We have the triangle 30° - 60° - 90°.
The lenght of the sides are in proportion: ![1:2:\sqrt3\to a:2a:a\sqrt3](https://tex.z-dn.net/?f=1%3A2%3A%5Csqrt3%5Cto%20a%3A2a%3Aa%5Csqrt3)
![a=y\\2a=x\\a\sqrt3=5\\\\a\sqrt3=5\qquad\text{multiply both sides by}\ \sqrt3\\\\3a=5\sqrt3\qquad\text{divide both sides by 3}\\\\a=\dfrac{5\sqrt3}{3}\\\\2a=2\cdot\dfrac{5\sqrt3}{3}=\dfrac{10\sqrt3}{3}\\\\Answer:\ x=\dfrac{10\sqrt3}{3},\ y=\dfrac{5\sqrt3}{3}](https://tex.z-dn.net/?f=a%3Dy%5C%5C2a%3Dx%5C%5Ca%5Csqrt3%3D5%5C%5C%5C%5Ca%5Csqrt3%3D5%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%7D%5C%20%5Csqrt3%5C%5C%5C%5C3a%3D5%5Csqrt3%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5C%5C%5Ca%3D%5Cdfrac%7B5%5Csqrt3%7D%7B3%7D%5C%5C%5C%5C2a%3D2%5Ccdot%5Cdfrac%7B5%5Csqrt3%7D%7B3%7D%3D%5Cdfrac%7B10%5Csqrt3%7D%7B3%7D%5C%5C%5C%5CAnswer%3A%5C%20x%3D%5Cdfrac%7B10%5Csqrt3%7D%7B3%7D%2C%5C%20y%3D%5Cdfrac%7B5%5Csqrt3%7D%7B3%7D)
There could be five in each class.
<h3>
Answer: 116.2°</h3>
Work Shown:
![c^2 = a^2 + b^2 - 2ab\cos(C)\\\\55^2 = 24^2 + 40^2 - 2*24*40\cos(C)\\\\3025 = 576 + 1600 - 1920\cos(C)\\\\3025 = 2176 - 1920\cos(C)\\\\3025 - 2176 = -1920\cos(C)\\\\849 = -1920\cos(C)\\\\-1920\cos(C) = 849\\\\\cos(C) = (849)/(-1920)\\\\\cos(C) \approx -0.4421875\\\\C \approx \cos^{-1}(-0.4421875)\\\\C \approx 116.243535748231^{\circ}\\\\C \approx 116.2^{\circ}\\\\](https://tex.z-dn.net/?f=c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20-%202ab%5Ccos%28C%29%5C%5C%5C%5C55%5E2%20%3D%2024%5E2%20%2B%2040%5E2%20-%202%2A24%2A40%5Ccos%28C%29%5C%5C%5C%5C3025%20%3D%20576%20%2B%201600%20-%201920%5Ccos%28C%29%5C%5C%5C%5C3025%20%3D%202176%20-%201920%5Ccos%28C%29%5C%5C%5C%5C3025%20-%202176%20%20%3D%20-1920%5Ccos%28C%29%5C%5C%5C%5C849%20%20%3D%20-1920%5Ccos%28C%29%5C%5C%5C%5C-1920%5Ccos%28C%29%20%3D%20849%5C%5C%5C%5C%5Ccos%28C%29%20%3D%20%28849%29%2F%28-1920%29%5C%5C%5C%5C%5Ccos%28C%29%20%5Capprox%20-0.4421875%5C%5C%5C%5CC%20%5Capprox%20%5Ccos%5E%7B-1%7D%28-0.4421875%29%5C%5C%5C%5CC%20%5Capprox%20116.243535748231%5E%7B%5Ccirc%7D%5C%5C%5C%5CC%20%5Capprox%20116.2%5E%7B%5Ccirc%7D%5C%5C%5C%5C)
The first equation is one of the three variations for the Law of Cosines.
Make sure your calculator is in degree mode.
Answer:
repeating non repeating non repeating non repeating
Step-by-step explanation:
The answer is A.
When replacing the variable 'x' by 'x + 2' the graph is shifted 2 units to the left. When we replace the variable, the function changes
from
![f(x) = |x - 3| + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Cx%20-%203%7C%20%2B%202)
To
![f(x) = |(x + 2) - 3| + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7C%28x%20%2B%202%29%20-%203%7C%20%2B%202)
![f(x) = |x - 1| + 2](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%7Cx%20-%201%7C%20%2B%202)
And therefore the function is shifted 2 to the left.