Question

1. what is the length of (overline{az})? use the following inform a is between y and z, (ya = 22), (az = 16x), and (yz) (\bigcirc 9) (\bigcirc 22) (\bigcirc 144) (\bigcirc 188)

Explanation:

Step1: Identify the segment addition postulate

Since \( A \) is between \( Y \) and \( Z \), we use the segment addition postulate: \( YA + AZ = YZ \). Wait, but the problem seems to have a missing part (the length of \( YZ \) or another equation to solve for \( x \)). Wait, maybe there was a typo, but looking at the options, if we assume that maybe \( YZ = YA + AZ \) and perhaps there was a value for \( YZ \) or another relation. Wait, maybe the original problem had \( YZ = 166 \) or something? Wait, no, the options include 144, which is \( 16 \times 9 \). Wait, maybe \( YA + AZ = YZ \), and if we assume that maybe \( YZ = 22 + 16x \), but maybe there was a value for \( YZ \) like \( 166 \)? Wait, no, let's check the options. The option 144 is \( 16 \times 9 \), and 22 + 144 = 166. Maybe \( YZ = 166 \), so \( 22 + 16x = 166 \). Let's solve that.

Step2: Solve for \( x \)

\( 22 + 16x = 166 \)
Subtract 22 from both sides: \( 16x = 166 - 22 = 144 \)
Then \( x = \frac{144}{16} = 9 \)

Step3: Find \( AZ \)

\( AZ = 16x = 16 \times 9 = 144 \)

Answer:

144