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Art
2 months ago
5

If DF = 9x -39 find EF

Mathematics
2 answers:
Svet_ta [12.7K]2 months ago
7 0

|DF| equals the sum of |DE| and |EF|.

|DF| = 9x - 36

|DE| = 47

|EF| = 3x + 10

Substitute the values:

9x - 39 = 47 + 3x + 10

9x - 39 = 3x + 57       |+39 both sides

9x = 3x + 96           |-3x both sides

6x = 96                |divide both sides by 6

x = 16

Now, substitute x back into |EF| equation:

|EF| = 3(16) + 10 = 48 + 10 = 58

Final answer: |EF| equals 58.

Zina [12.3K]2 months ago
5 0

Answer: The length of EF is 58 units.

Stepwise reasoning:

Given that DF = 9x - 39, DE is 47 units, and EF = 3x + 10,

we aim to determine EF's length.

Using the relationship:

DE+EF=DF\\\\\Rightarrow 47+(3x+10)=9x-39\\\\\Rightarrow 3x+57=9x-39\\\\\Rightarrow 9x-3x=57+39\\\\\Rightarrow 6x=96\\\\\Rightarrow x=\dfrac{96}{6}\\\\\Rightarrow x=16.

EF's length is calculated by:

EF=3\imes16+10=48+10=58.

Therefore, EF measures 58 units.

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