Question

example 3
find the value of the variable and yz if y is between x and z.

1. xy = 32, yz = 7d, xz = 74
2. xy = 3h, yz = 6h, xz = 135
3. xy = 3p, yz = 2p - 1, xz = 6p - 6
4. xy = 4k + 2, yz = 2k - 7, xz = 121
5. xy = 9m - 3, yz = 6m + 1, xz = 13m + 6
6. xy = 8s - 4, yz = 3s + 1, xz = 10s + 5
7. xy = 2t + 2, yz = 5t - 3, xz = 34
8. xy = 3g - 5, yz = 9g + 3, xz = 11g + 5

Explanation:

7.

Step1: Use segment - addition postulate

Since \(Y\) is between \(X\) and \(Z\), \(XY + YZ=XZ\). Substitute the given values: \(32 + 7d=74\).

Step2: Solve for \(d\)

Subtract 32 from both sides: \(7d=74 - 32\), so \(7d = 42\). Then divide both sides by 7: \(d=\frac{42}{7}=6\).

Step3: Find \(YZ\)

Substitute \(d = 6\) into the expression for \(YZ\). \(YZ=7d=7\times6 = 42\).

Step1: Apply segment - addition postulate

Given \(Y\) is between \(X\) and \(Z\), \(XY + YZ=XZ\). Substitute the values: \(3h+6h = 135\).

Step2: Combine like - terms

\(9h=135\).

Step3: Solve for \(h\)

Divide both sides by 9: \(h=\frac{135}{9}=15\).

Step4: Find \(YZ\)

Substitute \(h = 15\) into the expression for \(YZ\). \(YZ = 6h=6\times15=90\).

Step1: Use segment - addition postulate

Since \(Y\) is between \(X\) and \(Z\), \(XY + YZ=XZ\). Substitute the values: \(3p+(2p - 1)=6p-6\).

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

\(3p+2p-1=5p - 1\), so \(5p-1=6p - 6\).

Step3: Solve for \(p\)

Subtract \(5p\) from both sides: \(-1=p - 6\). Then add 6 to both sides: \(p=5\).

Step4: Find \(YZ\)

Substitute \(p = 5\) into the expression for \(YZ\). \(YZ=2p-1=2\times5-1=9\).

Answer:

\(d = 6\), \(YZ = 42\)

8.