a. a rotation of 270$text{textdegree}$ counterclockwise is the same as a rotation of 90$text{textdegree}$ clockwise.

An equilateral triangle has three sides with equal lengths:

$$
4x-3=2x+11
$$

Group like terms:

$$
4x-2x=11+3
$$

Simplify:

$$
2x=14
$$

Divide both sides of the equation by 2:

$$
x=7
$$

The perimeter is the sum of all sides:

$$
3(4x-3)=3(4(7)-3)=3(28-3)=3(25)=75
$$

$$
x=7
$$

Perimeter: 75

a. Correspoding angles:

$$
x+15=102
$$

Subtract 15 from both sides of the equation:

$$
x=87
$$

b. Vertical angles:

$$
x+21=7x-3
$$

Group like terms:

$$
x-7x=-3-21
$$

Simplify:

$$
-6x=-24
$$

Diivde both sides of the equation by $-6$:

$$
x=4
$$

c. Supplementary angles:

$$
3x+8+2x+2=180
$$

Combine like terms:

$$
5x+10=180
$$

Subtract 10 from both sides of the equation:

$$
5x=170
$$

Divide both sides of the equation by 5:

$$
x=34
$$

a. $x=87$

b. $x=4$

c. $x=34$

a. The multiplier is the $n$th root of the new price divided by the original price and $n$ the number of periods

$$
sqrt[3]{dfrac{75 }{250}}=sqrt[3]{dfrac{3}{10}}approx 0.7
$$

An equation for this situation is then:

$$
f(x)=250(0.7)^x
$$

b. The monthly multiplier was about 0.7. The percent of decrease is then 100% decreased by the monthly multiplier:

$$
100%-0.7=100%-70%=30%
$$

a. $f(x)=250(0.7)^x$

b. 0.7; 30%

a. The area of the rectangle is the product of the length and the width and is also equal to the sum of the subareas.
$$
(x+6)(3x-2)=3x^2+18x-2x-12=3x^2+16x-12
$$

b. The area of the rectangle is the product of the length and the width and is also equal to the sum of the subareas.
$$
(2y-7)(6y-4)=12y^2-42y-8y+28=12y^2-50y+28
$$

a. $(x+6)(3x-2)=3x^2+16x-12$

b. $(2y-7)(6y-4)=12y^2-50y+28$

c. See explanation

Let $x$ be the measure of $angle B$, then $3x+5$ is the measure of $angle A$ and $x-20$ is the measure of $angle C$. The sum of all angles in a triangle is 180$text{textdegree}$.

$$
3x+5+x+x-20=180text{textdegree}
$$

Combine like terms:

$$
5x-15=180text{textdegree}
$$

Add 15 to both sides of the equation:

$$
5x=195text{textdegree}
$$

Divide both sides of the equation by 15:

$$
x=39text{textdegree}
$$

Determine the measures of the other angles:

$$
mangle A=3x+5=3(39)+5=122text{textdegree}
$$

$$
mangle C=x-20=39-20=19text{textdegree}
$$

$$
mangle A=122text{textdegree}
$$

$$
mangle B=39text{textdegree}
$$

$$
mangle C=19text{textdegree}
$$