Question

4 fill in the blank 1 point if df = 9x - 39, find ef.
d---47---e---3x+10---f
ef = type your answer...

Explanation:

Step1: Determine the relationship between segments

From the number line, we know that \( DF = DE + EF \). Given \( DE = 47 \), \( EF = 3x + 10 \), and \( DF = 9x - 39 \). So we can set up the equation:
\( 9x - 39 = 47 + 3x + 10 \)

Step2: Solve for \( x \)

Simplify the right - hand side of the equation: \( 47+10 = 57 \), so the equation becomes \( 9x - 39=3x + 57 \).
Subtract \( 3x \) from both sides: \( 9x-3x - 39=3x - 3x+ 57 \), which simplifies to \( 6x - 39 = 57 \).
Add 39 to both sides: \( 6x-39 + 39=57 + 39 \), so \( 6x=96 \).
Divide both sides by 6: \( x=\frac{96}{6}=16 \).

Step3: Calculate \( EF \)

Since \( EF = 3x + 10 \) and \( x = 16 \), substitute \( x = 16 \) into the expression for \( EF \):
\( EF=3\times16 + 10=48 + 10 = 58 \)

Answer:

\( 58 \)