Question

1. if z is the midpoint of rt, what is the value of x?

a. 119
b. 17
c. 4.9
d. 73

1. if z is the midpoint of rt, what is the measure of rz?

a. 119
b. 17
c. 96
d. 73

Explanation:

Step1: Use the midpoint property

Since \(Z\) is the midpoint of \(RT\), then \(RZ = ZT\). So, \(7x-23 = 96\).

Step2: Solve the equation for \(x\)

Add \(23\) to both sides of the equation \(7x-23 = 96\):
\(7x-23 + 23=96 + 23\), which simplifies to \(7x=119\).
Divide both sides by \(7\): \(x=\frac{119}{7}=17\).

Step3: Find the measure of \(RZ\)

Substitute \(x = 17\) into the expression for \(RZ\): \(RZ=7x-23\).
\(RZ=7\times17 - 23\).
First, calculate \(7\times17=119\).
Then, \(119-23 = 96\).

Answer:

1. B. 17
2. C. 96