Question

question 1-5 find the value of x and the length of xz if y is between x and z, xy = 19, yz = 2x + 5, and xz = 6x + 12. the value of x is blank the length of xz is blank

Explanation:

Step1: Apply segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substituting the given expressions: \( 19 + (2x + 5) = 6x + 12 \).

Step2: Simplify and solve for \( x \)

Simplify left side: \( 2x + 24 = 6x + 12 \). Subtract \( 2x \) and 12 from both sides: \( 12 = 4x \). Then \( x = \frac{12}{4} = 3 \).

Step3: Find length of \( XZ \)

Substitute \( x = 3 \) into \( XZ = 6x + 12 \): \( XZ = 6(3) + 12 = 18 + 12 = 30 \).

Answer:

The value of \( x \) is \( 3 \), and the length of \( XZ \) is \( 30 \).