Question

solve for $x$. the polygons in each pair11)scale factor from a to b = $9:10$13)scale factor from a to b = $5:9$15)scale factor from a to b = $2:3$

Explanation:

Problem 11)

Step1: Set up proportion

$\frac{9}{10} = \frac{72}{6x-22}$

Step2: Cross-multiply to solve

$9(6x-22) = 10 \times 72$
$54x - 198 = 720$

Step3: Isolate x term

$54x = 720 + 198$
$54x = 918$

Step4: Solve for x

$x = \frac{918}{54}$

Problem 13)

Step1: Set up proportion

$\frac{5}{9} = \frac{60}{6x+6}$

Step2: Cross-multiply to solve

$5(6x+6) = 9 \times 60$
$30x + 30 = 540$

Step3: Isolate x term

$30x = 540 - 30$
$30x = 510$

Step4: Solve for x

$x = \frac{510}{30}$

Problem 15)

Step1: Set up proportion

$\frac{2}{3} = \frac{3x-39}{27}$

Step2: Cross-multiply to solve

$2 \times 27 = 3(3x-39)$
$54 = 9x - 117$

Step3: Isolate x term

$9x = 54 + 117$
$9x = 171$

Step4: Solve for x

$x = \frac{171}{9}$

Answer:

1. $x=17$
2. $x=17$
3. $x=19$