Question

find the value of x and yz if y is between x and z.
xy = 2x + 1, yz = 6x, and xz = 81
x=
yz =

Explanation:

Step1: Apply segment addition postulate

Since \(Y\) is between \(X\) and \(Z\), \(XY + YZ=XZ\). Substitute \(XY = 2x + 1\), \(YZ = 6x\), and \(XZ = 81\) into the equation: \((2x + 1)+6x=81\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+6x + 1=81\), which gives \(8x+1 = 81\).

Step3: Solve for \(x\)

Subtract \(1\) from both sides: \(8x+1-1=81 - 1\), so \(8x=80\). Then divide both sides by \(8\): \(x=\frac{80}{8}=10\).

Step4: Find the value of \(YZ\)

Substitute \(x = 10\) into the formula for \(YZ\). Since \(YZ = 6x\), then \(YZ=6\times10 = 60\).

Answer:

\(x = 10\), \(YZ=60\)