Question

use the diagram and segment addition postulate to set up an equation and find the requested values. sketch your thinking in the box. q 3y + 1 r 6y - 5 s 32 value qs y qr rs

Explanation:

Step1: Apply segment - addition postulate

By the Segment Addition Postulate, $QR + RS=QS$. Given $QR = 3y + 1$, $RS=6y - 5$ and $QS = 32$, we set up the equation $(3y + 1)+(6y - 5)=32$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3y+6y+1 - 5=32$, which simplifies to $9y-4 = 32$.

Step3: Solve for y

Add 4 to both sides of the equation: $9y-4 + 4=32 + 4$, getting $9y=36$. Then divide both sides by 9: $y=\frac{36}{9}=4$.

Step4: Find the length of QR

Substitute $y = 4$ into the expression for $QR$: $QR=3y + 1=3\times4+1=12 + 1=13$.

Step5: Find the length of RS

Substitute $y = 4$ into the expression for $RS$: $RS=6y - 5=6\times4-5=24 - 5=19$.

Answer:

	Value
$y$	4
$QR$	13
$RS$	19