Question

1. xy = 11a, yz = 9a - 2, xz = 5a + 28. textbook pg. 19 #24 - 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 $XY + YZ=XZ$. Substitute the given expressions: $(11a)+(9a - 2)=5a + 28$.

Step2: Combine like - terms on the left - hand side

$11a+9a−2 = 20a−2$. So, the equation becomes $20a−2 = 5a + 28$.

Step3: Isolate the variable terms

Subtract $5a$ from both sides: $20a-5a−2=5a - 5a+28$, which simplifies to $15a−2 = 28$.

Step4: Isolate the variable

Add 2 to both sides: $15a−2 + 2=28 + 2$, getting $15a=30$. Then divide both sides by 15: $a=\frac{30}{15}=2$.

Step5: Find the value of YZ

Substitute $a = 2$ into the expression for YZ. $YZ=9a−2$. So, $YZ=9(2)-2=18 - 2=16$.

Answer:

$a = 2$, $YZ = 16$