Question

find the value of n and yz if y is between x and z. xy = 4n + 3, yz = 2n - 7, xz = 20 n = \boxed{?} yz = \boxed{?} need help?

Explanation:

Step1: Apply segment addition postulate

Since \( Y \) is between \( X \) and \( Z \), we have \( XY + YZ = XZ \). Substitute \( XY = 4n + 3 \), \( YZ = 2n - 7 \), and \( XZ = 20 \) into the equation:
\( (4n + 3) + (2n - 7) = 20 \)

Step2: Simplify and solve for \( n \)

Combine like terms:
\( 4n + 2n + 3 - 7 = 20 \)
\( 6n - 4 = 20 \)

Add 4 to both sides:
\( 6n = 20 + 4 \)
\( 6n = 24 \)

Divide by 6:
\( n = \frac{24}{6} = 4 \)

Step3: Find \( YZ \)

Substitute \( n = 4 \) into \( YZ = 2n - 7 \):
\( YZ = 2(4) - 7 = 8 - 7 = 1 \)

Answer:

\( n = 4 \), \( YZ = 1 \)