Answer: ![\bold{5)\ \cos \theta=\dfrac{\sqrt{11}}{6}\qquad 6)\ \tan \theta =\dfrac{8}{17}\qquad 7)\ \cos \theta = \dfrac{4}{3}\qquad 8)\ \cos \theta = \dfrac{\sqrt{10}}{10}}](https://tex.z-dn.net/?f=%5Cbold%7B5%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Csqrt%7B11%7D%7D%7B6%7D%5Cqquad%206%29%5C%20%5Ctan%20%5Ctheta%20%3D%5Cdfrac%7B8%7D%7B17%7D%5Cqquad%207%29%5C%20%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B4%7D%7B3%7D%5Cqquad%208%29%5C%20%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7B%5Csqrt%7B10%7D%7D%7B10%7D%7D)
<u>Step-by-Step Explanation:</u>
Pythagorean Theorem is: a² + b² = c² , <em>where "c" is the hypotenuse</em>
![5)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{3\sqrt{11}}{18}\quad \rightarrow \large\boxed{\dfrac{\sqrt{11}}{6}}](https://tex.z-dn.net/?f=5%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bhypotenuse%20of%20triangle%7D%7D%3D%5Cdfrac%7B3%5Csqrt%7B11%7D%7D%7B18%7D%5Cquad%20%5Crightarrow%20%5Clarge%5Cboxed%7B%5Cdfrac%7B%5Csqrt%7B11%7D%7D%7B6%7D%7D)
Note: (15)² + (3√11)² = hypotenuse² → hypotenuse = 18
![6)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{8}{17}\quad =\large\boxed{\dfrac{8}{17}}](https://tex.z-dn.net/?f=6%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bhypotenuse%20of%20triangle%7D%7D%3D%5Cdfrac%7B8%7D%7B17%7D%5Cquad%20%3D%5Clarge%5Cboxed%7B%5Cdfrac%7B8%7D%7B17%7D%7D)
Note: 8² + 15² = hypotenuse² → hypotenuse = 17
![7)\ \tan \theta=\dfrac{\text{side opposite to}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{20}{15}\quad \rightarrow \large\boxed{\dfrac{4}{3}}](https://tex.z-dn.net/?f=7%29%5C%20%5Ctan%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20opposite%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%3D%5Cdfrac%7B20%7D%7B15%7D%5Cquad%20%5Crightarrow%20%5Clarge%5Cboxed%7B%5Cdfrac%7B4%7D%7B3%7D%7D)
Note: hypotenuse not needed for tan
![8)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{2}{2\sqrt{10}}\quad =\large\boxed{\dfrac{\sqrt{10}}{10}}](https://tex.z-dn.net/?f=8%29%5C%20%5Ccos%20%5Ctheta%3D%5Cdfrac%7B%5Ctext%7Bside%20adjacent%20to%7D%5C%20%5Ctheta%7D%7B%5Ctext%7Bhypotenuse%20of%20triangle%7D%7D%3D%5Cdfrac%7B2%7D%7B2%5Csqrt%7B10%7D%7D%5Cquad%20%3D%5Clarge%5Cboxed%7B%5Cdfrac%7B%5Csqrt%7B10%7D%7D%7B10%7D%7D)
Note: 2² + 6² = hypotenuse² → hypotenuse = 2√10
Answer:
20 lbs
Step-by-step explanation:
2/5ths of the food would be 20 pounds because:
2/5 * 50 = 20
2/10ths of the food would be 10 pounds because:
2/10 * 50 = 10
If we add those two together, we would get the total amount that the dog ate, which would be 30 pounds. SInce the dog ate 30 pounds of food out of the 50 pounds, there would be 20 pounds left in the bag at the end of two months:
50- ( 20+ 10) = 20
I believe x is equal to five. Try it. Hope this helps mate.
Answer: dont know just search it up