Respuesta :

kusidesmo

Answer:

EF =58

Step-by-step explanation:

from the illustration,

EF =DF - DE

given that DF =9x-39 , DE =47 EF=3x +10

substitute them into the formula,

3x +10=9x-39 - 47

solving for x

3x +10 =9x -86

grouping like terms

3x - 9x =-86 -10

-6x=-96

dividing through by -6

[tex] \frac{ - 6x}{ - 6} = \frac{ - 96}{ - 6} [/tex]

[tex]x = \frac{96}{6} [/tex]

[tex]x = 16[/tex]

but EF=3x+10

substitute x=16 into it to get the EF

EF= 3(16)+10

EF=48+10

EF=58

Ben

[tex]\huge\boxed{58}[/tex]

First of all, we know that [tex]DE+EF=DF[/tex], because these are two segments that make up one larger segment.

Write this as an equation.

[tex]DE+EF=DF[/tex]

[tex]47+(3x+10)=9x-39[/tex]

Remove the parentheses. [tex]47+3x+10=9x-39[/tex]

Combine the like terms. [tex]3x+57=9x-39[/tex]

Subtract [tex]9x[/tex] from both sides. [tex]-6x+57=-39[/tex]

Subtract [tex]57[/tex] from both sides. [tex]-6x=-96[/tex]

Divide both sides by [tex]-6[/tex]. [tex]x=16[/tex]

Now, find [tex]EF[/tex].

[tex]3x+10[/tex]

[tex]3(16)+10[/tex]

Multiply. [tex]48+10[/tex]

Add. [tex]\boxed{58}[/tex]

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