Question

1. xy = 6b, yz = 8b, xz = 175. find the value of the variable and yz if y is between x and z. draw a diagram to help you.

Explanation:

Step1: Apply segment - addition postulate

Since Y is between X and Z, we have $XY + YZ=XZ$. Substituting the given values, we get the equation $6b + 8b=175$.

Step2: Combine like - terms

Combining the terms on the left - hand side of the equation, $6b+8b=(6 + 8)b = 14b$. So the equation becomes $14b=175$.

Step3: Solve for b

Dividing both sides of the equation $14b = 175$ by 14, we have $b=\frac{175}{14}=12.5$.

Step4: Find the value of YZ

We know that $YZ = 8b$. Substituting $b = 12.5$ into the equation for YZ, we get $YZ=8\times12.5 = 100$.

Answer:

$b = 12.5$, $YZ=100$