In the triangle below, we can solve to find GH = 16. Explain each step you would do to solve for GH, and how you knew you could do
each step.
E
2x
Н.
F
3x - 8
G
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see explanation

Step-by-step explanation:

HF is a perpendicular bisector of Δ EGH

Then Δ EGH is an isosceles triangle with 2 congruent sides GH and EH , so

GH = EH

3x - 8 = 2x ( subtract 2x from both sides )

x - 8 = 0 ( add 8 to both sides )

x = 8

Then

GH = 3x - 8 = 3(8) - 8 = 24 - 8 = 16

From diagram, FG = EF

Solving fo HF and FG by Pythagorean Theorem

HF² = (3x -8)²  -FG²

HF² = (2x)² -FG²

We can eliminate HF² and FG² from BOTH equations because they cancel out.

The 2 equations become (3x -8)² = (2x)²

9x² -48x +64 = 4x²

5x² -48x +64 = 0

Using Quadratic Formula

X1 = 8

X2 = 1.6

2x = 16 AND 2x = 3.2

F is 90°

3x -8 = 16 AND 3x -8 = 2.8

Step-by-step explanation:

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option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.