Question

for questions 1 - 3, label each image as either a translation, a reflection, a rotation of the original image. the perimeter of the rectangle at right is 96 sq. cm. write an equation and solve for x.

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=3x - 4$ and $w=x + 5$, and $P = 96$. So the equation is $2((3x - 4)+(x + 5))=96$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $(3x - 4)+(x + 5)=3x - 4+x + 5=4x+1$. Then the equation becomes $2(4x + 1)=96$. Distribute the 2: $8x+2 = 96$.

Step3: Solve for x

Subtract 2 from both sides of the equation: $8x+2-2=96 - 2$, which gives $8x=94$. Then divide both sides by 8: $x=\frac{94}{8}=\frac{47}{4}=11.75$.

Answer:

$x = 11.75$