Functions – Vocabulary – Flashcards

question

Quadratic Function

answer

a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero

question

Parabola

answer

a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve

question

Parent Function

answer

the most basic function of a family of functions, or the original function before a transformation is applied

question

Vertex

answer

the point of intersection of lines or the point opposite the base of a figure

question

Axis Of Symmetry

answer

A line that divides a figure in half so that each half is the mirror image of the other

question

Minimum Value

answer

The lowest point of a parabola (when a>0)

question

Maximum Value

answer

The highest point of a parabola ( when a<0)

question

Intercept Form

answer

y=a(x-p)(x-q)

question

Quadratic Equation

answer

ax² + bx + c = 0

question

x-intercept

answer

x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero

question

Square Root

answer

√(xy) = √x · √y, a number that when multiplied by itself equals a given number

question

Zero Of a Function

answer

a value of x that makes the function's value zero

question

Roots

answer

the solutions to a quadratic equation

question

Perfect Square

answer

a square of a whole number

question

Linear Function

answer

a function in which the graph of the solutions forms a line

question

Exponential Function

answer

a function in which an independent variable appears as an exponent

question

Discriminant

answer

b²-4ac

question

Perfect Square Trinomial

answer

a trinomial in the form a²+2ab+b² or a²+2ab+b²

question

Axis of symmetry (mathematically)

answer

X = - b/2a

question

vertex has a x-coordinate of

answer

X = - b/2a, (X,Y)

Algebra
Algebra 1
Algebra 2
AP Macroeconomics
Macroeconomics
Principles Of Economics: Macroeconomics

Ap Macroeconomics Unit 2 Test Test Questions – Flashcards 87 terms
Henry Lowe

87 terms
Preview

Ap Macroeconomics Unit 2 Test Test Questions – Flashcards

question

A) Rate of Change [IR]

answer

Current Year-Base Year/Base Year [CPI,rGDP]

question

B) Inflation Rate [IR]

answer

Rate of Change x 100 [CPI,rGDP]

question

A) Rate of Change [PI]

answer

Current Year/Base Year

question

B) Price Index [PI]

answer

Rate of Change x 100

question

Real Wage

answer

Wage Rate/Price Level

question

Real Income

answer

Income/Price Level

question

A) Causes of Inflation-Demand Pull

answer

1) Increase in D for g/s 2) Over employment and wage inflation because of economic growth

question

B) Causes of Inflation-Cost & Push

answer

1) Increase in natural disasters, political disasters 2) Decrease in S because increase in input costs

question

C) Causes of Inflation-Political

answer

Government printing of money to cover debts

question

Fixed Rates

answer

1) Payment form loan and savings 2) Doesn't change based on interest rate from inflation

question

Adjusted Rates

answer

Payment could change based on interest rate from inflation

question

A) Frictional Unemployment

answer

Between jobs

question

B) Seasonal Unemployment

answer

Waiting for the right reason in which to work

question

C) Cyclical Unemployment

answer

Victims of the business cycle

question

D) Structural Unemployment

answer

Skills don't match available jobs

question

Labor Force Participation Rate [LFPR]

answer

Labor Force/Population x 100

question

Unemployment Rate [UR]

answer

Number of Unemployed/Labor Force x 100

question

A) GDP 4 Components

answer

C+Ig+G+Xn

question

B) Consumer Spending [C]

answer

Purchases of finished g/s excluding houses

question

C) Gross Private Business Investment Spending [Ig]

answer

1) Factory equipment maitnance-unsold innovatory bolt within a year, but not sold that year 2) New equipment 3) Construction of housing

question

D) Government Spending [G]

answer

Spending on purchases of g/s

question

E) Exports-Imports [Ex]

answer

1) Exports-cash inflow (credits) 2) Inports-cash outflow (debts)

question

Items NOT counted in GDP

answer

1) Intermediate g/s 2) Used Goods 3) Stocks & Bonds 4) Gifts & Transfers 5) Unreported Business Activity 6) Illegal Activity 7) Non-Market Activities

question

Business Cycle Aggregates

answer

1) Price Levels 2) Outputs 3) Unemployment Rates 4) Current Economy

question

Secular Trend [BC]

answer

Private assumption of long term growth

question

Expansion [BC]

answer

Growth for 6 months minimum

question

Peak [BC]

answer

Time expansion ends

question

Contraction Recession [BC]

answer

Decline for 6 months minimum of rGDP

question

Trough [BC]

answer

Time contractions end

question

Six Months [BC]

answer

Minimum time GDP data is relevant

question

Trough to Trough [BC]

answer

"Length" of a cycle

question

Six Years [BC]

answer

Average length of cycle in the US from 1776-2011

question

Fourteen Months [BC]

answer

Average length of recession in the US from 1900-2011

question

Stagflation [BC]

answer

Both expansion & recession at the same time

question

Misery Index [BC]

answer

Unemployment Rate and Inflation Rate together

question

Recession-Chart [BC]

answer

Increase in unemployment rate and inflation

question

Expansion-Chart [BC]

answer

Decrease in unemployment rate and deflation

question

Aggregate Output

answer

Total quantity of final goods and services produced within and economy

question

rGDP

answer

Total value of all final goods and services produced in the economy during a given year, calculated with base years

question

Nominal GDP

answer

Total value of all final goods and services produced in the economy during a given year, calculated with the prices current in the year in which the output is produced

question

Chain-Linking

answer

Method of calculating changes in real GDP using the average between the growth rate calculated using an early base year and the growth rate calculated using a late base year

question

GDP Per Capita

answer

GDP/total population of a country

question

Employed

answer

Currently holding a job in the economy, either full time or part time

question

Unemployed

answer

Not working and looking for work

question

Labor Force

answer

Employed+Unemployed

question

Discouraged Workers

answer

Individuals who would like to work but have given up looking for a job

question

Marginally Attached Workers

answer

A person who currently is neither working nor looking for work but has indicated that he or she wants and is available for a job

question

Underemployed

answer

People who have part- time jobs but want full- time work or whose jobs are below their experience and education level

question

Job Search

answer

Workers who spend time looking for employment

question

Efficiency Wages

answer

Above-equilibrium wages paid by firms to increase worker productivity

question

Natural Rate of Unemployment

answer

Frictional Unemployment + Structural Unemployment

question

Shoe Leather Costs

answer

The increased costs of transactions caused by inflation

question

Menu Costs

answer

The costs of changing prices

question

Unit-of-Account Costs

answer

Arise from the way inflation makes money a less reliable unit of measurement

question

Nominal Interest Rate

answer

Rate actually paid for a loan

question

Real Interest Rate

answer

Nominal Interest Rate - Inflation Rate

question

Disinflation

answer

A reduction in the rate of inflation

question

Aggregate Price Level

answer

A measure of the overall level of prices in the economy

question

Market Basket

answer

A representative collection of goods and services

question

Price Index

answer

1) A measure of price of a specified collection of goods and services in a given year 2) Equal to 100 in base year

question

Consumer Price Index [CPI]

answer

Measures the cost of the market basket of a typical urban American family

question

Producer Price Index [PPI]

answer

Measures changes in the prices of goods and services purchased by producers

question

GDP Deflator

answer

Nominal GDP/Real GDP x 100

question

National Accounts

answer

Keep track of the flows of money between different sectors of the economy

question

Household

answer

Person or group who share income

question

Firm

answer

Organization that produces g/s for sale

question

Product Markets

answer

Where g/s are bought and sold

question

Factor Markets

answer

Where resources, capital and labor, are bought and sold

question

Consumer Spending

answer

Household spending on g/s

question

Stock

answer

A share of ownership in a corporation held by a shareholder

question

Bond

answer

Loan in the form of an IOU that pays interest

question

Government Transfers

answer

Payments by the government to individuals for which no good or service is provided in return

question

Disposable Income

answer

Income remaining for a person to spend or save after all taxes have been paid

question

Private Savings

answer

1) Disposable Income - Consumer Spending 2) Disposable income that is not spent on consumption

question

Financial Markets

answer

Banking, stock, and bond markets, which channel private savings and foreign lending into investment spending, government and foreign borrowing

question

Government Borrowing

answer

The amount of funds borrowed by the government in the financial markets

question

Government Purchases of Goods and Services

answer

Spending by federal, state, and local governments on goods and services

question

Exports

answer

Goods and Services sold to other countries

question

Imports

answer

Goods and services bought from other countries

question

Inventories

answer

Stocks of goods and raw materials held to facilitate business operations

question

Investment Spending

answer

Spending on productive physical capital, such as machinery and construction of structures, and on changes to inventories

question

Final Goods and Services

answer

Goods and services produced for final use

question

Intermediate Goods and Services

answer

Goods and services purchased by firms for further reprocessing and resale for final use

question

GDP

answer

The total market value of all final goods and services produced annually in an economy

question

Aggregate Spending

answer

Consumer Spending + Investment Spending + Government Purchases of goods & services + (exports - imports)

question

Value Added

answer

Value of Sales-Value of Purchases of Inputs

question

Net Exports

answer

Exports - Imports

Algebra 2
Fish
Standard Deviation Of The Mean

Physics GRE 5. Quantum Mechanics and Atomic Physics – Flashcards 59 terms
Viola Marenco

59 terms
Preview

Physics GRE 5. Quantum Mechanics and Atomic Physics – Flashcards

question

5.1 Average Value of Operator, "A", on state psi

answer

question

5.2 Position-Probability Normalization of state psi

answer

question

5.3 Property of Hermitian Operator "Q" acting on states f and g

answer

question

5.4 Position and Momentum Operators

answer

question

5.5 Probability of Obtaining nth eigenvalue

answer

question

5.6 Expectation (Average) Value

answer

question

5.7 Inner product of and a and b (Bracket Notation)

answer

question

5.8 Bracket Notation Inner product commutative property

answer

question

5.9 Hermitian Conjugate Condition for inner product

answer

question

5.10 f(x), inner product relation for continuum states

answer

question

5.11 inner product relation for states f,g with continuous position locations x

answer

question

5.12 Schrodinger Equation

answer

question

5.13 Hamiltonian Operator

answer

question

5.14 Schrodinger, Eigenvalue Equation

answer

question

5.15 Position, Momentum commutation relation

answer

question

5.16 Uncertainty relation of operators A and B based off of their commutator

answer

question

5.17 Statistical variance/ Uncertainty

answer

question

5.18 Uncertainty Product for position and momentum

answer

question

5.19 Order of Magnitude estimate of position and momentum uncertainty

answer

question

5.20 Energy and Time order of magnitude momentum and position uncertainty

answer

question

5.21 One Dimensional Harmonic Oscillator Hamiltonian

answer

question

5.22 One dimensional Harmonic Oscillator Hamiltonian using raising and lowering operators

answer

question

5.23 Commutation relation of lowering and raising operators

answer

question

5.24 One Dimensional Harmonic Oscillator Energy Eigenvalues

answer

question

5.25 Virial's Theorem for Harmonic Oscillator

answer

question

5.26 Three Dimensional Harmonic Oscillator Energy Eigenvalues

answer

question

5.27 Eigenfunctions and Energy Eigenvalues of a free particle

answer

question

5.28 De Broglie Formula

answer

question

5.29 Einstein's relation (energy of a free particle)

answer

question

5.30 General Hamiltonian in Three Dimensions

answer

question

5.31 3 Dimensional, position-momentum commutation along same direction

answer

question

5.32 3 Dimensional, position-momentum commutation along different directions

answer

question

5.33 Radial Wave function Normalization conditions

answer

question

5.34 x component of orbital angular momentum

answer

question

5.35 y component of orbital angular momentum

answer

question

5.36 z component of orbital angular momentum

answer

question

5.37 Commutator relation of orthogonal components of orbital angular momentum

answer

question

5.38 Total orbital angular momentum

answer

question

5.39 Z component of angular momentum acting on a spherical harmonic state

answer

question

5.40 Total orbital angular momentum acting on a spherical harmonic state

answer

question

5.41 Allowed values of m (magnetic moment) in terms of l (orbital angular momentum)

answer

question

5.42 Orthonormaility of Spherical Harmonics

answer

question

5.43 Hamiltonian of Hydrogen Atom

answer

question

5.44 Bohr Radius

answer

question

5.45 Un-normalized Ground state of Hydrogen Atom

answer

question

5.46 Hydrogen Ground State Energy

answer

question

5.47 nth Energy Eigenvalues of Hydrogen considering quantum number n only

answer

question

5.48 fine structure constant

answer

question

5.49 spin up and down along x in the z basis

answer

question

5.50 spin up and down along y in z basis

answer

question

5.51 Raising and Lowering Operators for spin 1/2 in terms of spin along x and y

answer

question

5.54 Adding spins s and s'

answer

question

5.55 Adding z component of spin quantum number m

answer

question

5.56 Singlet State a system of 2 spin 1/2 particles

answer

question

5.57 Perturbation Theory, 1st order energy Shift

answer

question

5.58 Perturbation Theory, 2nd order energy shift

answer

question

5.59 Eigenvalues of Spin-Orbit Operator, fine structure perturbation

answer

question

5.60 Change in Hamiltonian from Stark Effect

answer

question

5.61 Change in Hamiltonian for Zeeman Effect

answer

Algebra 1
Algebra 2

The Hunger Games Vocabulary Chapter 22-27 20 terms
Alice Rees

20 terms
Preview

The Hunger Games Vocabulary Chapter 22-27

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

question

How would you go about doing x times 5%?

answer

1.05x

Algebra 1
Algebra 2
Fractions
Multiplication

Math study guide 29 terms
Marta Browning

29 terms
Preview

Math study guide

question

Write two equivalent fractions: 1/6

answer

2/12, 4/24

question

Write two equivalent fractions: 3/5

answer

6/10, 12/20

question

Write two equivalent fractions: 6/10

answer

12/20, 24/40

question

Add the sign (><= ) 1/3___1/5

answer

>

question

Add the sign (><= ) 13/14___3/14

answer

>

question

Add the sign (><= ) 3/7___6/14

answer

=

question

Add the sign (><= ) 5/16___3/5

answer

<

question

Write the set of fractions in order from small to big: 4/10, 3/10, 9/10, 7/10, 5/10

answer

3/10, 4/10, 5/10, 7/10, 9/10

question

Write the set of fractions in order from small to big: 1/3, 1/14, 1/2, 1/7, 1/8

answer

1/14, 1/8, 1/7, 1/3, 1/2

question

If the pattern block trapezoid is the whole, what fraction of the whole is the pattern block triangle.

answer

1/3

question

________________________________________ | | | | | | | | | | | | | | | | ---------------------------------------------------------------- What fraction of the given rectangle are 2 squares?

answer

1/2

question

________________________________________ | | | | | | | | | | | | | | | | ---------------------------------------------------------------- What fraction is 1 rectangle?

answer

1/2

question

________________________________________ | | | | | | | | | | | | | | | | ---------------------------------------------------------------- What fraction of the rectangle do 2 squares and 1 rectangle cover?

answer

1

question

If the cube represents 1/10, what represents the unit whole?

answer

1/10

question

Sara had 8 quarters. She spent 1/4 of them on video games. a. How many quarters did she spend?

answer

2

question

Sara had 8 quarters. She spent 1/4 of them on video games. b. How many quarters does she have left?

answer

6

question

Sara had 8 quarters. She spent 1/4 of them on video games. c. How much money does she have left?

answer

$1.50

question

Multiply. Use a paper and pencil algorithm of your choice. 40*65 = ______

answer

2,600

question

Multiply. Use a paper and pencil algorithm of your choice. _____=54*61

answer

3,294

question

Divide. Use a paper and pencil algorithm of your choice. 65/2=____

answer

32 r 1

question

Multiply. Use a paper and pencil algorithm of your choice. 7/495=___

answer

70r5

question

Which fraction is larger: 5/16 or 3/5? Explain how you know.

answer

...

question

Add or subtract. Use pattern blocks. ___/___=6/9 +3/9

answer

9/9

question

___/___=2/4+2/4

answer

4/4

question

3/4-1/4= ___/___

answer

2/4

question

6/9-1/9=___/___

answer

5/9

question

Solve using pattern blocks. Explain your strategy. 1/6+1/3=____

answer

1/6+2/6=3/6

question

It took Denise1/3 of an hour to drive from Zion to Platt and 2/6 of an hour to drive from Platt to Rome. To figure out her total driving time, Densie wrote the following number model: 1/3+2/6=3/9.

answer

2/6+2/6=4/6

question

Do you agree that it took her about 3/9 of an hour? Explain your answer.

answer

NO!!!! Because you don't add the top AND the bottom!!!!!

Algebra
Algebra 1
Algebra 2

College Algebra Final Exam 30 terms
Kevin Stewart

30 terms
Preview

College Algebra Final Exam

question

Remainder Theorem

answer

If polynomial p(x) of degree n>1 is divided by (x-a) where a is a constant, then the remainder is p(a)

question

Find minima or maxima

answer

find -b/2a and than plug back in to equation

question

What strategies can you use to find all the zeros of a polynomial?

answer

synthetic division, graphing, factoring

question

Percent Profit Formula

answer

Percentage Profit = ((selling price-cost price)/(cost price))*100

question

Polynomials

answer

Monomial- 5x2 Binomial- 2x2+5x Trinomial- 5x2+3x+6

question

The Rational Roots Test p/q

answer

This relationship is always true: If a polynomial has rational roots, then those roots will be fractions of the form (plus-or-minus) (factor of the constant term) / (factor of the leading coefficient). However, not all fractions of this form are necessarily zeroes of the polynomial. Indeed, it may happen that none of the fractions so formed is actually a zero of the polynomial. Find all possible rational x-intercepts of x4 + 2x3 - 7x2 - 8x + 12. The constant term is 12, with factors of 1, 2, 3, 4, 6, and 12. The leading coefficient in this case is just 1, which makes my work a lot simpler. The Rational Roots Test says that the possible zeroes are at: Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved ± 1, 2, 3, 4, 6, 12 = -12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12

question

Graphs of Polynomials: Predicting End Behavior of a Function

answer

The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph. The leading coefficient is significant compared to the other coefficients in the function for the very large or very small numbers. So, the sign of the leading coefficient is sufficient to predict the end behavior of the function.

question

Graphs of Polynomials: Predicting End Behavior of a Function (2)

answer

Polynomial End Behavior: 1. If the degree n of a polynomial is even, then the arms of the graph are either both up or both down. 2. If the degree n is odd, then one arm of the graph is up and one is down. 3. If the leading coefficient an is positive, the right arm of the graph is up. 4. If the leading coefficient an is negative, the right arm of the graph is down.

question

Graphs of Polynomials: Predicting End Behavior of a Function (3)

answer

To predict the end-behavior of a polynomial function, first check whether the function is odd-degree or even-degree function and whether the leading coefficient is positive or negative.

question

Graphs of Polynomials: Turning Points

answer

Turning Points A Turning Point is an x-value where a local maximum or local minimum happens:

question

How many turning points does a polynomial have?

answer

Never more than the Degree minus 1

question

How do you determine the degree of a polynomial?

answer

The Degree of a Polynomial with one variable is the largest exponent of that variable.

question

How do the graphs of polynomials behave?

answer

Graphs will be continuous and smooth Even exponents behave the same: above (or equal to) 0; go through (0,0), (1,1) and (-1,1); larger values of n flatten out near 0, and rise more sharply. Odd exponents behave the same: go from negative x and y to positive x and y; go through (0,0), (1,1) and (-1,-1); larger values of n flatten out near 0, and fall/rise more sharply Factors: Larger values squash the curve (inwards to y-axis) Smaller values expand it (away from y-axis) And negative values flip it upside down Turning points: there will be \"Degree-1\" or less. End Behavior: use the term with the largest exponent

question

Hooke's Law

answer

The formula for Hooke's Law is \"F = kd\", where \"F\" is the force and \"d\" is the distance. (Note that, in physics, \"weight\" is a force. These Hooke's Law problems are often stated in terms of weight, and the weight is the force.)

question

Variation Equations

answer

\"F varies as x\" means F = kx \"F varies jointly as x and y\" means F = kxy \"F varies as x + y\" means F = k(x + y) \"F varies inversely as x\" means F = k/x

question

Graphing Rational Functions

answer

To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then sketch in the graph.

question

Rational Functions: find the vertical asymptotes

answer

set the denominator equal to zero to find any forbidden points

question

Rational Functions: find the horizontal or slant asymptote

answer

If the numerator and denominator have the same degree (they're both linear), the asymptote will be horizontal, not slant, and the horizontal asymptote will be the result of dividing the leading coefficients

question

Vertical Asymptotes

answer

Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. (They can also arise in other contexts, such as logarithms, but you'll almost certainly first encounter asymptotes in the context of rationals.)

question

Suggested Attack to Finding Zeros of a Polynomial

answer

1. Identify the total number of real or complex zeros (corollary to Fundamental Theorem of Algebra). 2. Identify the possible number of positive, negative, and complex zeros (Descartes' Rule of Signs). 3. List the possible rational zeros (Rational Root Theorem) 4. Try possible rational zeros until you find one that works. 5. After each division by a positive value, check for possible upper bounds. 6. After each division by a negative value, check for possible lower bounds (Upper and Lower Bound Theorems) 7. After you find a possible rational root that actually works, take the quotient and continue to try to factor it until it is down to a quadratic or less. Once it is a quadratic or less, there are other ways to solve it. 8. Write the linear and or linear / irreducible quadratic factorization (next section)

question

Rational Root Test

answer

If a polynomial function has integer coefficients, then every rational zero will have the form p/q where p is a factor of the constant and q is a factor of the leading coefficient. Make sure the polynomial has integer coefficients. Multiply to get rid of fractions or decimals if need be (be sure to later divide). This only addresses the rational zeros. There may be real, but non-rational roots. There may be complex roots involving i. This says that rational zeros will have this form. It does not say that everything that has this form is a rational zero. What it does give you is a list of possible rational zeros Example: f(x) = 4x^5 - x^2 + 12 Possible rational zeros will be of the form (factor of 12) over (factor of 4). A division table can help you find all these values

question

Descartes' Rule of Signs

answer

The maximum number of positive real roots can be found by counting the number of sign changes in f(x). The actual number of positive real roots may be the maximum, or the maximum decreased by a multiple of two. The maximum number of negative real roots can be found by counting the number of sign changes in f(-x). The actual number of negative real roots may be the maximum, or the maximum decreased by a multiple of two. Complex roots always come in pairs. That's why the number of positive or number of negative roots must decrease by two. Consider: f(x) = 3x^6 + x^5 - x^4 + 3x^3 + 2x^2 - x + 1. The signs in f(x) are + + - + + - +. There are 4 sign changes (+ to -) or (- to +). Now, f(-x) = 3x^6 - x^5 - x^4 - 3x^3 + 2x^2 + x + 1. The signs in f(-x) are + - - - + + +. There are 2 sign changes (+ to -) or (- to +).

question

Complex Roots

answer

Complex solutions come in pairs. If (a+bi) is a solution, then its complex conjugate (a-bi) is also a solution.

question

Corollary to the Fundamental Theorem of Algebra

answer

Every polynomial in one variable of degree n, n > 0, has exactly n real or complex zeros.

question

Fundamental Theorem of Algebra

answer

Every polynomial in one variable of degree n, n > 0, has at least one real or complex zero.

question

Synthetic Division

answer

Synthetic Division To divide a polynomial synthetically by x-k, perform the following steps. Setup Write k down, leave some space after it. On the same line, right the coefficients of the polynomial function. Make sure you write the coefficients in order of decreasing power. Be sure to put a zero down if a power is missing. Place holders are very important For now, leave a blank line. Draw the left and bottom portions of a box. The left portion goes between the k and the coefficients. The bottom portion goes under the blank line you left. Synthetic Division Once you have things set up, you can actually start to perform the synthetic division. Bring the first coefficient down to the bottom row (below the line) Multiply the number in the bottom row by the constant k, and write the product in the next column of the second row (above the line). Add the numbers in the next column and write the total below the line. Repeat steps 2 and 3 until all the columns are filled. Interpreting the Results The very last value is the remainder. If the remainder is zero, you have found a zero of the function. The rest of the values are the coefficients of the quotient. Each term will be raised to the one less power than the original dividend. (If it was a fourth degree polynomial to start with, the quotient will be a third degree polynomial).

question

Remainder Theorem

answer

When a polynomial function f is divided by x-k, the remainder r is f(k). Okay, now in English. If you divide a polynomial by a linear factor, x-k, the remainder is the value you would get if you plugged x=k into the function and evaluated. Now, tie that into what we just said above. If the remainder is zero, then you have successfully factored the polynomial. If the remainder when dividing by (x-k) is zero, then the function evaluated at x=k is zero and you have found a zero or root of the polynomial. Plus, you now have a factored polynomial (the quotient) which is one less degree than the original polynomial. If the quotient is down to a quadratic or linear factor, then you can solve and find the other solutions.

question

What are the real zeroes of a polynomial?

answer

The real (that is, the non-complex) zeroes of a polynomial correspond to the x-intercepts of the graph of that polynomial. So you can find information about the number of real zeroes of a polynomial by looking at the graph, and conversely you can tell how many times the graph is going to touch or cross the x-axis by looking at the zeroes of the polynomial (or at the factored form of the polynomial).

question

Guidelines for Graphing Polynomial Functions

answer

1. Zeros 2. Test Points 3. End Behavior 4. Graph

question

How do you determine Local Extrema

answer

The amount of local extrema is determined by n - 1, where as N is the highest exponent in the graph. A graph of x4 will have 3 local extrema.

Algebra
Algebra 1
Algebra 2

College Algebra Final Review 48 terms
Margaret Bruce

48 terms
Preview

College Algebra Final Review

question

What is the special factorization of A^3-B^3?

answer

(A-B)(A^2+AB+B^2)

question

What is the special factorization of A^3+B^3?

answer

A+B)(A^2-AB+B^2)

question

When is a relation a function?

answer

If each member of the domain corresponds to exactly one member of the range

question

How can you test whether a graph is demonstrating a function?

answer

Use the vertical line test

question

A horizontal line is represented by

answer

y=#

question

A vertical line is represented by

answer

x=#

question

What is the equation for slope?

answer

(Y2-Y1/X2-X1)

question

What is the point slope form equation?

answer

Y-Y0=m(X-X0)

question

How do you test for an odd function?

answer

Replace x with -x and see if the resulting equation is completely opposite of the original.

question

Odd functions are symmetric with respect to the

answer

x-axis

question

How do you test for an even function?

answer

Replace x with -x and see if the resulting equation is identical to the original

question

What does the basic graph y=x look like?

answer

diagonal line going up towards right corner

question

What does the basic graph y-x^2 look like?

answer

U

question

What does the basic graph y=sqrt(x) look like?

answer

half parabola on right half of graph moving up towards right

question

What does the basic graph y=x^3 look like?

answer

two parabola halves, left bottom is left half of arch, right upper is right half of a u, more vertical

question

What does the basic graph y=cube root of x look like?

answer

two parabola halves, one on left and one on right, more horizontal

question

What does the basic graph y=1/x look like?

answer

Two flipped curves approaching horizontal and vertical asymptotes

question

What does the basic graph abs value (x) look like?

answer

V

question

A vertical reflection flips the graph over which axis?

answer

The x axis

question

A horizontal reflection reflects the graph over which axis?

answer

The y axis

question

What is the equation for a vertical reflection?

answer

-f(x)

question

What is the equation for a horizontal reflection?

answer

f(-x)

question

In the function af(x), the graph will stretch ____ by a factor of __ if ___

answer

vertically, a, abs value (a)>1

question

In the function af(x), the graph will shrink __by a factor of ___if ____

answer

vertically, a, 0<abs value (a)<1

question

In the function f(cx), the graph will stretch ___ by a factor of ___ if ___

answer

horizontally, 1/c, if 0<abs value (c)<1

question

In the function f(cx), the graph will shrink ___ by a factor of ___if ___

answer

horizontally, 1/c, abs value(c)>1

question

How would you find the axis from a quadratic equation?

answer

x: -b/2a, then plug into quadratic for y

question

What will the end behavior of a positive coefficient to the even degree leading an equation look like?

answer

Up on both ends

question

What will the end behavior of a negative coefficient to the even degree leading an equation look like?

answer

Down on both ends

question

What will the end behavior of a positive coefficient to an odd degree look like?

answer

Down on left up on right

question

What will the end behavior of a negative coefficient to an even degree look like?

answer

Up on left, down on right

question

How does one find horizontal asymptote?

answer

Divide leading coefficients of top and bottom

question

How does one find vertical asymptotes?

answer

Set bottom equal to zero

question

How does one find zeros?

answer

numerator equal to zero

question

When will an x-intercept be a bounce?

answer

if it's to an even degree

question

When will an x-intercept be a cross?

answer

if it's to an odd degree

question

How do you find a y-intercept of a rational function?

answer

replace x values with zero

question

What does it mean to be one to one?

answer

Each x corresponds with only one y and each y corresponds with only one x

question

How can we test for one-to-one functions?

answer

Horizontal and vertical line test

question

In exponential graphs, exponential growth occurs when in the function a^x ____

answer

A>1

question

In exponential graphs, exponential decay (lowercase L shape) occurs when in the function a^x___

answer

0<a<1

question

In the exponential graph y=a^x, the points (__,__) and (__,___) are always present

answer

(0,1) (1,a)

question

In exponenetial functions, the horizontal asymptote is always y=0 unless

answer

vertical shift occurs

question

To find the y intercept in an exponeniial function, replace x with

answer

zero

question

In logarithmic graphs, growth occurs (in the shape of the left half of an arch) when in the equation logbasea(x), __

answer

a>1

question

In logarithmic graphs, decay occurs (in the shale of a lowercase L) when in the function logbasea(x)__

answer

0<a<1

question

in logarithmic graphs logbasea(x), what two sets of points are always present?

answer

(1,0) (a,1)

question

What does the change of base formula look like for the equation logbasea(x)?

answer

lnx/lna

Algebra 2
Equations

college mathematics one finals 34 terms
Misty Porter

34 terms
Preview

college mathematics one finals

question

1) -42x + 36 < - 6 (6x-8)

answer

.

question

2) X12/X9

answer

.

question

3) 12X / 3X

answer

.

question

4) (X-5) (X + 5X)

answer

.

question

5) X - 13X + 36

answer

...

question

6) 5X-5 . 6X X 9X-9

answer

...

question

7) Identify which graphs corresponds to the point ( 5, -3 )

answer

...

question

8) Identify the intercepts on the ff graph: x-intercept is -1, y-intercept is 4

answer

...

question

9) When 5 is added to 4X a no. the number increases by 35, Find the no.

answer

...

question

10) (6+9i) - (-5+i)

answer

...

question

11) Find the value of X : 3X - 2 = 2

answer

...

question

12) Find the value of X: IxI = 8

answer

...

question

13) This relation is a function: {(-6,-7), (-1,4),(3,4),(3,-7)} True/False

answer

...

question

14) The ff graph represents a function True or False

answer

...

question

15) Which of the ff equations corresponds to the given graph? y = -2x - 3

answer

...

question

16) Given f(x)= 8x-2 and g(x)= 2x-3 find f-g

answer

...

question

17) Solid line=f(x), In which one of the 4 graphs does the dotted line represent g(x) = f(x-2) ?

answer

...

question

18) Find the midpoint of the line bet. two points (-5,2) and (2,7)

answer

...

question

19) Solve the system: 2y = x+16 5x + 10y = 0

answer

...

question

20) Solve the system x-6y=11, 4x-7y=10

answer

...

question

21)Solve the system: x+3y+4z=-14 4y+2z= -22, z = -1

answer

...

question

23) Solve the system of equations: -5x-y-8z= -49, -4x-6z= -36, 6y+z= 20

answer

...

question

24) Using Cramer's Rule solve the ff system 6x = -4y-10, 5x = -y-13

answer

...

question

25) Express the solution set of -27 < -4x + 1< -7 in interval notation

answer

...

question

26) Express the solution set of Ix+3I -9 < -3 in interval notation

answer

...

question

27) Determine the domain of the ff function [ 1, oo )

answer

...

question

28) Find the inverse of the ff function : f(x) = x + 5 if x > 0

answer

...

question

29) Which graph represents the solution to the following inequalities? x -3

answer

...

question

31) Write the equation of a line in slope-intercept form passing through (5,2) and parallel to y= -1/2x +2

answer

...

question

32) If f(x)= 4x + 4x + 8 and g(x)=4x-4 find ( g o f ) (x)

answer

...

question

33) Write the standard form of the equation of a circle with center (3, -1) and a radius of 6

answer

...

question

36) Solve (2x+9) +2 = 3(x+8)

answer

...

question

38) Solve 2x = -6x -2

answer

...

question

40) Use the rational zero theorem to list all the possible rational zeros for f(x)= x -5x +3x +2

answer

...

Algebra 2

College Prep Algebra I Midterm Vocabulary 60 terms
Ken Ericksen

60 terms
Preview

College Prep Algebra I Midterm Vocabulary

question

algebraic expression

answer

a collection of numbers, variables, and operations

question

base

answer

the number being multiplied in a power

question

domain

answer

the list of inputs in a function (x)

question

equation

answer

formed when an equal sign (=) is placed between two expressions creating a left and right side

question

evaluate

answer

replacing each variable in an expression by a number

question

exponent

answer

value that shows how many times the base is being multiplied by itself

question

function

answer

a rule that establishes a relationship between two quantities (input/output)

question

inequality

answer

formed when a symbol such as (<) is placed between two expressions

question

input

answer

(x) in a function

question

order of operations

answer

to evaluate an expression with more than one operation

question

ordered pair

answer

A pair of numbers that can be used to locate a point on a coordinate plane (x,y)

question

output

answer

(y) in a function

question

power

answer

an expression that contains a base and exponent

question

range

answer

the list of outputs in a function (y)

question

simplify

answer

to write an expression in a simpler form; also used to indicate "evaluation"

question

solution

answer

the value in place of the variable that makes the equation or inequality true

question

variable

answer

a letter that is used to represent one or more numbers

question

absolute value

answer

The distance a number is from zero on a number line

question

coefficient

answer

A number multiplied by a variable in an algebraic expression

question

constant

answer

a term that does not contain a variable in an expression or equation

question

coordinate

answer

a number that identifies a position relative to an axis

question

Distributive Property

answer

a(b + c) = ab + ac; a number outside the parentheses can be multiplied to each term within the parentheses

question

integer

answer

numbers on a number line that can be positive, negative or zero

question

like terms

answer

terms that have identical variables and exponents; when simplifying an expression, you can combine these

question

matrix

answer

a rectangular array of numbers into horizontal rows and vertical columns

question

opposites

answer

two numbers that are the same distance from zero on a number line, but are in opposing directions. (-2 and 2)

question

real number

answer

all rational or irrational numbers; these numbers can be represented on the number line

question

reciprocal

answer

The inverse of a fraction; when multiplied by the original fraction, it results in a product that equals one

question

speed

answer

a rate at which something happens

question

terms

answer

values in an equation or expression that are separated by operations such as multiplying, adding, subtracting, or dividing

question

velocity

answer

speed in a given direction

question

Division Property of Equality

answer

if you divide the same number to each side of an equation, the two sides remain equal

question

Addition Property of Equality

answer

if you add the same number to each side of an equation, the two sides remain equal

question

formula

answer

an expression or equation that is set to solve real-life fundamental principles

question

inverse operations

answer

operations that undo each other, such as addition and subtraction

question

linear equation

answer

an equation whose graph is a line

question

Multiplication Property of Equality

answer

if you multiply the same number to each side of an equation, the two sides remain equal

question

ratio

answer

a comparison of two quantities by division

question

simplest form

answer

an algebraic expression in this form has no like terms and no parentheses; also a fraction that cannot be reduced

question

Subtraction Property of Equality

answer

if you subtract the same number to each side of an equation, the two sides remain equal

question

unit rate

answer

a rate per one given unit, such as 60 miles per one gallon

question

constant of variation

answer

the slope, or rate of change, in the equation y=kx, represented by k

question

coordinate plane

answer

formed by a horizontal number line called the x-axis and a vertical number line called the y-axis

question

direct variation

answer

an equation of the form y=kx, where k does not equal 0

question

function notation

answer

an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x

question

origin

answer

the point of intersection of coordinate axes (0,0)

question

slope

answer

the steepness of a line on a graph, equal to its vertical change divided by its horizontal change (rise over run)

question

slope intercept form

answer

y=mx+b, where m is the slope and b is the y-intercept of the line.

question

standard form

answer

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative

question

x-axis

answer

the horizontal axis on a coordinate plane

question

x-coordinate

answer

The value on the x-axis used to locate a point on the coordinate graph. It is the first value in an ordered pair.

question

x-intercept

answer

the x-coordinate of a point where a graph crosses the x-axis

question

y-axis

answer

the vertical axis on a coordinate plane

question

y-coordinate

answer

The value on the y-axis used to locate a point on the coordinate graph. It is the second value in an ordered pair.

question

y-intercept

answer

the y-coordinate of the point where the line crosses the y-axis

question

Communitive Property

answer

when adding or multiplying, you can switch the numbers

question

Associative Property

answer

states you can change the groupings of additions or multiplications ex. (4+5)+8=4+(5+8)

question

Property of Zero

answer

any number multiplied by 0 will equal 0

question

Identity Property of Multiplication

answer

the product of any number and 1 is equal to the original number (a x 1 = a)

question

Identity Property of Addition

answer

The property that states: the sum of any number & zero is that number; n + 0 = n

Algebra 2
Expressions
Geometry

Geometry for College Students 29 terms
Bernice Cooper

29 terms
Preview

Geometry for College Students

question

Let P,Q, and R be the points of tangency of the incircle of ∆ABC with sides BC, CA, and AB, respectively. Then lines AP, BQ, and CR:

answer

are concurrent.

question

Gergonne point

answer

Point of congruency of lines AP, BQ, and CR, where P,Q, and R are the points of tangency of the incircle of ∆ABC.

question

Ceva's Theorem: Let AP, BQ, and CR be three lines joining the vertices of ∆ABC to pints P, Q, and R on the opposite sides. Then these three lines are concurrent if and only if:

answer

(AR/RB)(BP/PC)(CQ/QA) = 1

question

Given distinct points A and B and a positive number µ, there is exactly ______ point X such that _________________. Also there is at most _________ other point on the line ____ for which this equation holds.

answer

one AX/XB = µ one AB

question

Let AP, BQ, and CR be Cevians in ∆ABC, where P, Q, and R lie on sides BC, CA, and AB respectively. If these Cevians are concurrent at point T, then:

answer

AT/AP = [(AR·CQ) + (QA·RB)] / [AR·CQ) + (QA·RB) + (RB·CQ)]

question

Let T be the Gergonne point of ∆ABC. If coincides with the incenter or the circumcenter or the orthocenter or the centroid of ∆ABC, then:

answer

The triangle must be an equilateral.

question

Let U and V be points on sides of AB and AC, respectively, of ∆ABC and suppose UV is parallel to BC. Then the intersection of UC and VB:

answer

lies on the median of AM.

question

The lines joining the vertices of a triangle to the points of tangency of the opposite exscribed circles are:

answer

concurrent.

question

Given three concurrent Cevians in a triangle, the the lines obtained by joining the midpoints of the Cevians to the midpoints of the coorresponding sides are:

answer

concurrent.

question

Suppose Cevians AP, BQ, and CR are concurrent at point T so that ∆ABC is decomposed into six small triangles. If areas of ∆ART, ∆BPT, and ∆CQT are equal, then:

answer

All six small triangles have equal areas.

question

General Form of Ceva's Theorem: Let AP, BQ, and CR be Cevians of ∆ABC, where points P, Q, and R lie on lines BC, CA, and AB, respectively. Then these Cevians are either concurrent OR parallel if and only if:

answer

an ODD number of them are interior and (AR/RB)(BP/PC)(CQ/QA) = 1

question

In figure 4.5 on p 135, BQ/QC = ___ and XP/PY = ______. And if XP/PY =BQ/QC, then:

answer

st/ru; [s(t+u)]/[u(r+s)] then both ratios are equal to 1 and in that case XY is parallel to BC.

question

If Cevians AP, BQ, and CR are parallel, then:

answer

the Cevian product is trivial.

question

Angular Cevian Product: Suppose that AP, BQ, and CR are Ceviansin ∆ABC. Then the corresponding Cevian product is equal to:

answer

[sin(∠ACR)sin(∠BAP)sin(∠CBQ)]/[sin(∠RCB)sin(∠PAC)sin(∠QBA)] In particular, the three Cevians are concurrent or parallel if and only if an odd number of them are interior and this angular Cevian product is equal to 1.

question

Given an arbitrary ∆ABC, build three outward-pointing triangles BCU, CAB, and ABW, each sharing a sides with the original triangle. Assume that ∠BAW = ∠CAV, ∠CBU = ∠ABW, and ∠ACV = ∠BCU. And assume that AU, BV, and CW cut across the interior of ∆ABC. Then:

answer

lines AU, BV, and CW are concurrent.

question

The pedal triangle of acute ∆ABC is ∆DEF, and perpendicular AU, BV, and CW are dropped from the vertices of the original triangle to the sides of the pedal triangle. Then lines AU, BV, and CW are:

answer

concurrent and the point of concurrence is at the circumcenter.

question

If Cevians AP, BQ, and CR of ∆ABC are concurrent or parallel, then:

answer

their isogonal Cevians are also concurrent or parallel.

question

Isogonal line:

answer

The line reflected across an angle bisector.

question

Symmedians:

answer

The isogonals of the medians.

question

Lemoine point:

answer

The point of concurrence of the symmedians.

question

Isogonal conjugate:

answer

The point of concurrence of the isogonal lines.

question

Let X be a point other than A, B, or C on the circumcircle of ∆ABC. Then:

answer

the isogonal Cevians of AX, BX, and CX are parallel.

question

Let X be any point in the interior of ∆ABC and let Y be the circumcenter of the triangle whose vertices are the reflections of X in the sides of ∆ABC. Then:

answer

Y is the isogonal conjugate of X with respect to ∆ABC.

question

Let ABCDEF be a hexagon inscribed in a circle. Then the diagonals AD, BE, and CF are concurrent if and only if:

answer

(AB/BC)(CD/DE)(EF/FA)=1

question

Given and acute angled ∆ABC, show that the lines joining A, B, and C to the midpoints of the nearer sides of the pedal triangle are:

answer

concurrent

question

The only point in the interior of ∆ABC that is its own isogonal conjugate is:

answer

the incenter.

question

If ∆ABC is not a right triangle then the circumcenter and orthocenter are:

answer

isogonal conjugates.

question

If ∠C = 90 in ∆ABC, then the Lemoine point of the triangle lies on:

answer

the altitude from vertex C.

question

If the Lemoine point of ∆ABC lies on the altitude from vertex C, then:

answer

either AC = BC or ∠C = 90.

Algebra
Algebra 1
Algebra 2
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Algebra 2 – Flashcards 602 terms
Brandon Ruffin

602 terms
Preview

Algebra 2 – Flashcards

question

What is an equation for a direct variation whose graph passes through the point (-5, 3)?

answer

y=-3/5x

question

Which line, having the given slope and passing through the given point, represents a direct variation?

answer

m= 2/3 ; (9, 6)

question

The length of an object's shadow varies directly with its height. If a can that is 13 cm tall casts a shadow that is 7.5 cm long, a bottle that is 25 cm tall will cast a shadow that is approximately 14.42 cm long.

answer

True Test: “Study Guide Algebra”

question

A linear model for the situation below passes through the origin. A manufacturer can produce 4,200 gears in 8 hours. How many gears can be made in 1 hour?

answer

525

question

The scatter plot below contains the points (2, 7), (-2, 1), (5, 13), (-4, 5), and (0,5). What equation best represents the trend line drawn on the scatter plot?

answer

y = x + 6

question

A data set that appears to be a random group of dots spread throughout the graph has a negative correlation.

answer

False

question

What is the vertex of the graph of y = |x| - 6?

answer

(0, -6)

question

Which is the graph of the equation y = |x - 1|?

answer

Graph C

question

The graph of an absolute value function will always be an upward-pointing V shape.

answer

False

question

Which is the graph of 0.4x + 0.1y ≥ 1?

answer

Graph B

question

What is the graph of

answer

Graph D

question

This is the graph of y < |x - 3|.

answer

True

question

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.

answer

no solution

question

What is true about the system

answer

The system is consistent and independent.

question

A dependent system of equations will have infinitely many answers.

answer

True

question

Jim's wages vary directly with the numbers of hours he works. For 7 hours, he makes $38.85. How much will he make in 37 hours?

answer

$205.35

question

Which line, having the given slope and passing through the given point, represents a direct variation?

answer

C.

question

The graph below models the burning of a candle. At time t = 0, the candle was 8 inches tall. If the candle burns at a rate of 2 inches per hour, what equation models the height h of the candle after burning for t hours?

answer

h = -2t + 8

question

The scatter plot below shows the weights in ounces of several kittens at various ages. What is the best equation of the trend line through these points?

answer

y = 4x + 10

question

What is the equation of the graph?

answer

y = |x + 5|

question

What is an inequality for this graph?

answer

y - 3x ≥ -5

question

Which is the graph of

answer

Graph C

question

Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.

answer

no solution

question

Which ordered pair is the solution to the given system of equations?

answer

(-3, -4)

question

Two parallel lines form an inconsistent system of equations that has no solution.

answer

True

question

Solve the system of equations. 2x - 4y = 3 -3x + 5y = 1

answer

B.

question

Use substitution to solve the system of equations given below.

answer

(-10, -12)

question

Using substitution, the equations 2x - y = 4 and 3x + 2y = 13 give a solution of (3,2).

answer

True

question

Use elimination to solve the system given below. 5x - 2y = 25 5x + 3y = 5

answer

A.

question

Use elimination to solve the system of equations given by 10x - 40y = 60 and 15x + 40y = -10.

answer

(2, -1)

question

Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3.

answer

True

question

Which point is in the solution set of this system of inequalities?

answer

(0, 4)

question

Identify the graph that shows the solution to the system of inequalities.

answer

A.

question

A graph showing the inequalities "greater than or equal to" or "less than or equal to" will use dotted lines.

answer

False

question

What is the maximum for the objective function for this graph?

answer

560

question

A factory can produce two products, x and y, with a profit P approximated by P = 12x + 15y. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1000. What production levels yield maximum profit?

answer

x = 1000; y = 0

question

When finding the maximum value for an objective function, it is necessary to check the vertices of the graph.

answer

True

question

Which point lies in the plane represented by the equation 2x + 7y + 3z = 25?

answer

(6, 4, -5)

question

A point (x, y, z) can be used to represent the location of a geographical point in space, where x represents the latitude in degrees, y represents the longitude in degrees, and z represents the elevation in feet above or below sea level. Jerimoth Hill is the highest point of elevation in Rhode Island. It is 812 feet above sea level and lies at about 42° north latitude and 72° west longitude. What ordered triple represents the location of Jerimoth Hill?

answer

(42°, -72°, 812)

question

An equation using three variables is graphed in coordinate space.

answer

True

question

A bus leaves a terminal traveling at a rate of 45 miles per hour. When the bus has traveled 90 miles, a car leaves the same terminal, traveling at a rate of 60 miles per hour. Which pair of equations model the distances d covered by each vehicle after t hours?

answer

Bus: d1 = 45t + 90; Car: d2 = 60t

question

An electronics store makes a profit of $55 for every standard CD player sold and $77 for every portable CD player sold. The manager's goal is to make at least $385 a day on sales of both standard and portable CD players. If s represents the number of standard CD players sold, and p represents the number of portable CD players sold, which inequality and graph represent the manager's daily goal?

answer

Graph C

question

Classify the system.

answer

independent

question

If you use the elimination method to solve the system of equations 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations.Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.

answer

Method II

question

A computer supply store sells two types of printers. Type A, costs $135, and the store makes a $40 profit on each sale. Type B, costs $120, and the store makes a $35 profit on each sale. The store manager expects to sell at least 100 printers this month and to make at least $4,400 profit on them. If x represents the number of type A printers sold, and y represents the number of type B printers sold, what are the constraints for a linear program that models this problem?

answer

A.

question

A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have?

answer

question

In chemistry, Charles Law states that if the pressure remains constant, the volume of an ideal gas varies directly with the temperature in degrees Kelvin. Suppose a gas has a volume of 100 mL at 250°K. Which proportion could you use to find the volume v of the gas if the temperature decreases to 150°K?

answer

C.

question

Brenda and Anne left their homes for their morning runs at the same time. Brenda can run a 10-minute mile and Anne can run a 12-minute mile. Combined, they ran 15 miles in a total of 2 hours and 42 minutes (162 minutes). How many miles did each woman run?

answer

Brenda ran 9 miles; Anne ran 6 miles

question

Solve the system of equations. x = 3y + 2z 2x + 3y + 2z = 3 -x + y - z = 6

answer

(1, 3, -4)

question

Solve the system of equations. 2x + y - z = 3 x + y + z = 5 x - 2y + z = 2

answer

(2, 1, 2)

question

Solve the system of three equations by elimination: 5x + 2y - 3z = 10 2x - 2y + 4z = 6 x - y + 2z = 3

answer

infinitely many solutions

question

The value of y varies directly with x. If y = 64 when x is 16, what is x when y is 288?

answer

72

question

The value of y varies directly with x. If y is 24 when x is 72, what is the value of y when x is 144?

answer

48

question

What steps would you use to plot (-3, -4, 0) in a three-dimensional coordinate system?

answer

From the origin, move back 3 units and left 4 units.

question

Which statement about 5y = 2x is true?

answer

A.

question

Which steps would you use to plot the point (7, -6, -5) in a three-dimensional coordinate system?

answer

From the origin, move forward 7 units, left 6 units, and down 5 units.

question

The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?

answer

Graph A

question

The points in the table have been graphed in the scatter plot below. What is the best equation for the trend line, and the value of y when x is 16?

answer

y = 1.25x + 1; y = 21

question

You can use a linear model to represent the relationship between the hours worked h and the money earned m. When h = 0, then m = 0. If a person earned $39 after working 6 hours, how much will the person earn after working 25 hours?

answer

$162.50

question

Which system of equations is graphed below?

answer

C.

question

Solve the system of equations by using substitution. -2x + 3y = 7 4x - 6y = 8

answer

no solution

question

Solve the system of equations by using substitution. y = 2x + 1 3x - y = 4

answer

(5, 11)

question

Use substitution to solve the system of equations given below.

answer

no solution

question

Use elimination to solve the system of equations given by -7x + 3y = 14 and 7x - 2y = -11.

answer

A.

question

Use elimination to solve the system of equations given by 3x - 2y = 10 and 5x + 2y = 6.

answer

(2, -2)

question

Use elimination to solve the system of equations. -x + 2y = 18 x + 8y = -38

answer

(-22, -2)

question

Which of the following describes the system of equations 2x - y + 4 = 0 and 4x - 2y + 7 = 0?

answer

inconsistent

question

Graph the system of inequalities.

answer

A.

question

Which system of inequalities has this graph?

answer

A.

question

A small fish market sells only tuna and salmon. A tuna costs the fish market $0.75 per pound to buy and $2.53 per pound to clean and package. A salmon costs the fish market $3.00 per pound to buy and $2.75 per pound to clean and package. The fish market makes $2.50 per pound profit for each tuna it sells and $2.80 per pound profit for each salmon it sells. The fish market owner can spend only $159.00 per day to buy fish and $197.34 per day to clean and package the fish. The graph below represents the feasible region for this linear programming model. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function?

answer

(0, 0), (0, 53), (71.76, 0), (28, 46); t = 28 and s = 46.

question

An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. On a typical Saturday, it sells between 60 and 80 small cones and 120 and 150 large cones. The total sales have never exceeded 200 cones. If x represents the number of small cones sold, and y represents the number of large cones sold, what inequalities represent the constraints and what is the objective function in this linear programming problem?

answer

B.

question

Find the values of x and y that maximize the objective function for this graph.

answer

(1, 8)

question

The objective function for this graph is P = 5x + y. What values of x and y maximize this function?

answer

(1000, 0): The maximum is 5000.

question

Using substitution, the equations 2x - 3y = -21 and 3x + 3y = -24 give a solution of (-9,-1).

answer

False

question

Which set of numbers best describes the number -4?

answer

integers

question

Which set of numbers best describes the number π (pi)?

answer

irrationals

question

The expression | -2 | - |-7 | simplifies to 5.

answer

false

question

The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 0.75 seconds.

answer

191 feet

question

The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 2.5 seconds.

answer

100 feet

question

The expression 2y - 7x + 3y + 3x evaluated for x = 2 and y = 4 is 12.

answer

True

question

Solve 3(x - 5) - 15 = 48.

answer

x = 26

question

Solve w + 12 = -6 - 2w.

answer

w = -6

question

In the expression 2(x+4) - 12 = 44, x = 24.

answer

True

question

Solve and graph -2x + 7 ≥ 2(3 - x).

answer

Graph A

question

A car salesman receives $50 for each car sale plus 2% of the purchase price. How much must a car sell for in order for the salesperson to earn at least $500?

answer

The car must sell for at least $22,500.

question

The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.

answer

False

question

Solve |5x - 3| ≤ 3.

answer

b

question

Solve |8 - m| + 4 = 21.

answer

m = -9, m = 25

question

The expression | 2 + 4n | - 4 = 14 produces the answers n = 4 and n = 5.

answer

False

question

Simplify the expression |-3| - |-5|.

answer

-2

question

Evaluate 2a - 5b - 3a for a = -2 and b = 5.

answer

-23

question

Find the perimeter of the figure shown below. Simplify the answer. 8a + 2b 10a + 4b 10a + 2b 10a - 2b

answer

10a + 2b

question

One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.

answer

9 1/3, 13 1/3, 15 1/3

question

A certain box of cereal should have a net weight that is within 1.5 grams of 510. After the first phase of production, the weight of the cereal is 308 grams. By how much should the weight of the cereal increase to remain within the specified weight?

answer

between 200.5 and 203.5 grams

question

Graph the solution of -7x + 4 ≥ 11 and 10 - 3x > 1.

answer

Graph D

question

Solve and graph 13 - 3y < -5.

answer

Graph A

question

Solve |5x - 7| = 3.

answer

2, 4/5

question

In the expression 3(x - 6) - 12 = 33, x = 21.

answer

True

question

Suppose that 80% of people surveyed answered 'Yes' to a certain question. Let the digits 0-7 to represent 'Yes' and let 8 and 9 represent 'No.' Use the random numbers shown below to determine how many people out of 20 answered 'No.'

answer

5

question

Suppose you take a true/false quiz that contains five true/false questions. Let an even digit represent a correct answer and an odd digit represent an incorrect answer. In the five trials shown, how often did you get at least 3 questions correct? (Note: Assume there is a 0 before the number 4908 in the first trial.)

answer

3

question

A jar contains 7 red marbles, 4 blue marble, and 6 green marbles. You draw one marble from the jar. The probability of drawing a blue or red marble is 11/17.

answer

True

question

Find f(-5) if f(x) = -8x - 1.

answer

39

question

Find the slope of the line that passes through (5, -5) and (9, -5).

answer

question

The slope of the line that passes through (-2, 6) and (1, 15) is 3.

answer

True

question

Find the equation of the line that passes through the point (-7, 2) and has a slope m = -5 in point-slope form.

answer

y - 2 = -5(x + 7)

question

Find the equation of the line that passes through the points (-6, 3), (5, -2) in point-slope form.

answer

y-3=-5/11(x+6)

question

The point-slope formula of a line that passes through the point (8,5) and has a slope of ¼ is y = 1/4x + 3.

answer

false

question

Which equation represents the line whose slope is 1 and whose y-intercept is (0, 0).

answer

y = x

question

Determine the coordinates of the y-intercept of 2x + 4y = 8.

answer

(0, 2)

question

The line y = 7x - 2 has a slope of 7 and a y-intercept of (-2 ,0).

answer

False

question

A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wishes to have the length be three times the width. If the side of the barn accounts for the length of the fence, find the dimensions of the fence.

answer

144 feet by 48 feet

question

Solve |x + 4| ≥ 1.

answer

x ≤ -5 or x ≥ -3

question

A group of students rolled two number cubes 100 times and recorded a sum of six 14 times. Find the experimental probability of rolling a sum of six.

answer

14%

question

A line passes through the point (-6, 1) and has slope m = -4. Find the equation in point-slope form.

answer

y - 1 = -4(x + 6)

question

Find the slope and the y-intercept of the line. y = 5x - 7

answer

slope: 5 y-intercept: (0, -7)

question

Determine the coordinates of the x-intercept of 3x - 4y = 24.

answer

(8, 0)

question

The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.

answer

False

question

Point M is at the coordinates (-5, 5).

answer

False

question

Find the opposite and reciprocal of -1.8.

answer

1.8, -5/9

question

Name the property of real numbers illustrated by the equation 3(2x - 14) = 6x - 42.

answer

Distributive Property

question

Evaluate -1x + 7y + 4x + 1y for x = 4 and y = -2.

answer

-4

question

Evaluate 3(2m - 3n) - 2(m + 2n) for m = -9 and n = -7.

answer

55

question

Solve 11c - 2(2c + 1) = 3(c - 6).

answer

-4

question

Solve and graph 5x - 2 ≤ 8.

answer

Graph B

question

Solve |x + 8| ≤ 5.

answer

-13 ≤ x ≤ -3

question

Solve |x + 9| = 8.

answer

x = -17, x = -1

question

Write the specification 14.35 ≤ d ≤ 15.15 as an absolute value inequality.

answer

|d - 14.75| ≤ 0.4

question

A jar contains 12 blue marbles, 8 red marbles, and 20 green marbles. You pick one marble from the jar. Find the theoretical probability, P(blue or green).

answer

4/5

question

There are 135 girls in the junior class at West High School. Of these 135 girls, 16 are on the volleyball team (V), 22 are on the softball team (S), and 8 are on both the volleyball and softball team. One student is selected at random. Find the probability that the student plays on the softball team but not the volleyball team.

answer

about 10%

question

You roll a twelve-sided die with the numbers 1 through 12 on the faces of the die. You roll the die once. Find the theoretical probability P(factor of 12).

answer

1/2

question

Find g(-2) if g(x) = 4x + 3.

answer

-5

question

What is the domain and range of this function? Domain: all real numbers; Range: y ≥ -4 Domain: -2 ≤ x ≤ 2; Range: y ≥ -4 Domain: x ≥ -4; Range: all real numbers Domain: x ≥ 0; Range y ≥ 0

answer

Domain: all real numbers; Range: y ≥ -4

question

What is the domain and range of this function? Domain: x > 0; Range: y > 0 Domain: x ≥ 0; Range: y ≥ 0 Domain: all real numbers; Range: all real numbers Domain: positive integers; Range: positive integers

answer

Domain: x > 0; Range: y > 0

question

What point has coordinates of (-5, 4)?

answer

Point N

question

Graph 2x + 3y = 9.

answer

Graph A

question

Match the given graph with its corresponding equation.

answer

x + 4y = -4

question

What is the slope of the line through the points P(-5, -6) and Q(-12, 5)?

answer

-11/7

question

Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).

answer

y + 3 = - 2(x - 4)

question

The expression 2y - 5x + 3y + 2x evaluated for x = 3 and y = 2 is -11.

answer

False

question

Solve the question below.

answer

C. h= 3v/piR^2

question

Is y = (2x)2 + 5x - 7 + 1 linear or quadratic? Identify the quadratic, linear, and constant terms.

answer

quadratic function quadratic term: 4x2 linear term: 5x constant term: -6

question

Find a quadratic model for the values in the table.

answer

f(x) = 3x2 + 7x - 9

question

The vertex of a parabola will never be on the axis of symmetry.

answer

False

question

Find the quadratic function

answer

A.

question

Graph

answer

C.

question

The minimum value of a parabola that opens upward will be its vertex.

answer

True

question

Write y = -4x2 - 64x - 265 in vertex form.

answer

y = -4(x + 8)2 - 9

question

Graph y = - (x - 1)2 + 4.

answer

C.

question

The vertex of f(x) = 3(x+2)2 - 4 is (-2,-4).

answer

True

question

Factor x2 - 81.

answer

(x + 9)(x - 9)

question

Use the GCF to factor 15x2 + 6x.

answer

3x(5x + 2)

question

4y is the greatest common factor of 4y2 + 6y.

answer

False

question

Factor x2 - 6x + 8.

answer

(x - 4)(x - 2)

question

Factor 5r2 + 13r - 6.

answer

(5r - 2)(r + 3)

question

3x2 -5x - 2 factors to (3x+1)(x-2).

answer

True

question

A biologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake's population of waterfowl for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8.

answer

P(x)= 41x2 - 162x + 433; 1761 waterfowl

question

Identify the vertex and the axis of symmetry of the parabola.

answer

vertex: (1, -6); axis of symmetry: x = 1

question

Graph

answer

D. vertex (-3,-1) x= -3

question

Graph y = (x - 3)2 + 1.

answer

D.

question

Identify the vertex and y-intercept of the graph of f(x) = -4(x + 3)2 + 7.

answer

(-3, 7), y-intercept -29

question

Write y = -3x2 + 12x - 21 in vertex form.

answer

y = -3(x - 2)2 - 9

question

Factor x2 - 16.

answer

(x + 4)(x - 4)

question

Factor 4x2 - 49.

answer

(2x + 7)(2x - 7)

question

What is the GCF of 3n3 + 5np2 + n2p2?

answer

n

question

Factor t2 - 10t + 25.

answer

(t - 5)2

question

Factor 4y2 - 3y - 1.

answer

(4y + 1)(y - 1)

question

The vertex of f(x) = 2(x-2)2 +10 is (-2, 10).

answer

False

question

Factor 8ac + 12ad + 10bc + 15bd.

answer

(2c + 3d)(4a + 5b)

question

Factor 3xy - 2by + 3ax - 2ab.

answer

(y + a)(3x - 2b)

question

4n3 + 5n2 + 6n + 15 factors to (3n2 + 2) (3n + 5).

answer

False

question

Solve 6x2 = 48. If necessary, round your answer to the nearest hundredth.

answer

A.

question

Solve x2 - 6x = 0 by graphing or by factoring.

answer

x = 0, x = 6

question

A quadratic equation factored to 0 = (x-4)(x+3) would have solutions of x = -4 and x = 3.

answer

False

question

Simplify C. -500i

answer

B.

question

The square root of a negative number is an imaginary number.

answer

True

question

Solve 9x2 + 6x + 1 = 64.

answer

D.

question

Rewrite y = x2 + 4x + 5 in vertex form. Then find the vertex.

answer

y = (x + 2)2 + 1; (-2, 1)

question

When solving a quadratic equation by completing the square, the coefficient of the highest power must be any positive integer.

answer

False

question

Solve 3x2 - 9x - 12 = 0 using the Quadratic Formula.

answer

x = 4, x = -1

question

Without graphing, tell how many x-intercepts y= 2x2 + 4x + 2 has.

answer

1 intercept

question

Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.

answer

True

question

A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.

answer

P(x)= 42x2 - 186x + 762; 1962 geese

question

Factor 18ab + 9ax -4b - 2x.

answer

(9a - 2)(2b + x)

question

A rocket is launched from atop a 54-foot cliff with an initial velocity of 119 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t2 + 119t + 54. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.

answer

C. 7.87 sec

question

Evaluate the discriminant of 25x2 + 350x + 49 = 0. Tell how many solutions the equation has and whether the solutions are real or imaginary.

answer

two real solutions

question

An expression for the area of a rectangle is xy - 2x + 3y - 6. Express this area in factored form.

answer

(x + 3)(y - 2)

question

Complete the square: x2 + 2x + ____ .

answer

1

question

Identify the vertex and the axis of symmetry of the parabola.

answer

A.

question

Solve -11x + 9 + 5x2 = 0 using the Quadratic Formula.

answer

C.

question

Solve -9x + 6 + 5x2 = 0 using the Quadratic Formula.

answer

B.

question

Graph y = -x2 - 1.

answer

A.

question

Randex Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -2x2 + 4x + 2 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.

answer

a. 1000 units; b. $400

question

Write the equation of the parabola in vertex form.

answer

y = (x + 1)2 - 3

question

Factor 8a4b - 3ab2c.

answer

ab(8a3 - 3bc)

question

Find the GCF of 14a2b4c and 56ab2c2.

answer

14ab2c

question

Factor 4x2 + 5x - 21.

answer

(4x - 7)(x + 3)

question

Factor m3 - 4m2 + 6m - 24.

answer

(m - 4)(m2 + 6)

question

Factor xy - 6 + 2y - 3x.

answer

(x + 2)(y - 3)

question

Solve x2 - 4x - 5 = 0 by factoring.

answer

x = -1, x = 5

question

Find the additive inverse of 6 - 3i.

answer

-6 + 3i

question

Simplify (3 + 3i) - (7 + 6i).

answer

-4 - 3i

question

Simplify 2i(5 - i).

answer

2 + 10i

question

Write A. 1 - 4i B. 1 + 4i C. 3i D. -3i

answer

1 - 4i

question

Complete the square: x2 + 6x + ____ .

answer

9

question

Rewrite y = x2 - 10x + 3 in vertex form. Then find the vertex.

answer

y = (x - 5)2 - 22; (5, -22)

question

Solve 7x2 + 28x = 49 by completing the square.

answer

C.

question

Solve 8x2 - 80x = -24 by completing the square.

answer

C.

question

15x3 - 10x2 + 3x -2 factors to (5x2 + 1) (3x - 2).

answer

True

question

Classify 2x3 - 2x by degree and by number of terms.

answer

cubic binomial

question

The table shows the number of oak trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of oaks planted in 1998.

answer

T(x) = 0.2x3 + 0.7x2 + 0.2x + 0.1; 353.2 thousand trees

question

4x3y4 is a 4th degree monomial.

answer

False

question

The roots of a certain polynomial are -2/5, -6 and 4/3. What might the linear factors of the polynomial be?

answer

(5x + 2)(x + 6)(3x - 4)

question

Write 2r3 + 8r2 - 10r in factored form.

answer

2r(r - 1)(r + 5)

question

The polynomial 3x2 - 7 + 4x3 + x6 is written in standard form.

answer

False

question

Find the zeros of y = (x - 2)(x + 1)(x + 3).

answer

x = 2, x = -1, x = -3

question

Find the zeros of y = (x - 2)(x + 9).

answer

x = 2, x = -9

question

A multiple zero has a multiplicity equal to the number of times the zero occurs.

answer

True

question

Divide (5x3 - 6 - 5x) ÷ (10 + 5x) using synthetic division.

answer

x2 - 2x + 3, R -36

question

Use synthetic division and the Remainder Theorem to find P(-3) if P(x) = x4 + 19x3 + 108x2 + 236x + 176.

answer

8

question

When dividing polynomials, every term of the numerator must be divided by the entire denominator.

answer

True

question

Solve x2 - 12x + 41 = 0

answer

D.

question

Factor 3q3 - 81.

answer

3(q - 3)(q2 + 3q + 9)

question

4x2 - 36 = 0 has a solution of x = +/- 3.

answer

True

question

Classify -4x3 - 2x2 - 2x by degree and by number of terms.

answer

cubic trinomial

question

Classify 2 by degree and by number of terms.

answer

constant monomial

question

Find a polynomial function to model the data.

answer

f(x) = 4.68x3 + 8.87x2 + 4.25x + 6.32

question

Find the zeros of y = (x - 1)(x + 2).

answer

x = 1, x = -2

question

Find the zeros of y = x(x + 5)(x - 8).

answer

x = 0, x = -5, x = 8

question

Divide (3x3 + 4x2 - 5x - 2) ÷ (x + 2) using long division.

answer

3x2 - 2x - 1

question

Factor x4 - 8x2 + 15.

answer

C.

question

Solve x - x3 = 2x4 + 3x2 - 5.

answer

x = ±1

question

Solve x2 - 10x + 29 = 0.

answer

No Solution

question

Solve 8x3 + 27 = 0.

answer

B.

question

The polynomial x4- 2x2 + x4 - x is written in standard form.

answer

False

question

Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.

answer

0 = x3 + 4x2 - 2x - 20

question

Use the Rational Root Theorem to determine all possible rational roots of 5x3 + 4x2 + 4x + 10 = 0. Do NOT find the actual roots.

answer

B.

question

The possible rational roots of x3 + 3x2 - 4x + 2 are +/- 3 and +/- 2.

answer

False

question

For 3x9 -7x6 + 4x3 + 15 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

answer

D.

question

For 8 - 4x3 + 4x6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

answer

D.

question

The equation f(x) = 4x4 + 4x2 + 9x - 2 can have at most four distinct real roots.

answer

True

question

Evaluate. 9!/6!

answer

504

question

There are 17 students participating in a spelling bee. How many ways can the students who go first and second be chosen?

answer

272 ways

question

7! Is another way of writing 7 * 6 * 5.

answer

False

question

Determine whether the following situation would require calculating a permutation or a combination. Assigning students to their seats on the first day of school.

answer

permutation

question

Ten candidates are running for three seats in the student government. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?

answer

176 ways

question

Order does not matter when examining combinations, but order does matter in permutations.

answer

true

question

What is the probability of getting two heads when tossing a coin four times?

answer

3/8

question

Use Pascal's Triangle to expand (s - v)5.

answer

s5 - 5s4v + 10s3v2 - 10s2v3 + 5sv4 - v5

question

If flipping a coin is equally likely to result in heads or tails, the odds of flipping a coin six times and getting only one head are 3 out of 16.

answer

False

question

A fifth-degree polynomial equation with rational coefficients has the roots 2, -7i, and -7 + i. Find the remaining roots.

answer

7i, -7 - i

question

Divide (x4 - 11x3 - 49x2 + 899x - 2506) ÷ (x - 8).

answer

x3 - 3x2 - 73x + 315, R 14

question

Assume red and green are equally likely occurrences. What is probability that you will get one green light in a row of five lights?

answer

5/32

question

A school bought a special type of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9. How many different pass codes are possible?

answer

5,040

question

A summer reading list has 20 books on it. In how many ways can you choose four books to read?

answer

4,845 ways

question

Use Pascal's Triangle to expand (3a - b)4.

answer

81a4 - 108a3b + 54a2b2 - 12ab3 + b4

question

Write in standard form. Then classify by degree and by number of terms.

answer

D.

question

Write (x - 2)(x + 9) as a polynomial in standard form.

answer

x2 + 7x - 18

question

Find the zeros of the function. State the multiplicity of multiple zeros. y = (x - 4)2

answer

x = 4 multiplicity 2

question

Divide (2x3 + 4x2 + 3x + 4) ÷ (x + 1) using long division.

answer

2x2 + 2x + 1, R 3

question

Which polynomial is NOT a factor of 3x4 - 10x3 - 29x2 + 16x + 20?

answer

x - 2

question

Which polynomial is NOT a factor of 3x4 - 16x3 - 3x2 + 36x + 20?

answer

x - 1

question

Factor 3q3 - 81.

answer

3(q - 3)(q2 + 3q + 9)

question

Solve x3 + 4x2 - x - 4 = 0.

answer

x = -4, x = -1, x = 1

question

Solve x3 + 5x2 - 9x - 45 = 0.

answer

x = -5, x = -3, x = 3

question

Find only the rational roots of x4 - 9x3 + 16x2 + 18x - 36 = 0.

answer

x = 6, x = 3

question

Find the roots of x3 - x2 + 2 = 0.

answer

x = 1 + i, x = 1 - i, x = -1

question

For x7 - 2x6 + 3x2 - 2x + 5 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

answer

7 complex roots; 1, 3, 5, or 7 real roots possible rational roots: ±1, ±5

question

For 3x3 -2x + 6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.

answer

C.

question

Which polynomial function has the highest degree?

answer

the quotient of f(x) and g(x), where f(x) = x9 - 3x and g(x) = 3x2 - 4

question

Seven skiers enter a downhill race. First, second, and third places will be given to the three fastest skiers. How many arrangements of first, second, and third places are possible with seven skiers?

answer

210

question

Evalute 9!

answer

362,880

question

Find 8P3.

answer

336

question

How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?

answer

42 ways

question

In how many ways can the three letters A, B, and C be arranged?

answer

6

question

Determine whether the following situation would require calculating a permutation or a combination. Selecting four teachers to attend a math seminar.

answer

combination

question

Four cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of four cards are possible?

answer

270,725

question

How many combinations of four can you make from the set? {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

answer

210 combinations

question

The polynomial 5x3 - 2x2 + x - 13 is written in standard form.

answer

True

question

What is the vertex of the graph of y = |x| - 6?

answer

(0, -6)

question

Which statement describes the relationship between the graph of the equation

answer

C.

question

Graph y = x2 - 6.

answer

C.

question

Write the equation of the parabola in vertex form.T

answer

y = (x - 1)2 - 3

question

The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998.

answer

T(x) = 0.1x3 + 0.3x2 + 0.3x + 0.1; 172.8 thousand trees

question

Use Pascal's Triangle to expand (s - v)6.

answer

v6 - 6v5s + 15v4s2 - 20v3s3 + 15v2s4 - 6vs5 + s6

question

Evaluate 8C3.

answer

56

question

Solve 5x - 4 = |2x + 1|. Check for extraneous solutions.

answer

...

question

Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?

answer

1/32

question

Write an explicit formula for the sequence

answer

n+1/n^2+3

question

Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.

answer

an = 2an - 1 - 4 where a1 = 15; 356

question

The next three terms of the sequence 1, 3, 5, 7, ... are 9, 11, 13.

answer

True

question

A grocery clerk sets up a display of 12-pack cartons of cola. There are 40 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?

answer

820 cartons

question

Is the sequence -9.9, -13, -16, -19.2, ... arithmetic? If so, identify the common difference.

answer

no

question

The missing term of the arithmetic sequence 13, __, 27 is 21.

answer

False

question

Find the missing terms of the geometric sequence 480, ___, ___, ___, 12.288, .... (Hint: The geometric mean of the first and fifth terms is the third term.)

answer

192, 76.8, 30.72

question

Is the sequence

answer

A. yes .5

question

The sequence 3, 6, 9, 12 is geometric.

answer

False

question

For the sum

answer

6 terms, 25, 0; 75

question

Write the related series for the finite sequence 7.6, 6.3, 5, ... , -1.5. Then evaluate the series.

answer

7.6 + 6.3 + 5 + ... + (-1.5) = 24.4

question

5, 7, 11, 15, 21 is an infinite series.

answer

False

question

Which series will converge?

answer

A.

question

Evaluate the infinite geometric series 2.1 + 0.21 + 0.021 + ... .

answer

7/3

question

The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.

answer

False

question

Describe the pattern

answer

Add 1 to the numerator and 2 to the denominator of the previous number.

question

Describe the pattern 16, -8, 4, -2, 1, ....

answer

Divide the previous number by -2.

question

Which formula does NOT describe the sequence 8, 6, 3, -1, -6, ... ?

answer

an = -0.5n2 - n + 9

question

Find the arithmetic mean an of the terms

answer

19/40

question

Find the missing term of the arithmetic sequence 25, ___, 49, ....

answer

37

question

Determine whether the series -1024 + 256 -64 + 16 - ... is arithmetic or geometric. Then evaluate the series to the ninth term.

answer

geometric; -819.203125

question

Evaluate the infinite geometric series

answer

-12

question

Evaluate the series 3 - 12 + 48 - 192 + ... to the seventh term. Round your answer to the nearest hundredth, if necessary.

answer

9831

question

The sequence 2, 6, 18, 54, ... is a geometric sequence.

answer

True

question

Evaluate the area under g(x) = -x2 - 3x + 7 for -4 ≤ x ≤ 1.

answer

C. 35.83

question

Use inscribed rectangles to approximate the area under g(x) = -0.5x2 + 7 for -3 ≤ x ≤ 0 and rectangle width 0.5.

answer

15.3 units2

question

The area approximated by circumscribed rectangles is greater than the area under the curve.

answer

True

question

Use the frequency table to find P(more than 3 children).

answer

20%

question

Use the frequency table to find P(0 - 2 children).

answer

68%

question

A situation may not be described by more than one sample space.

answer

False

question

The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 64%. Find the probability that a bus chosen at random has a working radio given that it is ready for service.

answer

75.3%

question

Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.

answer

1/3 .33333333

question

If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second.

answer

True

question

Find the mean, the median, and mode of the set of values. 5, 20, 6, 5, 15, 18, 12, 13, 14

answer

mean: 12, median: 13, mode: 5

question

The cost of ten different portable MP3 players is shown in the table. What is the mean cost?

answer

$90

question

The mode of the set 2, 3, 3, 4, 5, 8, 9, 10 is 3.

answer

True

question

The scores of 36 students on a recent geography test are in the table. If Lupe got a 69 on the test, what percentile would that score represent?

answer

44%

question

The box-and-whisker plot represents the test scores of 25 students. What percent of the scores were between 88.5 and 65?

answer

50%

question

If x is at the 63rd percentile, then 37% of the data are less than or equal to x.

answer

False

question

A rubber ball dropped on a hard surface takes a sequence of bounces,

answer

C. 54 24/125

question

Evaluate the infinite geometric series 1.9 + 0.19 + 0.019 + ....

answer

19/9

question

Decide whether the formula an = -4n(n - 1) is explicit or recursive. Then find the first five terms of the sequence.

answer

explicit; 0, -8, -24, -48, -80

question

A spinner is divided into eight equally-sized areas. The central angle for pink is 90°, for teal is 225°, and for blue is 45°. Which is the correct frequency table for this spinner?

answer

2 5 1

question

Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.

answer

D. 1/6

question

A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.

answer

True

question

How do the medians of the two sets of exam scores compare?

answer

The median of Exam A is greater than the median of Exam B.

question

Make a box-and-whisker plot for the set of values. 5.2, 9.2, 5.2, 3.2, 3.2, 7.2, 6.2, 8.2, 5.2, 4.2, 5.2, 6.2, 9.2, 9.2, 8.2

answer

B.

question

Make a box-and-whisker plot for the set of values. 7.2, 3.2, 5.2, 3.2, 4.2, 7.2, 5.2, 3.2, 6.2, 4.2, 6.2, 3.2, 6.2, 2.2, 4.2

answer

2.2 7.2

question

Is the sequence 5.1, 10.5, 15.9, 21.3, ... arithmetic? If so, identify the common difference.

answer

yes, 5.4

question

For the geometric sequence 2, -10, 50, -250, ..., find the seventh term.

answer

31, 250

question

Write the explicit formula for the sequence with a1 = 120 and r = 0.3. Then generate the first five terms.

answer

D. an = 120 • 0.3n - 1; 120, 36, 10.8, 3.24, 0.972

question

Evaluate the series 3 + 9 + 15 + 21 + 27 + ... to the 16th term.

answer

128

question

Tell whether 3, 10, 17, 24, ... , 73 is a sequence or a series. Then tell whether it is finite or infinite.

answer

sequence, finite

question

The sequence -12, -6, 0, 6, ... , 48 has 11 terms. Evaluate the related series.

answer

198

question

Use summation notation to write the arithmetic series -3.9 + (-1.9) + 0.1 + ... for six terms.

answer

6 x=1 -5.9 +2n

question

Evaluate the series

answer

C. 5461/ 16,384

question

A class of 30 students has 11 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.

answer

C. 10/19

question

The table gives data about municipal waste collected and recycled by type. Find P(recycled | glass).

answer

about 6.7%

question

The table lists the results of a survey of the students at a community college. Suppose a student is selected at random. Find P(male | student takes physiology).

answer

13/22

question

Find the arithmetic mean an of the terms

answer

91/60

question

You cannot use a table or graph to show a probability distribution.

answer

False

question

A percentile is a number from 0 to 100 which can be associated with x to indicate the percent of the data that are less than or equal to x.

answer

True

question

A large asteroid crashed into a moon of another planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 20, 60, 100, 140, .... Find the distance that the projectile traveled in the 9th second.

answer

340 ft

question

What does the dot at 47 represent?

answer

lower quartile

question

The sequence -14, -9, -4, 1, ... , 41 has 12 terms. Evaluate the related series.

answer

162

question

Inscribed rectangles are completely under the curve.

answer

True

question

Evaluate the infinite series

answer

It does not have a sum.

question

Which number is an outlier in the data shown in the table?

answer

19

question

The table gives data about municipal waste collected and recycled by type. Find P(paper | not recycled).

answer

31.7%

question

Evaluate the series

answer

-5.81

question

Write and evaluate a sum to approximate the area under y = (x - 4)2 - 1 for the domain 0 ≤ x ≤ 2. a. Use inscribed rectangles 0.5 units wide. b. Use circumscribed rectangles 0.5 units wide.

answer

a. 13.75 units2; b. 19.75 units2

question

Write an explicit and a recursive formula for the sequence -7, -5.6, -4.2, -2.8, -1.4, ....

answer

explicit: an = -8.4 + 1.4n; recursive: an = an - 1 + 1.4, where a1 = -7

question

Probability over a continuous range of events is cumulative probability.

answer

True

question

Use inscribed rectangles to approximate the area under f(x) = -x2 + 6 for -1.5 ≤ x ≤ 0 and rectangle width 0.5.

answer

7.25 units2

question

Given the set of axes y-axis: a car's velocity, x-axis: time, what does the area under the curve represent?

answer

the total distance traveled by the car

question

Identify the outlier in the temperature data shown.

answer

71°

question

The number of patients treated at Dr. Oster's dentist office each day was recorded for nine days. Using the data 7, 4, 18, 14, 14, 11, 13, 21, and 6, find the mean, median, and mode.

answer

mean: 12, median: 13, mode: 14

question

The number of patients treated at Dr. Holman's dentist office each day was recorded for seven days. Using the data 3, 10, 18, 9, 22, 20, and 2, find the mean, median, and mode.

answer

mean: 12, median: 10, no mode

question

A frequency table is a list of the outcomes in a sample space and the number of times each outcome occurs.

answer

True

question

Ms. Chin collected data about how long students in two of her classes spent doing homework. This table shows the result. Suppose a student from her third or fourth period class is selected at random.

answer

5/23

question

Use the frequency table to find P(2 or 3 children).

answer

42%

question

Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15

answer

mean: 15, standard deviation: 5.66

question

The range of the set 12, 18, 19, 22, 25 is 19.

answer

False

question

Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12

answer

range: 32, interquartile range: 16.5

question

Which sample size will produce a margin of error of ±4.1%?

answer

595

question

Which sample size will produce a margin of error of ±3.5%?

answer

816

question

From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.

answer

True

question

If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.

answer

True

question

The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

answer

260 fish

question

The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?

answer

2.5%

question

Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15

answer

mean: 15, standard deviation: 5.66

question

The range of the set 12, 18, 19, 22, 25 is 19.

answer

False

question

Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12

answer

range: 32, interquartile range: 16.5

question

Which sample size will produce a margin of error of ±4.1%?

answer

595

question

Which sample size will produce a margin of error of ±3.5%?

answer

816

question

From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.

answer

True

question

If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.

answer

True

question

The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

answer

260 fish

question

The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?

answer

2.5%

question

Find 49° in radians.

answer

0.86 radians

question

An angle in standard position with a positive measurement will extend below the x-axis.

answer

False

question

pi/3 radians in degrees

answer

60°

question

The amplitude of y = 3 sin(2x) is 3.

answer

True

question

Use the graph to find the value of y = sin θ for θ = 270°.

answer

-1

question

Find the amplitude and period of y = -5 sin (5x).

answer

amplitude=5,period=2/5

question

For a circle of radius 9 feet, find the arc length s cut off by a central angle of 6°.

answer

3/10

question

In which quadrant does the terminal side of a 117° angle lie?

answer

second quadrant

question

Find 311° in radians.

answer

5.43 radians

question

When 2251 voters were polled, 52% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.

answer

±2.1%; between 49.9% and 54.1%

question

Write an equation of the cosine function with amplitude 2 and period 8π.

answer

2 cos 1/4 x

question

The range of the set 2, 5, 8, 19, 33, 45 is 43.

answer

True

question

Graph y= 2.5 tan 4x/5

answer

/ closer together

question

Graph y = 5 cos x.

answer

far apart 5 -5

question

Evaluate sec 3.

answer

-1.0101

question

Reciprocal functions cannot be evaluated in radians.

answer

False

question

Evaluate sec 131°.

answer

-1.52

question

Simplify cos θ sec θ.

answer

1

question

Simplify cot/cos

answer

csc θ

question

The tangent of an angle is equal to the ratio of its sine divided by its cosine.

answer

True

question

The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.

answer

False

question

Solve 2 cos θ + 4 = 3 for 0 ≤ θ < 2π.

answer

2pi/3 4pi/3

question

The diagram shows one solution to the equation 3 - sin θ = 5 sin θ. Find the complete solution of the equation.

answer

30° + n • 360°, 150° + n • 360°

question

The length of side RP is approximately 42 cm.

answer

False

question

Find the area of the triangle. Round your answer to the nearest tenth, if necessary.

answer

67.3 in.2

question

Solve the problem below.

answer

3.1 m2

question

The law of cosines is used to find the measures of a triangle when only the three sides are known, because the law of sines requires at least one angle measure.

answer

True

question

Find the angles in the triangle when a = 19, b = 20, and c = 10. Round your answers to the nearest tenth.

answer

69 80 29

question

Solve the problem below.

answer

80.3°

question

Determine the number of standard deviations which include all data values listed for the situation.The mean time employees take of a company to commute to work is 40.75 minutes; the standard deviation is 12.9 minutes.42 min, 45 min, 53 min, 34 min, 12 min, 48 min, 52 min, 24 min, 56 min, 47 min, 28 min, 48 min

answer

3 standard deviations

question

Simplify cot θ tanθ.

answer

1

question

A set of data that is normally distributed has a mean of 35.6 and standard deviation of 2.5. Which number is between 1 and 2 standard deviations of the mean?

answer

38.3

question

In one survey, the shoe sizes of women are distributed normally about the mean. The mean of the data is 7.17, and the standard deviation is 1.44. About what percent of the women are within two standard deviations of the mean in shoe size?

answer

96%

question

Find the angles in the triangle when a = 13, b = 12, and c = 11. Round your answers to the nearest tenth.

answer

68 59 52

question

Solve cot θ sin θ = 1/5 for 0 ≤ θ < 2π.

answer

pi/3 5pi/3

question

Find the range and the interquartile range of the set of values.37, 21, 44, 19, 22, 47, 26, 32, 25, 43, 11, 15

answer

range: 36, interquartile range: 20

question

Which expression completes the equation to make it an identity? cos+ sin + cos / 1+ sin

answer

cos θ

question

In a survey of 368 people, 81 drink milk straight from the milk carton. For the sample, find the sample proportion, the margin of error, and the interval likely to contain the true population proportion.

answer

a. 22%; b. ±5%; c. 17% to 27%

question

Use the Law of Sines to solve for c to the nearest tenth.

answer

51.4

question

Which expression completes the equation to make it an identity?

answer

1+csc2 0 / 1-sin 0

question

What is the period of y = 3 tan 4x + 5?

answer

pi/4

question

Write 11pi/18 radians in degrees

answer

110°

question

Find the value of csc 165°. Round your answer to the nearest hundredth.

answer

3.86

question

In ΔABC, b = 4, c = 1, and ma =118

answer

4.56

question

In ΔABC, b = 1, c = 3 ma= 138

answer

3.8

question

Use the Law of Sines to solve for a to the nearest tenth.

answer

38.1

question

The class average on a math test was 84.5 and the standard deviation was 4.4. Find the z-score for a test score of 94.

answer

≈ 2.16

question

Find the degree measures of the angles whose tangent is sqr 3

answer

60° + n • 180°

question

Find the mean and standard deviation for the set of values. 25, 19, 5, 21, 18, 22, 17, 10, 7

answer

mean: 16, standard deviation: 6.62

question

Solve the problem below.

answer

80.3°

question

Graph Y=-pi/4 cot ( x-pi/4)

answer

about 112 women

question

Solve 3 cos 0 = cos 0 - sqr2 for 0 < 0 < 2pi

answer

3pi/4 5pi/4

question

Which sample size will produce a margin of error of ±6.3%?

answer

252

question

Use the graph to find the value of y = sin θ for θ = 150°.

answer

0.5

question

Simplify sin θ sec θ.

answer

tan θ

question

Find the radian measures of the angles whose sine is -0.8. Round to the nearest hundredth.

answer

-0.93 + 2πn and 4.07 + 2πn

question

When 876 voters were polled, 67% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.

answer

±3.4%; between 63.6% and 70.4%

question

Use the Law of Sines to solve for a to the nearest tenth.

answer

21.2

question

On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 265 feet at an angle of 35° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?

answer

218.2 ft

question

A matrix with 4 columns and 3 rows is a matrix of dimensions 4x3.

answer

False

question

Identify a31 in the matrix.

answer

10

question

What are the dimensions of the matrix?

answer

5 × 4

question

Find

answer

-3 5 9 0

question

Two matrices can be subtracted if they have an equal number of rows, regardless of how many columns they have.

answer

False

question

Solve for each variable

answer

-6 -1/4

question

Find AB,

answer

[-25 25] TALL

question

Two matrices with dimensions 2x2 and 2x2 will result in a product matrix with dimensions 2x2 when multiplied.

answer

-32 28

question

Graph the figure and its image after the given rotation.

answer

4

question

Transforming a figure 3 units to the right and 2 units up can be accomplished by adding 3 to each x-coordinate of the vertices and subtracting 2 from the y-coordinates.

answer

False

question

What are the coordinates of the image after a rotation of 90°?

answer

0 1 -4 0 -3 1

question

Find the inverse of -2 2 -1

answer

-1/2 1 -1/10

question

The determinant of this matrix is 7.

answer

False

question

Which matrix has determinant -7?

answer

-14 -1 7 1

question

Find

answer

[21 -63]

question

Find

answer

-70 44 70 -24 71 -73 -71 -71 -35

question

Use matrices A, B, and C. Find B-C if possible.

answer

-2 -7 14 -4 7 0

question

Write the coordinates of the image after a dilation three times the original size.

answer

-21 -12

question

Find

answer

13 -9 -12 -1 -6 18 1 -1 2

question

Find

answer

-3 9 1 -3 -6 9 -14 0 6

question

Solve

answer

13/3 2/3

question

Determine whether

answer

1/10 -3/10 -1/5 -2/5

question

Find

answer

[6 -34]

question

Simplify

answer

3|x5|y4

question

-25 has no real 4th root.

answer

True

question

Find all the real cube roots of

answer

-8/9

question

The fifth root of 12 is equal to the fifth root of 7 times the fifth root of 5.

answer

False

question

Simplify

answer

4a^2b sqr 3a

question

Divide and simplify sqr 24/ sqr 2

answer

2 sqr 3

question

Rationalize the denominator of

answer

-5 -2 sqr 6

question

Multiply

answer

22 + 8 sqr 6

question

These are two like radicals.

answer

False

question

17 1/3 is the same as the cube root of 17.

answer

True

question

Simplify

answer

x -1/2 y 3/4

question

Simplify

answer

1/ 4 sqr x^7

question

The solution to this equation is x = 11.

answer

False

question

Refer to the question below.

answer

x = 60

question

Solve

answer

3/2

question

Find AB,

answer

-22 74

question

Solve

answer

x = 3

question

Multiply and simplify

answer

m^2 sqr 12 m^2

question

Multiply and simplify

answer

6x^2 sqr3^ x

question

Find the coordinates of the image after the reflection in the given line.

answer

-5 6 -1 -3 -9

question

Find

answer

-14 -1 3 7

question

Write

answer

3^13^ sqr x^7

question

The formula for the volume of a sphere is

answer

1.63 in.

question

Two matrices with dimensions 3x1 and 2x4 will produce a product matrix with dimensions 3x4 when multiplied.

answer

False

question

Find all the real square roots of 0.0036.

answer

0.06 and -0.06

question

Solve

answer

-1/3

question

Multiply

answer

5

question

Which matrix is the multiplicative inverse of

answer

0 1 -1 -5 5 -4 1 -1 1

question

Simplify

answer

81

question

What are the dimensions of the matrix?

answer

2 × 1

question

The velocity of sound in air is given by the equation

answer

none of these

question

Find the coordinates of the image of

answer

-14 -3 10 14

question

Solve

answer

f = 0, g = -4, h = 9 or -9

question

Rationalize the denominator of

answer

3 sqr t

question

Determine whether

answer

0 -1/3 -1/2 1/6

question

What are the dimensions of the matrix?

answer

3 × 2

question

What are the dimensions of the matrix?

answer

5 × 4

question

Find the real-number root of

answer

5/7

question

Solve

answer

4/3

question

Write the coordinates of the image after a translation 3 units right and 2 units down.

answer

-1 3 -1 -6 -6 -3

question

In May, Suzanne bought 32 styrofoam balls and decorated them as toy figurines. In June, she sold 12 figurines. In May, Carrie bought 36 styrofoam balls to decorate and in June, she sold 22 figurines. Which matrix represents all of their May purchases and their June sales?

answer

32 -12 36 -22

question

Multiply

answer

180 sqr 10

question

What are the dimensions of the matrix? Identify a12.

answer

3 × 2, -4

question

In May, Marcus bought 48 styrofoam balls and decorated them as toy figurines. In June, he sold 19 figurines. In May, Lin bought 44 styrofoam balls to decorate and in June, she sold 21 figurines. Which matrix represents all of their May purchases and their June sales?

answer

48 -19 44 -21

question

Write

answer

8x -15/7

question

Let f(x) = 3x + 7 and g(x) = 4x - 2. Find (f composited with g) (-6).

answer

-71

question

Let f(x) = 3x2 + 10x- 8 and g(x) = x + 4.

answer

-9x + 6, all real numbers x ≠ -4

question

If f(x) = 3x + 7 and g(x) = 5x - 2 then (f+g)(x) = 8x + 5.

answer

True

question

The domain of a relation and its inverse are the same.

answer

False

question

Find the inverse of f(x) = 3x2. Is the inverse a function?

answer

x/3 no

question

Identify the graph of y = 2x2 - 5 and its inverse.

answer

up right

question

Write an exponential function to model this situation: a population of 260 animals increases at an annual rate of 9%.

answer

f(x) = 260(1.09)x

question

For an annual rate of change of -31%, find the corresponding growth or decay factor.

answer

0.69

question

An annual rate of change is -10%. The corresponding growth or decay factor is 0.10.

answer

False

question

Graph y = 4x - 3 as a translation of its parent function.

answer

backwards L low

question

Evaluate e4.

answer

54.5982

question

y = -4* 2x is a reflection of y = -1/4* 2x.

answer

False

question

Log4 64 = 3

answer

True

question

Given log 15 = B and log 3 = C , find log 5.

answer

B - C

question

Use the properties of logarithms to evaluate log4 256.

answer

4

question

Find the equation of the graph.

answer

y = 1.5x

question

Solve the question below.

answer

-6

question

A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?

answer

$13,616.61

question

Find the inverse of y = 3x2 + 4. Is the inverse a function?

answer

x-4 / 3 no

question

Let f(x) = 4 - x2 and g(x) = 2 - x. Find f(x) • g(x).

answer

x3 - 2x2 - 4x + 8

question

Solve the question below.

answer

505

question

Find the annual percent increase or decrease that y = 0.35(2.3)x models.

answer

+130%

question

Write 5 log x - 4 log (x - 4) as a single logarithm.

answer

log x^5/x-4^4

question

How much money invested at 5% compounded continuously for 2 years will yield $1150?

answer

$1040.56

question

Solve the question below.

answer

29/4

question

Find the inverse of the relation. Graph the given relation and its inverse.

answer

-2 1 5 10

question

Suppose that x and y vary inversely. Write a function rule for the function that x = 4 when y = 7.

answer

28/x

question

If m varies directly as the square root of y, inversely as p2, and directly as n, what happens to m when y is quadrupled, p is tripled, and n is multiplied by 5?

answer

multiply 10/9

question

If y varies inversely with x and y = 6 when x = 9, then y = 96/x.

answer

False

question

State the excluded values of x in the expression

answer

2 or 3

question

Simplify

answer

2a3/3b

question

This statement simplifies to 16a2.

answer

True

question

Divide

answer

x-4/x-3 3 4

question

The only restriction of the variable in this equation is that x cannot equal positive or negative 5.

answer

False

question

Multiply

answer

xy/2 0 0

question

Solve the question below.

answer

13x-30/x^2-36

question

A complex fraction is a fraction that has a fraction in either its numerator or denominator, or in both its numerator and denominator.

answer

True

question

Simplify

answer

x+3/2

question

Solve

answer

1

question

An extraneous solution is a solution of the derived equation, but not of the original equation.

answer

True

question

Solve

answer

-1/16

question

After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?

answer

87

question

Expand

answer

log b (1/2 -

question

State the excluded value(s) of

answer

x cannot equal 5, -5

question

Given log 5 = P and log 2 = Q , find log 10.

answer

P + Q

question

After taking 7 quizzes, your average is 75 out of 100. What must your average score be on the next five quizzes to increase your average to 80?

answer

87

question

Simplify

answer

2y +1 / y+1

question

Simplify

answer

4/3

question

It is not necessary to check all solutions of the derived equation in the original equation to find whether any of them are not solutions of the original equation.

answer

False

question

Write an exponential function to model this situation: a population of 300 animals increases at an annual rate of 13%.

answer

f ( x ) = 300(1.13) x

question

State the excluded values of a and b in the expression

answer

0 0

question

Simplify

answer

21 16 50 54 / 72

question

State the excluded value(s) of

answer

x cannot equal -4

question

Find

answer

x+4 / x+2

question

Which property was used to rewrite log

answer

power property

question

Identify the graph of y = 2 x + 7 and its inverse.

answer

up cross

question

Multiply

answer

x ; x ≠ -7, -4, 0

question

The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P . The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000.

answer

25,200 coats

question

Graph y = 3 x + 1 as a translation of its parent function.

answer

backwards L high

question

Solve the question below.

answer

4

question

Simplify

answer

5x

question

Simplify

answer

x-7 /2

question

Use the properties of logarithms to evaluate

answer

2/3

question

Let f ( x ) = x 2 + 2 x - 1 and g ( x ) = 2 x - 4. Find 2 f ( x ) - 3 g ( x ).

answer

2 x 2 - 2 x + 10

question

A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Nita can paint a certain room in 3 hours. Jorge can paint the same room in 4 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

answer

x/3 + x/4 =1, 1.71 h

question

The selling price of x number of a certain stereo can be modeled by the function R ( x ) = 160 x . The total cost of making x stereos is C ( x ) = 71 x - 0.02 x 2. What is the percent markup for 31 stereos?

answer

127%

question

Use the properties of logarithms to evaluate log7343.

answer

3

question

Graph f ( x ) = 2 x + 1 + 3 as a translation of its parent function.

answer

backwards L high

question

For f ( x ) = 5 - 3 x and g ( x ) = x 2 - 1, find f ( g ( x )) and g ( f ( x )).

answer

f ( g ( x )) = -3 x 3 + 8, g ( f ( x )) = 9 x 2 - 30 x + 24

question

For the function f ( x ) = (4 - 2 x )2, find f -1 and the domain and range of f and f -1. Determine whether f -1 is a function.

answer

2 x/2 0

question

Simplify

answer

x-1 / 5(x-3) 1 and 3

question

Find the next three terms in the sequence 1, 2, 4, 8, ....

answer

16, 32, 64

question

Simplify csc θ sin θ.

answer

1

question

Divide

answer

x-5/x-3

question

Find

answer

2

question

Find

answer

4ax^2 /3by

question

Find the 11th term of the sequence 11, 19, 27, 35, ....

answer

91

question

Solve the question below.

answer

7

question

Simplify sin2 θ(1 - csc2 θ).

answer

sin2 θ - 1

question

Divide

answer

x-6 / x-5

question

Find the next two terms in the sequence -5, 8, -13, 20, -29, .... Write a formula for the nth term. Identify the formula as explicit or recursive.

answer

none of these

question

Multiply

answer

x; x ≠ -6, -3, 0

question

A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Katalin can paint a certain room in 3 hours. Lena can paint the same room in 8 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?

answer

2.18

question

Find the exact coordinates of the point at which the terminal side of -135° intersects the unit circle.

answer

- sqr 2 / 2

question

Solve

answer

x = 6

question

Find the values of cos θ and sin θ for -25°. Round your answers to the nearest hundredth.

answer

0.91, -0.42

question

Solve

answer

no solution

question

In which quadrant does the terminal side of a 314° angle lie?

answer

fourth quadrant

question

Is the sequence -5.4, 5.1, 15.6, 26.1, ... arithmetic? If so, identify the common difference.

answer

yes, 10.5

Algebra 1
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Study Guide Algebra. Line, numb, fit, model, time. – Flashcards 316 terms
Sarah Adrian

316 terms
Preview

Study Guide Algebra. Line, numb, fit, model, time. – Flashcards

question

Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution?

answer

4p - 7 = 13

question

Fiona solved the equation shown. What is the missing step of her solution?

answer

Simplify by combining like terms

question

Which input value produces the same output value for the two functions on the graph? G1

answer

Check Graph #1 in notebook x=1

question

Consider the functions shown on the graph. What is the input value for which the statement f(x) = g(x) is true? G2

answer

Check graph #2 1.5

question

Solve the equation. −10x + 1 + 7x = 37

answer

x = −12

question

Rahul solved the equation 2(x - ) - x = . In which step did he use the addition property of equality?

answer

Step 3

question

The Apache Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?

answer

1.95x + 2.50 = 27.46; Isaac traveled 12.8 miles.

question

Which input value produces the same output value for the two functions on the graph? GRAPH3

answer

x-2 G3

question

What is the solution to the linear equation? 2/5 + p = 4/5 + 3/5p

answer

P=1

question

Solve the equation. -3x + 1 + 10x = x + 4

answer

X=1/2

question

The International Business Club starts the school year with $250.50 in their account. They spend $35 each month on activities. The Future Agricultural Leaders Club starts with $300 and spends $45.25 each month.Which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money?

answer

250.5 - 35m = 300 - 45.25m

question

What is the solution to the linear equation? 6k + 10.5 = 3k + 12

answer

k=0.5

question

What is the solution to the linear equation? d - 10 - 2d + 7 = 8 + d - 10 - 3d

answer

d=1

question

Which number can each term of the equation be multiplied by to eliminate the fractions before solving? -3/4m-1/2=2+1/4m

answer

4

question

What is the solution to the linear equation? 2.8y + 6 + 0.2y = 5y - 14

answer

y=10

question

How many solutions exist for the given equation? 3(x - 2) = 22 - x

answer

One

question

Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"?

answer

3 - (n - 1) = 1/2(3n - 4)

question

Which equation has no solution?

answer

5 + 2(3 + 2x) = x + 3(x + 1)

question

How many solutions exist for the given equation? 1/2(x + 12) = 4x - 1

answer

One

question

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?

answer

4

question

How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2

answer

infinitely many

question

Solve for n. n + 1 = 4(n - 8)

answer

n=11

question

Karissa begins to solve the equation 1/2(x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below. When she subtracts 4 from both sides, x = -x results. What is the value of ?

answer

question

How many solutions exist for the given equation?

answer

one

question

Which equation can be used to represent "three minus the difference of a number and one equals one-half of the difference of three times the same number and four"?

answer

3 - (n - 1) =1/2 (3n - 4)

question

How many solutions exist for the given equation? 1/2(x + 12) = 4x - 1

answer

one

question

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?

answer

4

question

How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2

answer

infinitely many

question

Solve for n. n + 1 = 4(n - 8)

answer

n=11

question

Karissa begins to solve the equation 1/2(x - 14) + 11 = 1/2x - (x - 4). Her work is correct and is shown below.

answer

question

Two cars that are 150 miles apart start driving toward each other on parallel roads. The average speed of the first car is 60 miles per hour. The average speed of the second car is 55 miles per hour. Which equation can be used to determine t, the time it takes for the two cars to pass each other?

answer

60t + 55t = 150

question

Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 minutes, while it would take Simon 30 minutes to do the job working alone. If Sophie and Simon work together to peel the potatoes, how long will it take them?

answer

18 minutes

question

Craig ran the first part of a race with an average speed of 8 miles per hour and biked the second part of a race with an average speed of 20 miles per hour. The entire two-part, 15-mile race took him 1.125 hours to complete. Which table correctly represents his rates, times, and distances for each part of the race?

answer

Check notebook. RUN/BIKE graph

question

It takes 5 minutes to fill the sink using only the cold water. If both the hot water and the cold water are turned on, it takes 2 minutes to fill the sink. Which is the correct table that can be used to determine x, the time in minutes it takes to fill the sink using only the hot water?

answer

Check notebook. HOT/COLD graph.

question

If Judy completes a puzzle by herself, it takes her 3 hours. Working with Sal, it only takes them 2 hours.

answer

1/3

question

Lea and Marie are washing all the windows in their house. It would take Lea 80 minutes to wash the windows by herself, and it would take Marie 60 minutes to wash them by herself. Lea creates a table so she can find out how long it will take to wash the windows if they work together. What is the missing value in the table that represents the rate for Marie?

answer

1/60

question

Working together, Katherine and Marina can sand a large cabinet in 2 hours. It would take Katherine 10 hours to do the job alone. What is the value of r, the part of the job that Marina can complete in 1 hour?

answer

0.4

question

It would take Marco 6 hours to paint a fence by himself. It would take Jaylyn 5 hours to paint the same fence by herself. Marco is creating this table to help him determine how long it would take them to paint the fence together. Which heading should be written above the first column of numbers?

answer

Rate (part/hour)

question

The slope-intercept form of a linear equation is y = mx + b, where x and y are coordinates of an ordered pair, m is the slope of the line, and b is where the line crosses the y-axis. Which is an equivalent equation solved for the slope, m?

answer

m=y-b/x

question

The formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference. The equation solved for r is r = .

answer

r = 8

question

In physics class, Carrie learns that a force, F, is equal to the mass of an object, m, times its acceleration, a. She writes the equation as F = ma, then realizes that each of her homework problems asks her to solve for acceleration. She rewrites the formula as f/m = a. Using this formula, what is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms? Express your answer to the nearest tenth.

answer

2.2 m/s^2

question

Solve for a. 7a - 2b = 5a + b

answer

a=3/2b

question

Marta is solving the equation S = 2Πrh + 2Πr2 for h. Which should be the result?

answer

S/2(pi)r - r = h

question

The goals against average (A) for a professional hockey. hich is an equivalent equation solved for g?

answer

At/60=g

question

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is

answer

C = K - 273.15

question

Solve for k. 8k + 2m = 3m + k

answer

k = m/7

question

Solve the equation for a. K = 4a + 9ab

answer

a=k/4+9b

question

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h?

answer

h = (p/0.7- b)÷ r

question

Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?

answer

Notes. Line graph Name3

question

Step 1: Subtract 3 from both sides of the inequality. Step 2: __________ Step 3: Divide both sides of the inequality by the coefficient of x.What is the missing step in solving the inequality 5 - 8x < 2x + 3?

answer

Add 8x to both sides of the inequality.

question

What value of x is in the solution set of 8x - 6 > 12 + 2x?

answer

5

question

Which is a correct first step in solving the inequality -4(2x - 1) > 5 - 3x?

answer

Distribute -4 to get -8x + 4 > 5 - 3x.

question

What value of x is in the solution set of 4x - 12 ≤ 16 + 8x?

answer

-7

question

What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?

answer

-1

question

Which number line represents the solution set for the inequality -1/2x ≥ 4?

answer

Notes Line graph Name 8

question

What value of x is in the solution set of 3(x - 4) ≥ 5x + 2?

answer

-10

question

Solve the inequality. 2(4x - 3) ≥ -3(3x) + 5x?

answer

x ≥ 0.5

question

The solution is n = -2 verified as a solution to the equation 1.4n + 2 = 2n + 3.2. What is the last line of the justification?

answer

-0.8 = -0.8

question

Solve the equation. 2x − 3 + 4x = 21

answer

x=4

question

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

answer

2v + 4 = 8

question

How many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12)

answer

infinitely many

question

Which number line represents the solution set for the inequality 3x < -9?

answer

Notes line graph name -3

question

What interval includes all possible values of x, where -3(6 - 2x) ≥ 4x + 12?

answer

[15, ∞)

question

Sara wants to find the input value that produces the same output for the functions represented by the tables. What is the input value that produces the same output value in both charts?

answer

2

question

What value of x is in the solution set of -2(3x + 2) > -8x + 6?

answer

6

question

The sum of the interior angles, s, in an n-sided polygon can be determined using the formula s = 180(n - 2), where n is the number of sides. Benita solves this equation for n and writes the equivalent equation n = + 2. Using this formula, how many sides does a polygon have if the sum of the interior angles is 1,260°?

answer

9 sides

question

Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number"?

answer

6 + 2(x + 4) = 1/2(3 - x)

question

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p - 10.1 = 6.5p - 4 - 0.01p? Check all that apply.

answer

230p - 1010 = 650p - 400 - p

question

What is the solution to -4(8 - 3x) ≥ 6x - 8?

answer

x ≥ 4

question

Nikita ran a 5-kilometer race in 39 minutes (0.65 of an hour) without training beforehand. In the first part of the race, her average speed was 8.75 kilometers per hour. For the second part of the race, she started to get tired, so her average speed dropped to 6 kilometers per hour. Which expression represents Nikita's distance for the second part of the race?

answer

6(0.65 - t)

question

Bianca wrote the steps for her solution to the equation 2.3 + 8(1.3x - 4.75) = 629.9. She left out the description for the last step.

answer

Divide both sides of the equation by 10.4.

question

Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

answer

1/4(x) = (30 + 60)

question

Which graph shows the equation c = 10+ 3t, where c is the total cost of going to the carnival and t is the number of $3 tickets purchased?

answer

graph in notes Name $3 ti ckets

question

Each day that a library book is kept past its due date, a $0.30 fee is charged at midnight. Which ordered pair is a viable solution if x represents the number of days that a library book is late and y represents the total fee?

answer

(8, 2.40)

question

Otto used 6 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?

answer

y=x+6; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 6.

question

Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. Let y represent the length of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine the total length of all of the yarn that she ends up cutting, t? Is the graph of the equation continuous or discrete?

answer

t=4y+7.75; continuous

question

The graph shows the relationship between the total cost and the number of gift cards that Raj bought for raffle prizes.

answer

$100

question

What is the lowest value of the range of the function shown on the graph?

answer

See graph 3,-2 in notes -2

question

What is the range of the given function? {(-2, 0), (-4, -3), (2, -9), (0, 5), (-5, 7)}

answer

{y | y = -9, -3, 0, 5, 7}

question

What is the range of the given function?

answer

{y | y = -7, -1, 0, 9}

question

The table shows ordered pairs of the function y = 8 - 2x. When x = 8, the value of y is

answer

Graph y=8-2x

question

What is the domain of the function shown in the mapping?

answer

{x | x = -5, -3, 1, 2, 6} Input output graph -3,4

question

What is the domain of the function on the graph?

answer

all real numbers greater than or equal to -3

question

Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. What is the range of the function?

answer

all real numbers greater than or equal to 11

question

Which ordered pair could be removed from the graph to create a set of ordered pairs that represents a function?

answer

(1, 3)

question

The function h(t) = -16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot. What does h(3.2) represent?

answer

the height of the rock 3.2 seconds after it is propelled

question

The table represents a function. Which value is an output of the function?

answer

-2 function table in notes

question

Which is true regarding the graphed function f(x)?

answer

f(5)=-1

question

The table represents a function. What is f(5)?

answer

-8

question

The function f(x) is given by the set of ordered pairs. {(1,0), (-10,2), (0,6), (3,17), (-2,-1)} Which equation is true?

answer

f(0)=6

question

The function V(r)=4/3(pi)r^3 can be used to find the volume of air inside a basketball given its radius. What does V(r) represent?

answer

the volume of the basketball when the radius is r

question

The table represents a function. What is f(-2)?

answer

1

question

If point (4, 5) is on the graph of a function, which equation must be true?

answer

f(4)=5

question

Hiroto's texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia's plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?

answer

Both plans cost the same when 50 texts are sent.

question

Which statement is true regarding the functions on the graph?

answer

f(-3) = g(-3)

question

What is f(3)?

answer

9

question

Which statement is true regarding the graphed functions?

answer

f(2) = 0 and g(-2) = 0 View graph EF in notes

question

Which represents where f(x) = g(x)?

answer

f(2) = g(2) and f(0) = g(0) GRAPH EF2

question

When f(x) = -3, what is x?

answer

-1

question

Which represents where f(x) = g(x)?

answer

f(-4) = g(-4) and f(0) = g(0) graph EF3

question

If f(x) = 6x - 4, what is f(x) when x = 8?

answer

44

question

Which statement is true about the end behavior of the graphed function?

answer

As the x-values go to positive infinity, the function's values go to negative infinity.

question

Which statement is true about the graphed function?

answer

F(x) > 0 over the interval (-∞, -4)

question

What are the x-intercepts of the graphed function?

answer

(-3, 0) and (1,0)

question

Which statement is true about the end behavior of the graphed function?

answer

As the x-values go to positive infinity, the function's values go to positive infinity.

question

Which is a y-intercept of the graphed function?

answer

(0, -9) Graph 1 in analyzing graphs

question

Which interval for the graphed function contains the local maximum?

answer

[0, 2]

question

Which lists all of the y-intercepts of the graphed function

answer

(0, -3)

question

Which lists all of the x-intercepts of the graphed function?

answer

(1, 0), (2, 0), and (-3, 0)

question

Which statement is true about the graphed function?

answer

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

question

Which is a valid prediction about the continuous function f(x)?

answer

f(x) ≥ 0 over the interval [5, ∞).

question

Which is a valid prediction about the continuous function f(x)?

answer

f(x) ≥ 0 over the interval [-1, 1].

question

Which lists all of the y-intercepts of the continuous function in the table?

answer

(0, 0)

question

Which is a possible turning point for the continuous function f(x)?

answer

(0, -2)

question

Which is an x-intercept of the continuous function in the table?

answer

(3, 0)

question

Based on the table, which best predicts the end behavior of the graph of f(x)?

answer

As x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.

question

Which is an x-intercept of the continuous function in the table?

answer

(-1, 0)

question

What are all of the x-intercepts of the continuous function in the table?

answer

(-4, 0), (4, 0)

question

Adita has two options for how to invest $1,000. Plan A: Put the $1,000 in an account that pays $100 per year. Plan B: Put the $1,000 in an account that pays 5 percent interest per year. Which statement is true?

answer

Plan A will be worth more than plan B after two years.

question

What type of graph is shown, and what is the growth factor?

answer

exponential function; growth factor of 4

question

Which graph represents an exponential function?

answer

LOOK IN NOTES at linear growth #1

question

Which table represents a linear function?

answer

linear growth #2

question

What kind of growth model (pattern) is shown in the table?

answer

exponential 3

question

What is the missing number in the table?

answer

1,296 #4

question

Which of the following best describes how the y values are changing over each interval?

answer

They are being multiplied by 2 each time.

question

Over which interval are the exponential and linear function approximately the same?

answer

from 0.75 to 1.0

question

The table below represents a function. Which statement would best describe the graph of the function?

answer

The graph starts flat but curves steeply upward.

question

Sabrina is tracking the growth rates of a colony of ants and of a bee hive. From her research, she has developed a function to represent the population growth of each type of insect, where y represents the population and x represents the number of weeks since Sabrina began her research. Which insect population is growing at a faster rate?

answer

The ant colony is growing at a faster rate. It will multiply by 3.8 each week while the bee hive will add 3.8 each week

question

Which of the following describes the function shown in the table below?

answer

Comparing notes 1 exponential, there is a constant rate of decay or decrease

question

Which number is missing in the table of values below?

answer

216 g2

question

3 4 5 6 8 9 10 Which statement best describes the growth rates of the functions below?

answer

The exponential function grows faster than the quadratic function over two intervals; 2<x<4.

question

Which rule can be used to describe the growth of the y-values of the function mc018-1.jpg over each interval from mc018-2.jpg to mc018-3.jpg?

answer

multiply by 12

question

A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval mc016-1.jpg?

answer

The exponential function decays at three-fourths the rate of the quadratic function.

question

Which of the following describes the growth rate of the exponential function in the graph below?

answer

For each x increase of 1, the y increases by a common factor of 3.

question

What is f(0)?

answer

unit review 1 -6 only

question

Lara made the table below of the predicted values for h(t), the height, in meters, of a penny t seconds after it is dropped off of the back of the bleachers. To the nearest tenth of a second, how much time would it take the penny to hit the ground?

answer

0.6 seconds

question

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?

answer

the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

question

Consider the function represented by the graph. What is the domain of this function?

answer

{x| x >0}

question

A ball is thrown straight up into the air. The height, in feet, h(t), of the ball collected over t seconds is shown in the table. Which statement is true?

answer

The maximum height of the ball was 2.5 seconds after it was thrown.

question

Which ordered pair could be removed so that the set of ordered pairs is a function?

answer

(4, -2)

question

According to the table, which ordered pair is a local minimum of the function, f(x)?

answer

(0, 9)

question

The graph represents a functional relationship. Which value is an input of the function?

answer

4

question

The graph shows the relationship between the total cost and the number of erasers bought at the student store. Which statement is true?

answer

Seven erasers cost $3.50.

question

Which statement is true regarding the functions on the graph?

answer

f(2) = g(2)

question

Which could be the entire interval over which the function, f(x), is negative?

answer

(-∞, -6)

question

Which interval for the graphed function contains the local minimum?

answer

g2 [-3, -1]

question

Analyze the graph of the function f(x) to complete the statement.

answer

F(x) < 0 over the intervals (-∞, -3) and (-1.1,0.9)

question

Which ordered pair can be removed so that the resulting graph represents a function?

answer

(1,3)

question

Which graph represents a function?

answer

g3

question

The table below shows the amount that must be repaid, y, when x dollars are borrowed.

answer

y=5/4x+10

question

The table below shows the predicted number of words Janae can type, y, in x minutes. Which describes the pattern in the table?

answer

Janae types 30 words each minute.

question

There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?

answer

TAbles graph 1

question

Which table of values corresponds to the graph below?

answer

graph 2

question

The table below shows the relationship between the approximate number of hours and the corresponding number of days on Saturn.

answer

658 2/3

question

Four representations of the same data are shown below. Which two representations are considered to be only partial representations?

answer

the verbal description and the graph

question

Which table of values corresponds to the graph below?

answer

g3

question

Some states pay $0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states?

answer

this is a graph- points are 1,20 2,40, 3,60

question

1 2 3 4 7 8 10 The graph below represents the number of books Jaleel has read over the past x weeks. Which equation represents the graph?

answer

y = 3x

question

Anderson is a plumber and is paid a fixed amount just to make a house visit. The remainder of his fee, y, is determined by the number of hours that he works, x, as shown below. Which equation represents the graph?

answer

y = 10x + 50

question

Which table represents a linear function?

answer

Introduction g1

question

The graph shows the amount of money Miguel earns after working x hours. What is the ratio of the change in y-values to the change in x-values for this function?

answer

13:1

question

The table shows the number of grapes eaten over several minutes. What is the rate of change for the function on the table?

answer

15 grapes eaten per minute

question

Which functions have an additive rate of change of 3? Check all that apply.

answer

4,6 is a point

question

The table shows the distance traveled over time while traveling at a constant speed. What is the ratio of the change in y-values to the change in x-values?

answer

1,200:1

question

Which table represents a linear function?

answer

g2

question

A data set contains an independent and dependent variable. Which must be true of the data set if a linear function can be used to represent the data?

answer

The set must have a constant additive rate of change.

question

The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?

answer

$1.50

question

The table below shows measurements (in inches) from cubes with different side lengths. Which pairs of variables have a linear relationship? Check all that apply.

answer

side length and perimeter of 1 face perimeter of 1 face and area of 1 face side length and volume

question

The graph shows the increase in temperature over time in an oven. What is the change in the y-values and x-values on the graph?

answer

The change in the y-values is 40 and the change in the x-values is 1.

question

Which relationship has a zero slope?

answer

g1 slope of a line

question

At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temperature should remain constant over time. What word describes the slope of a line showing the temperature of the freezer as a function of time in hours when the freezer is working properly?

answer

The slope of the line will be zero

question

The graph of a linear function is shown. Which word describes the slope of the line?

answer

negative

question

Which graph has a slope of 4/5?

answer

g2

question

The graph represents the balance on Harrison's car loan in the months since purchasing the car. Which statement describes the slope of the line?

answer

Harrison makes a monthly payment of $250.

question

The graph shows the relationship between the volume of a rectangular prism and the volume of a square pyramid with an identical base and height. What is the slope of the line?

answer

2

question

The graph of a linear function is shown. Which word describes the slope of the line?

answer

zero g3

question

The table represents a linear function. What is the slope of the function?

answer

-6

question

Aaron tracks the time it takes him to mow lawns by writing coordinate points relating x, the time in hours it takes to mow a lawn, and y, the size of the lawn in acres. Two of his points are (3, 1.5) and (5, 2.5). Which statement describes the slope of the line through these two points?

answer

Aaron's rate for mowing lawns is 0.5 acres per hour.

question

The sequence below represents Marisa's fine at the library for each day that she has an overdue book: $0.50, $0.65, $0.80, $0.95, $1.10, ... Which equation represents Marisa's library fine as a function of a book that is n days overdue?

answer

f(n) = 0.15n + 0.35

question

What is the constant of variation, k, of the direct variation, y = kx, through (-3, 2)?

answer

k = -2/3

question

Three points of a function are graphed. Which statement describes the function through the points?

answer

The function is linear but is not a direct variation function.

question

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

answer

y = 7x

question

The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table. The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?

answer

9.8 m/s^2

question

Which graph represents a function with direct variation?

answer

g4

question

The table represents a bicycle rental cost in dollars as a function of time in hours. Which explains whether or not the function represents a direct variation?

answer

This function represents a direct variation because it passes through the origin and has a constant rate of change of $5 per hour.

question

A catering company uses different functions to estimate the itemized costs for a party. The table below represents the included tip for wait staff as a function of the number of guests served. If the tip varies directly with the number of guests, which equation represents the relationship between the tip, t, and the number of guests, g?

answer

t = 1.8g

question

The pattern of numbers below is an arithmetic sequence: 14, 24, 34, 44, 54, ... Which statement describes the recursive function used to generate the sequence?

answer

The common difference is 10, so the function is f(n + 1) = f(n) + 10 where f(1) = 14.

question

What is the common difference in the following arithmetic sequence? 7, 3, -1, -5, ....

answer

-4

question

Which of the following is true about the sequence graphed below?

answer

The sequence is arithmetic because the terms have a common difference.

question

Ms. Clark earned $29,600 in her third year as a banker and $32,600 in her seventh year. How much did she make in her tenth year? Assume that her yearly salaries form an arithmetic sequence.

answer

$34,850

question

What is the common difference of the arithmetic sequence graphed below?

answer

2

question

Which of the following is an arithmetic sequence?

answer

1/2,2,7/2,5,...

question

Which of the following is true regarding the sequence graphed below?

answer

The sequence is not arithmetic because the terms do not have a common difference.

question

What is the next term in the sequence 58, 47, 36, 25, ...?

answer

14

question

A karate studio charges $35 for the first course and $22.50 for each course after that, even if the student leaves the course early. Cena paid $170 for her son to take courses. How many courses did he take?

answer

7 courses

question

What is the explicit rule for the arithmetic sequence shown in the graph?

answer

an-9.5+2(n-1)

question

What is the common difference in the following arithmetic sequence?

answer

11

question

Which of the following is an arithmetic sequence?

answer

unit review 1

question

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

answer

-2/5

question

The table below shows the amount of money Sarah spends for a craft demonstration. Number of People Attending Cost 5$15 8$18 10$20 15$25 Sarah spends a total of $60. Based on the information in the table, how many people attended the craft demonstration

answer

50

question

The table represents a linear function. What is the slope of the function?

answer

-4 g2 unit review

question

The depth of snow after n hours of a snowstorm is represented by the function f(n + 1) = f(n) + 0.8 where f(0) = 2.5. Which statement describes the sequence of numbers generated by the function?

answer

The depth of snow was 2.5 inches when the storm began, and increased by 0.8 inches each hour.

question

A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?

answer

y=x/3

question

Javier and his study group designed a word problem, equation, table, and graph that were all supposed to represent the same information, as shown below. Which piece of information does not represent the same information as the other three parts?

answer

graph

question

Based on the information in the graph, if David's bill came to $66 after the coupon was applied, how much would his bill have been if he hadn't used the coupon?

answer

$68

question

A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?

answer

The line does not represent a direct variation because it does not go through the origin.

question

Which table represents a linear function?

answer

g3

question

What is the constant of variation, k, of the line y = kx through (3,18) and (5,30)?

answer

6

question

Mrs. Jackson gives the table below to her students. In order for the function to be linear, what must m be and why?

answer

m = 20 because the rate of change is -3.

question

Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?

answer

m = 90 - 6d

question

The table represents the function f(x). Which function of t has the same slope and y-intercept as f(x)?

answer

f(t) =2/3 t + 4

question

What are the slope and y-intercept of the linear function graphed to the left?

answer

slope: -1/2; y-intercept: 1

question

A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could represent the leaf's height in feet as a function of time, in seconds, after leaving the branch?

answer

graph with point 8,12

question

A store offers packing and mailing services to customers. This table is given to customers to help them estimate the cost of shipping a box based on its weight in pounds, and a flat rate of $5 for packing. Which equation represents the shipping cost as a function of x, the weight in pounds?

answer

f(x) = 2.25x + 5

question

What is the slope of the line represented by the equation y = -1/2-x +1/4 ?

answer

-1/2

question

Which equation represents the graphed function?

answer

y=-1/3x+3

question

Which equation represents the graphed function?

answer

y=-2x+3

question

Which equation shows the point-slope form of the line that passes through (3, 2) and has a slope of 1/3

answer

y - 2 = 1/3(x - 3)

question

What is the slope of the line?

answer

-1/2

question

Which equation represents a line that passes through (5, 1) and has a slope of 1/2/?

answer

y-1=1/2(x-5)

question

Which steps should be used to graph the equation y - 4 = (x + 2)?

answer

1. Plot the point (-2,4). 2. From that point, count left 3 units and down 1 unit and plot a second point. 3. Draw a line through the two points.

question

Which linear function represents the line given by the point-slope equation y + 1 = -3(x - 5)?

answer

f(x) = -3x + 14

question

Alejandra correctly wrote the equation y - 3 =1/5 (x - 10) to represent a line that her teacher sketched. The teacher then changed the line so it had a slope of 2, but still went through the same point. Which equation should Alejandra write to represent the new line?

answer

y - 3 = 2(x - 10)

question

Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4 ?

answer

y-1/3+3/4(x-4)

question

What is the slope of the line?

answer

5/2 points are 0,-1 and 2,4

question

Harita must memorize 90 measures of music for her cello solo at a concert. She plans on memorizing 18 new measures for every 3 days of practice. Which equation can be used to determine m, the number of measures Harita still needs to memorize, as a function of d, the number of days of practice since she began learning the piece?

answer

m=90-6d

question

The table represents the function f(x). Which function of t has the same slope and y-intercept as f(x)?

answer

f(t) =2/3 t + 4

question

What are the slope and y-intercept of the linear function graphed to the left?

answer

slope:-1/2 ; y-intercept: 1

question

Which shows a graph of a linear equation in standard form Ax + By = C, where A = 0, B is positive, and C is negative?

answer

g1

question

Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?

answer

y - 1 = 3x

question

The graph of the equation x - 2y = 5 has an x-intercept of 5 and a slope of 1/2 . Which shows the graph of this equation?

answer

:Line passes through longitude of 5 and lat of in between -2 & -3

question

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

answer

-9

question

The table represents a linear equation. Which equation correctly uses point (-2, -6) to write the equation of this line in point-slope form?

answer

y + 6 =2/5 (x + 2)

question

A line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation y = (x - 2). Which equations also represent this line? Check all that apply.

answer

y = -5/3x+10/3 3y = -5x + 10 5x + 3y = 10

question

Which linear function represents the line given by the point-slope equation y - 8 = (x - 4)?

answer

f(x) =1/2 x + 4

question

Which is true of the standard form of the equation of the line graphed?

answer

The value of A can only be 1, the value of C can only be -3, and the value of B is 0.

question

How does the slope of g(x) compare to the slope of f(x)?

answer

The slope of g(x) is less than the slope of f(x).

question

What is the equation of the graphed line written in standard form?

answer

x - 4y = 4

question

What is the equation of the line that is perpendicular to the line y = 6 and passes through the point (-4, -3)?

answer

x = -4

question

What is the equation of the line in slope-intercept form that is perpendicular to the line y = 3/4x - 2 and passes through the point (-12, 10)?

answer

y = -4/3x - 6

question

Which equation represents the graphed function?

answer

y=1/4x-2

question

Timmy writes the equation f(x) = x - 1. He then doubles both of the terms on the right side to create the equation g(x) = x - 2. How does the graph of g(x) compare to the graph of f(x)?

answer

The line of g(x) is steeper and has a lower y-intercept.

question

Raphael graphed the functions g(x) = x + 2 and f(x) = x - 1. How many units below the y-intercept of g(x) is the y-intercept of f(x)? The y-intercept of f(x) is

answer

3

question

MOST RECENT TEST STARTS ON 245

answer

question

A pattern of rectangles is formed by decreasing the length and increasing the width, each by the same amount. The relationship between x, the amount of increase, and A, the area of the rectangle represented by the increase, is quadratic. Which graph could represent the area of each rectangle in terms of the change in the length and width?

answer

Points located on 0.40 1,45 2,47 8,25

question

Daniel is on an airplane flying to a destination 825 miles away. After one hour, the pilot announces that the plane is 495 miles away from its destination airport. In another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles. Which equation represents the remaining distance, in miles, to the destination in terms of t, the time, in hours, since leaving the airport?

answer

d = 825 - 330t

question

The graph shows the population of a bacteria in an experiment, measured every hour. Which function represents the population of the bacteria after t hours?

answer

f(t) = 10(1.4)t

question

Alicia bought a notebook and several erasers at the student store. The graph shows the relationship between the total cost of her items and the number of erasers she purchased. What is the cost of each eraser?

answer

$1.50

question

The half life of a certain substance is about 4 hours. The graph shows the decay of a 50 gram sample of the substance that is measured every hour for 9 hours. Which function can be used to determine the approximate number of grams of the sample remaining after t hours?

answer

y = 50(0.85)x

question

Sophia plots points on a graph to represent the shape of a concave lens. Which type of function should Sophia use to model the shape of the lens?

answer

quadratic

question

If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?

answer

Ppoints 0,15 1,25

question

Teddy is preparing to sell some wooden blocks at a garage sale. Before pricing individual bags of blocks, he decides to determine the approximate number of blocks per pound by researching the weights of different sets of blocks. The graph shows his data. About how many blocks are there per pound? Round to the nearest block.

answer

20 blocks

question

Amanda is studying relationships between the values and ages of different items. She decides to ask teachers at her school to estimate the values and ages of their cars. She will exclude any antique cars and knows that the value of a car depreciates over time. Which correlation is expected between the age and value of a car?

answer

negative

question

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. According to the line of best fit, about how many minutes will it take for the temperature to reach 100°C, the boiling point of water?

answer

5

question

Mr. Palmer does an experiment to investigate the effects of distractions on studying and learning. He gives each participant a line with 10 words to memorize in 5 minutes. Some of the participants are interrupted during the 5 minutes with text messages from friends. The graph shows the number of words remembered after 5 minutes and the number of text messages sent to the participants as distractions. According to the line of best fit, about how many words would a person remember if he or she is distracted by 7 text messages?

answer

5 words

question

The table shows the ages and weights of babies at a hospital. What is the correlation between age and weight as shown in the table?

answer

positive

question

Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data. According to the line of best fit, about how many times would the coin land heads up in 100 flips?

answer

53

question

Latitude and longitude describe locations on the Earth with respect to the equator and prime meridian. The table shows the latitude and daily high temperatures on the first day of spring for different locations with the same longitude. Which statement describes the slope of the line of best fit for the data?

answer

The temperature decreases by about 1.7° for each 1 degree increase north in latitude.

question

Which table shows a negative correlation?

answer

graph 1 in most recent

question

Which is most likely the correlation coefficient for the set of data shown?

answer

0.19

question

Which r-value represents the strongest negative correlation?

answer

-0.7

question

Which is most likely the correlation coefficient for the set of data shown?

answer

-0.91

question

Which r-value represents the weakest correlation?

answer

0.11

question

Which relationships would most likely be causal? Check all that apply.

answer

a positive correlation between the number of homework assignments completed and the grade on the exam a positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by hikers

question

What is the correlation coefficient for the data shown in the table?

answer

R=1

question

Which r-value represents the most moderate correlation?

answer

0.56

question

Which relationships would most likely be causal? Check all that apply.

answer

a negative correlation between the temperature and the amount of snow still on the ground a negative correlation between the number of digital photos uploaded to a website and the amount of storage space that is left

question

The table shows the time a patient spends at the dentist and the amount of the bill. What is the correlation coefficient for the data in the table?

answer

0.93

question

The table shows the relationship between time spent running and distance traveled. Which type of model best describes the relationship?

answer

linear, because the r value for the linear model is closest to 1

question

Janna is making a prediction of the frequency of a key that is 12 keys from middle C. Which best describes her prediction?

answer

extrapolation, because a key that is 12 keys from middle C is outside the data set

question

Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments. She calculates two regression models. Which is true?

answer

The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.

question

The table compares x, the number of minutes of television Sam watched each day, to y, the number of minutes she spent exercising. The function y = -0.78x + 95 models the data in the table. Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?

answer

72 minutes

question

The quadratic regression graphed on the coordinate grid represents the height of a road surface x meters from the center of the road. What does the graph of the regression model show?

answer

The height of the surface decreases from the center out to the sides of the road.

question

Marta's mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online. About how many people had viewed the video once it had been online for 20 days?

answer

6,271

question

The table shows the wavelength of the sound produced by keys on a piano x keys away from the A above middle C. Using the exponential regression model, which is the best prediction of the wavelength of the key that is 8 above the A above middle C?

answer

49.44

question

The table shows the population of a small town over time. The function P = 10,550(1.1)x models the population x years after the year 2000. For which year would this model most likely be sufficient to make a prediction of the population?

answer

2005

question

The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?

answer

According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

question

The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants. According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5?

answer

13

question

The table shows the height of a candle as it is continuously burned. Which statement describes the candle?

answer

The candle starts at a height of 25 centimeters and burns at a rate of 2.5 centimeters per hour.

question

Which is most likely the correlation coefficient for the set of data shown?

answer

-0.21

question

A line of best fit is drawn for the set of points shown on the graph. Which point is an approximate extrapolation for x = 30 from the line of best fit?

answer

(30, 38)

question

The table shows the value of a savings bond that doubles in value after 5 years. Which statement describes the bond?

answer

The bond had an original value of $50 and grows at a rate of 15%.

question

The graph shows the exponential regression model for data representing a rabbit population after x years. Which is true of the regression model?

answer

The graph of the regression model is limited to whole-number values for y

question

The data in the table represents the predicted price of a gallon of milk, y, for number of years, x. Which form of an equation was used to model the price of a gallon of milk?

answer

y = abx

question

What function models the data shown on the graph?

answer

f(x) = -2(x - 5)(x - 1)

question

The equation for the line of best fit is f(x) ≈ 1.8x − 5.4 for the set of values in the table. Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30?

answer

20

question

Which best describes the strength of the model with an r-value of -0.93?

answer

a strong negative correlation

question

The table shows the average number of hours of daylight per day for the last four months of the year. What is the correlation coefficient for the data in the table?

answer

-0.993

question

The table shows the shoe sizes of women of different ages. Which best describes the strength of the model?

answer

a weak positive correlation

question

The table shows the approximate height of an object x seconds after the object was dropped. The function h(x) = -16x2 + 100 models the data in the table. For which value of x would this model make the least sense to use?

answer

-2.75

question

The table shows a company's profit based on the number of pounds of food produced. Using the quadratic regression model, which is the best estimate of the profit when 350 pounds of food are produced?

answer

$5,300

question

Consider the function represented by the graph. What is the domain of this function?

answer

{x| x >0}

question

Using the equation for the line of best fit, what is a good approximation for x when f(x) = 30?

answer

20

question

On his first day of school, Kareem found the high temperature in degrees Fahrenheit to be 76.1°. He plans to use the function C(f)=5/9(f-32) to convert this temperature from degrees Fahrenheit to degrees Celsius. What does C(76.1) represent?

answer

the temperature of 76.1 degrees Fahrenheit converted to degrees Celsius

question

What is the equation of the line in slope-intercept form that is perpendicular to the line y = x - 2 and passes through the point (-12, 10)?

answer

y = -4/3x - 6

question

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?

answer

-9

question

Tracie rides the bus home from school each day. The graph represents her distance from home relative to the number of minutes since the bus left the school. What does the slope of the graph mean?

answer

Tracie's bus travels towards her home at an average speed of 1/2 mile per minute.

question

The graph represents a functional relationship. Which value is an input of the function?

answer

4

question

Which explains how the table can be used to predict the cost of any number of students attending the game?

answer

The table is a partial representation of a larger data set. It can be used to generate an equation that is a complete representation of the data set.

question

Which is most likely the correlation coefficient for the set of data shown?

answer

-0.21

question

For each additional slice of pizza that is purchased, by how much does the total cost of lunch increase?

answer

$2.50

question

Which equation can be used to find h, the number of hours Lindsay worked last week?

answer

1/15(10h+60)=1/10(10h)

question

Which graph represents a function?

answer

Sideways porabla

question

To graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?

answer

-2/5

question

Use properties to rewrite the given equation. Which equations have the same solution as 2.3p - 10.1 = 6.5p - 4 - 0.01p? Check all that apply.

answer

2.3p - 10.1 = 6.49p - 4 230p - 1010 = 650p - 400 - p

question

What is the value of r, the part of the tile that Hector could install in 1 hour?

answer

1/18

question

According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5?

answer

13

question

Which form of an equation was used to model the price of a gallon of milk?

answer

y=ab^x

question

To the nearest tenth of a second, how much time would it take the penny to hit the ground?

answer

0.6

question

Line QR goes through points Q(0, 1) and R(2, 7). Which equation represents line QR?

answer

y - 1 = 3x

question

How much money will she have if she doesn't buy any packs of baseball cards?

answer

$20

question

A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?

answer

According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground

question

The explicit rule for an arithmetic sequence is mc023-1.jpg What is the value of the 47th term? Round to the nearest tenth, if necessary.

answer

-55.7

question

How many solutions exist for the given equation? 3(x + 10) + 6 = 3(x + 12)

answer

infinitely many

question

F(x) < 0 over the intervals (-∞, -3) and

answer

(-1.1, 0.9)

question

Hiroshi spends 30 minutes on history homework, 60 minutes on English homework, and x minutes on math homework. One fourth of his total homework time is spent on math. Which equation can be used to find the amount of time Hiroshi spends on his math homework?

answer

1/4(x) = x(30 + 60)