Answer:
[tex]EF = 58[/tex]
Step-by-step explanation:
Given
[tex]DF = 9x - 39[/tex]
[tex]DE = 47[/tex]
[tex]EF = 3x + 10[/tex]
See attachment
Required
Find [tex]EF[/tex]
Because E is a point between D and F, then:
[tex]DF = DE + EF[/tex]
Substitute values for DF, DE and EF
[tex]9x - 39 = 47 +3x + 10[/tex]
Collect Like Terms
[tex]9x -3x = 47 +39 + 10[/tex]
[tex]6x = 96[/tex]
Make x the subject
[tex]x = \frac{96}{6}[/tex]
[tex]x = 16[/tex]
Recall that:
[tex]EF = 3x + 10[/tex]
Substitute 16 for x
[tex]EF = 3 *16 + 10[/tex]
[tex]EF = 48 + 10[/tex]
[tex]EF = 58[/tex]
