Question

1. if df = 9x - 39, find the value of ef.

Explanation:

Step1: Set up equation based on segment - addition postulate

Since $DF=DE + EF$, and $DF = 9x-39$, $DE = 47$, $EF=3x + 10$, we have $9x-39=47+(3x + 10)$.

Step2: Simplify the right - hand side of the equation

$9x-39=47 + 3x+10$, so $9x-39=3x + 57$.

Step3: Isolate the variable terms

Subtract $3x$ from both sides: $9x-3x-39=3x-3x + 57$, which gives $6x-39=57$.

Step4: Isolate the variable term further

Add 39 to both sides: $6x-39 + 39=57+39$, so $6x=96$.

Step5: Solve for x

Divide both sides by 6: $\frac{6x}{6}=\frac{96}{6}$, then $x = 16$.

Step6: Find the value of EF

Substitute $x = 16$ into the expression for $EF$: $EF=3x + 10=3\times16+10=48 + 10=28$.

Answer:

28