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, $XY + YZ=XZ$. Substitute the given expressions: $(4n + 3)+(2n-7)=20$.

Step2: Combine like - terms

$4n+2n+3 - 7=20$, which simplifies to $6n-4 = 20$.

Step3: Add 4 to both sides

$6n-4 + 4=20 + 4$, resulting in $6n=24$.

Step4: Solve for n

Divide both sides by 6: $\frac{6n}{6}=\frac{24}{6}$, so $n = 4$.

Step5: Find the value of YZ

Substitute $n = 4$ into the expression for YZ. $YZ=2n-7$. $YZ=2\times4-7=8 - 7=1$.

Answer:

$n = 4$, $YZ = 1$