Question

find the value of a and yz if y is between x and z. xy = 3a − 4, yz = 6a + 2, xz = 5a + 22 a = yz = need help with this question? get a hint

Explanation:

Step1: Apply segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substitute the given expressions:
\( (3a - 4) + (6a + 2) = 5a + 22 \)

Step2: Simplify and solve for \( a \)

Combine like terms on the left:
\( 9a - 2 = 5a + 22 \)
Subtract \( 5a \) from both sides:
\( 4a - 2 = 22 \)
Add 2 to both sides:
\( 4a = 24 \)
Divide by 4:
\( a = 6 \)

Step3: Find \( YZ \)

Substitute \( a = 6 \) into \( YZ = 6a + 2 \):
\( YZ = 6(6) + 2 = 36 + 2 = 38 \)

Answer:

\( a = 6 \); \( YZ = 38 \)