Answer:
![\frac{1}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%7D)
Step-by-step explanation:
Since it is -1, put 1/something
![i^5+i^{-25}+i^{45}](https://tex.z-dn.net/?f=i%5E5%2Bi%5E%7B-25%7D%2Bi%5E%7B45%7D)
Rewrite the term ![i^{-25}](https://tex.z-dn.net/?f=i%5E%7B-25%7D)
![=i^5+\dfrac{1}{i^{25}}+i^{45}](https://tex.z-dn.net/?f=%3Di%5E5%2B%5Cdfrac%7B1%7D%7Bi%5E%7B25%7D%7D%2Bi%5E%7B45%7D)
Expand each term so we have
![=i(i^2)^2+\dfrac{1}{i(i^2)^{12}}+i(i^2)^{22}](https://tex.z-dn.net/?f=%3Di%28i%5E2%29%5E2%2B%5Cdfrac%7B1%7D%7Bi%28i%5E2%29%5E%7B12%7D%7D%2Bi%28i%5E2%29%5E%7B22%7D)
Use the fact that ![i^2=-1](https://tex.z-dn.net/?f=i%5E2%3D-1)
![=i(-1)^2+\dfrac{1}{i(-1)^{12}}+i(-1)^{22}](https://tex.z-dn.net/?f=%3Di%28-1%29%5E2%2B%5Cdfrac%7B1%7D%7Bi%28-1%29%5E%7B12%7D%7D%2Bi%28-1%29%5E%7B22%7D)
Use the fact that
when a is an even number
![=i+\dfrac{1}{i}+i](https://tex.z-dn.net/?f=%3Di%2B%5Cdfrac%7B1%7D%7Bi%7D%2Bi)
Simplify
![=i-i+i](https://tex.z-dn.net/?f=%3Di-i%2Bi)
![=i](https://tex.z-dn.net/?f=%3Di)
Let me know if you need any clarifications, thanks!
(H)ypotenuse (L)eg, right-triangle theorem.
based on the provided graph, we know the hypotenuses are equal, thus the tickmarks, so H is true, now the L part, we only need either of the pair of legs to be equal DM = NB or AM = CN, if either one is true, we're golden.
Answer:
20 marbles total...7 are green
Step-by-step explanation:
probability on first draw is 7/20...and since the marble was not replaced, the probability on the second draw is 6/19. And since they cant happen at the same time, we multiply
7/20 * 6/19 = 42/380 which reduces to 21/190