Question

find the value of n and yz if y is between x and z. xy = 4n + 3, yz = 2n - 7, xz = 20

Explanation:

Step1: Apply segment - addition postulate

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

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4n+2n+3 - 7=20\), which simplifies to \(6n-4 = 20\).

Step3: Solve for n

Add 4 to both sides of the equation: \(6n-4 + 4=20 + 4\), so \(6n=24\).
Divide both sides by 6: \(n=\frac{24}{6}=4\).

Step4: Find the value of YZ

Substitute \(n = 4\) into the expression for YZ. \(YZ=2n-7\), so \(YZ=2\times4-7=8 - 7=1\).

Answer:

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