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LekaFEV [45]
3 years ago
8

Find the area of the shaded region. Give the exact answer. 60° 0 6 A =

Mathematics
1 answer:
kakasveta [241]3 years ago
8 0

Answer:

25.35

Step-by-step explanation:

Area of the shaded portion = Area of semicircle - Area of the right triangle

Area of semicircle = πr²/2

Area of semicircle = 3.14(6)²/2

Area of semicircle = 3.14 * 18

Area of semicircle = 56.52

Area of triangle = 1/2 * base * height

Get the height using the SOH CAH TOA identity

sin 60 = H/12

H = 12sin60

H = 12(0.8660)

H = 10.39

Get the base

12² = b²+10.39²

144 = b²+108

b² = 144 - 108

b² = 36

b = 6

Area of triangle = 1/2 * 6 * 10.39

Area of triangle = 3 * 10.39

Area of triangle = 31.17

Area of shaded portion = 56.52 - 31.17

Area of shaded portion = 25.35

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2 years ago
In Image:
iris [78.8K]

Answer:

The answer to your question is          x ≠ -10   x ≠ 2     x ≠ -2

Solution                                                \frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}      

Step-by-step explanation:

Process

1.- Factor all the polynomials

              \frac{x^{2} -3x - 40}{x^{2} + 8x - 20} / \frac{x^{2}+ 13x + 40}{x^{2}+ 12x + 20} = \frac{(x-8)(x + 5)}{(x + 10)(x- 2)} / \frac{(x+ 8)(x + 5)}{(x + 10)(x + 2)}

2.- Invert the second term

                                             = \frac{(x- 8)(x + 5)}{(x +10)(x - 2)}  \frac{(x+ 10)(x + 2)}{(x + 8)(x +5)}

3.- Simplify

                                              = \frac{(x- 8)(x + 2)}{(x + 8)(x - 2)}

4.- x must be different to

            x ≠ -10   x ≠ 2     x ≠ -2

This values are from the factor expressions and then equal to zero.

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