Answer:
x=4
Step-by-step explanation:
tangent lines from the same point to a circle are congruent in length, so we can say that
5x+8 = 8x-4
5x -5x +8 = 8x - 5x -4
8 = 3x - 4
8+4 = 3x -4 + 4
3x = 12
3x/3 = 12/3
x=4
Answer:
GH = 6.3 units
Step-by-step explanation:
Assuming that 1 box represents 1 unit, the coordinate pair of G = (-2, -3), while H = (0, 3).
Distance between G and H = ![d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}](https://tex.z-dn.net/?f=%20d%20%3D%20%5Csqrt%7B%28x_2%20-%20x_1%29%5E2%20%2B%20%28y_2%20-%20y_1%29%5E2%7D%20)
Let,
![G(-2, -3) = (x_1, y_1)](https://tex.z-dn.net/?f=%20G%28-2%2C%20-3%29%20%3D%20%28x_1%2C%20y_1%29%20)
![H(0, 3) = (x_2, y_2)](https://tex.z-dn.net/?f=%20H%280%2C%203%29%20%3D%20%28x_2%2C%20y_2%29%20)
![GH = \sqrt{(0 - (-2))^2 + (3 - (-3))^2}](https://tex.z-dn.net/?f=%20GH%20%3D%20%5Csqrt%7B%280%20-%20%28-2%29%29%5E2%20%2B%20%283%20-%20%28-3%29%29%5E2%7D%20)
![GH = \sqrt{(2)^2 + (6)^2}](https://tex.z-dn.net/?f=%20GH%20%3D%20%5Csqrt%7B%282%29%5E2%20%2B%20%286%29%5E2%7D%20)
![GH = \sqrt{4 + 36} = \sqrt{40}](https://tex.z-dn.net/?f=%20GH%20%3D%20%5Csqrt%7B4%20%2B%2036%7D%20%3D%20%5Csqrt%7B40%7D%20)
(nearest tenth)
21:3
9:3
3:1
there all a 3:1 ratio
Answer: There are 6 pieces of cloth are rectangles and 9 pieces of cloth are triangles.
Explanation:
Since we have given that
For every 5 pieces of cloth, 2 are rectangles
So, remaining piece will be of triangle so,
![5-2=3](https://tex.z-dn.net/?f=5-2%3D3)
3 are triangles.
Ratio of rectangles to triangles is 2:3.
Now, she needs 15 pieces of cloth to complete her scarf,
So, Number of rectangles is needed is given by
![\frac{2}{5}\times 15\\\\=2\times 3\\\\=6](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%5Ctimes%2015%5C%5C%5C%5C%3D2%5Ctimes%203%5C%5C%5C%5C%3D6)
Number of triangles is needed is given by
![\frac{3}{5}\times 15\\\\=3\times 3\\\\=9](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%5Ctimes%2015%5C%5C%5C%5C%3D3%5Ctimes%203%5C%5C%5C%5C%3D9)
Hence, there are 6 pieces of cloth are rectangles and 9 pieces of cloth are triangles.