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svetlana [45]
3 years ago
12

X-5=7 X-8=20X+2=-1X-9=12X+-6=-7X-8=-3-7-X=-9HELPPP MEE!!​

Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

Answer:

look below

Step-by-step explanation:

x - 5 = 7

x = 12

.................

x - 8 = 20

x = 28

.................

x + 2 = -1

x = -3

................

x - 9 = 12

x = 21

...............

x + -6 = -7

x = -1

.................

x - 8 = -3

x = 5

..................

-7 - x = -9

-7 = x - 9

2 = x

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Step-by-step explanation:

OPQ originally forms a sector, the formula for sector is

\frac{x}{360} \pi {r}^{2}

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16 =  \sqrt{10 {}^{2} + 10 {}^{2}   - 2(100) \times  \cos(o) }

This isn't the standard formula, it's for this problem

16 =  \sqrt{200 - 200 \times  \cos(o) }

16 =  \sqrt{200  - 200 \cos(o) }

256 = 200 - 200 \cos(o)

56 =  - 200 \cos(o)

-  \frac{7}{25}  =  \cos(o)

\cos {}^{ - 1} (  - \frac{7}{25} )  =  \cos {}^{ - 1} ( \cos(o) )

106.26 = o

So we found our angle of rotation, which is 106.26

Now, we do the sector formula.

\frac{106.26}{360} (100)\pi

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is the area of sector.

Now let find the area of triangle, we can use Heron formula,

The area of a triangle is

\sqrt{s(s - a)(s - b)(s - c)}

where s is the semi-perimeter.

To find s, add all the side lengths up, 10,10,16 and divide it by 2.

Which is

\frac{36}{2}  = 18

\sqrt{18(18 - 10)(18 - 10)(18 - 16)}

\sqrt{18(8)(8)(2)}

\sqrt{(36)(64)}

6  \times 8 = 48

So our area of the triangle is 48. Now, to find the shaded area subtract the main area,( the sector of the circle) by the area of the triangle so we get

\frac{10626}{360}  - 48

Which is an approximate or

44.73

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