Answer:
B. 50 degrees
Step-by-step explanation:
I am not 100% sure and if this is a right triangle, then it's measure is 90 degrees. So, 140 degrees minus 90 degrees would total, 50 degrees.
The answer is TRUE. The parallelogram must be a rectangle
Answer:
![3^{75}](https://tex.z-dn.net/?f=3%5E%7B75%7D)
Step-by-step explanation:
We are asked to divide our given fraction:
.
We will simplify our division problem using rules of exponents.
Using product rule of exponents
we can write:
![45^{45}=(3*15)^{45}=3^{45}*15^{45}](https://tex.z-dn.net/?f=45%5E%7B45%7D%3D%283%2A15%29%5E%7B45%7D%3D3%5E%7B45%7D%2A15%5E%7B45%7D)
![75^{30}=(5*15)^{30}=5^{30}*15^{30}](https://tex.z-dn.net/?f=75%5E%7B30%7D%3D%285%2A15%29%5E%7B30%7D%3D5%5E%7B30%7D%2A15%5E%7B30%7D)
Substituting these values in our division problem we will get,
![\frac{3^{45}*15^{45}*15^{15}}{5^{30}*15^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A15%5E%7B45%7D%2A15%5E%7B15%7D%7D%7B5%5E%7B30%7D%2A15%5E%7B30%7D%7D)
Using power rule of exponents
we will get,
![\frac{3^{45}*15^{45+15}}{5^{30}*15^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A15%5E%7B45%2B15%7D%7D%7B5%5E%7B30%7D%2A15%5E%7B30%7D%7D)
![\frac{3^{45}*15^{60}}{5^{30}*15^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A15%5E%7B60%7D%7D%7B5%5E%7B30%7D%2A15%5E%7B30%7D%7D)
Using quotient rule of exponent
we will get,
![\frac{3^{45}*15^{60-30}}{5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A15%5E%7B60-30%7D%7D%7B5%5E%7B30%7D%7D)
![\frac{3^{45}*15^{30}}{5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A15%5E%7B30%7D%7D%7B5%5E%7B30%7D%7D)
Using product rule of exponents
we will get,
![\frac{3^{45}*(3*5)^{30}}{5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A%283%2A5%29%5E%7B30%7D%7D%7B5%5E%7B30%7D%7D)
![\frac{3^{45}*3^{30}*5^{30}}{5^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B3%5E%7B45%7D%2A3%5E%7B30%7D%2A5%5E%7B30%7D%7D%7B5%5E%7B30%7D%7D)
Upon canceling out
we will get,
![3^{45}*3^{30}](https://tex.z-dn.net/?f=3%5E%7B45%7D%2A3%5E%7B30%7D)
Using power rule of exponents
we will get,
![3^{45+30}](https://tex.z-dn.net/?f=3%5E%7B45%2B30%7D)
![3^{75}](https://tex.z-dn.net/?f=3%5E%7B75%7D)
Therefore, our resulting quotient will be
.
Step-by-step explanation:
use the midpoint formula
![( \frac{xs + xt}{2} \: \: \frac{ys + yt}{2} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bxs%20%2B%20xt%7D%7B2%7D%20%5C%3A%20%20%5C%3A%20%20%5Cfrac%7Bys%20%2B%20yt%7D%7B2%7D%20%29)
substitute into the midpoint formula
![( \frac{ - 8 + 2}{2} \: \: \frac{3 + ( - 1)}{2} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B%20-%208%20%2B%202%7D%7B2%7D%20%20%5C%3A%20%20%5C%3A%20%20%20%5Cfrac%7B3%20%2B%20%28%20-%201%29%7D%7B2%7D%20%29)
solve the above
(
![(3 \: \: 1)](https://tex.z-dn.net/?f=%283%20%5C%3A%20%20%5C%3A%201%29)
so the x coordinate if your midpoint is 3
the y coordinate of your midpoint is 1
(3;1)