Question

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

Explanation:

Step1: Set up the equation

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

Step2: Simplify the right - hand side

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

Step3: Move the terms with $x$ to one side

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

Step4: Isolate the term with $x$

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 $EF$

Substitute $x = 16$ into the expression for $EF$: $EF=3x + 10=3\times16+10$.
$EF = 48+10=58$.

Answer:

$58$