Question

find the value of d and yz if y is between x and z. xy = 11d, yz = 9d - 2, xz = 5d + 28

Explanation:

Step1: Apply segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given expressions: \( 11d + (9d - 2) = 5d + 28 \).

Step2: Simplify and solve for \( d \)

Combine like terms: \( 20d - 2 = 5d + 28 \). Subtract \( 5d \) from both sides: \( 15d - 2 = 28 \). Add 2 to both sides: \( 15d = 30 \). Divide by 15: \( d = 2 \).

Step3: Find \( YZ \)

Substitute \( d = 2 \) into \( YZ = 9d - 2 \): \( YZ = 9(2) - 2 = 18 - 2 = 16 \).

Answer:

\( d = 2 \)
\( YZ = 16 \)