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Agata [3.3K]
3 years ago
9

Fine FG , given that line HF is perpendicular bisector or EG

Mathematics
1 answer:
Marta_Voda [28]3 years ago
8 0

Answer:

FG = 7

Step-by-step explanation:

We'll begin by calculating HF. This can be obtained by using the pythagoras theory as illustrated below:

EF = 7

EH = 3

HF =?

EF² = EH² + HF²

7² = 3² + HF²

49 = 9 + HF²

Collect like terms

49 – 9 = HF²

40 = HF²

Take the square root of both side

HF = √40

Finally, we shall determine FG. This can be obtained as follow:

GH = 3

HF = √40

FG =.?

FG² = GH² + HF²

FG² = 3² + (√40)²

FG² = 9 + 40

FG² = 49

Take the square root of both side

FG = √49

FG = 7

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[ Answer ]

\boxed{5x^{2} \ + \ 13x \ + \ 27}

[ Explanation ]

  • Simplify: 5(x + 3)(x + 2) - 3(x2 + 2x + 1)

--------------------------------------

  • Add Similar Elements: 2x + 2x = 4x

5(x + 3)(x + 2) - 3(4x + 1)

  • Expand: 5(x + 3)(x + 2) - 3(4x + 1): 5x^{2} + 25x + 30

5x^{2} + 25x + 30 - 3(4x + 1)

  • Expand: - 3(4x + 1): -12x - 3

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  • Simplify: 5x^{2} + 25x + 30 - 12x - 3: 5x^{2} + 13x + 27

= 5x^{2} + 13x + 27

\boxed{[] \ Eclipsed \ []}

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