Question

1. mathematical connections write an expression for the length of the segment.

a. $overline{ac}$
a $x + 2$ b $7x - 3$ c
b. $overline{qr}$
p $8y + 5$ q $13y + 25$ r

Explanation:

Step1: Use segment - addition postulate for $\overline{AC}$

The length of $\overline{AC}$ is the sum of the lengths of $\overline{AB}$ and $\overline{BC}$. So, $AC=(x + 2)+(7x-3)$.

Step2: Simplify the expression for $AC$

Combine like - terms: $AC=(x+7x)+(2 - 3)=8x-1$.

Step3: Use segment - addition postulate for $\overline{QR}$

The length of $\overline{PR}$ is $13y + 25$ and the length of $\overline{PQ}$ is $8y + 5$. Then $QR=PR - PQ$. So, $QR=(13y + 25)-(8y + 5)$.

Step4: Simplify the expression for $QR$

Distribute the negative sign: $QR=13y+25 - 8y - 5$. Combine like - terms: $QR=(13y-8y)+(25 - 5)=5y + 20$.

Answer:

a. $8x - 1$
b. $5y + 20$