Question

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

d ----47---- e ----3x + 10---- f

Explanation:

Step1: Relate DF, DE, and EF

From the segment, \( DF = DE + EF \). We know \( DE = 47 \), \( EF = 3x + 10 \), and \( DF = 9x - 39 \). So, \( 9x - 39 = 47 + 3x + 10 \).

Step2: Solve for x

Simplify the equation: \( 9x - 39 = 3x + 57 \). Subtract \( 3x \) from both sides: \( 6x - 39 = 57 \). Add 39 to both sides: \( 6x = 96 \). Divide by 6: \( x = 16 \).

Step3: Find EF

Substitute \( x = 16 \) into \( EF = 3x + 10 \): \( EF = 3(16) + 10 = 48 + 10 = 58 \).

Answer:

58