Answer:
The value of y = 0
Step-by-step explanation:
Given the equation
![8^3\cdot 8^{-5}\cdot 8^{\:y}=8^{-2}](https://tex.z-dn.net/?f=8%5E3%5Ccdot%208%5E%7B-5%7D%5Ccdot%208%5E%7B%5C%3Ay%7D%3D8%5E%7B-2%7D)
Apply exponent rule: ![a^b\cdot \:a^c=a^{b+c}](https://tex.z-dn.net/?f=a%5Eb%5Ccdot%20%5C%3Aa%5Ec%3Da%5E%7Bb%2Bc%7D)
so
![8^3\cdot \:\:8^{-5}=8^{3-5}=8^{-2}=\frac{1}{8^2}=\frac{1}{64}](https://tex.z-dn.net/?f=8%5E3%5Ccdot%20%5C%3A%5C%3A8%5E%7B-5%7D%3D8%5E%7B3-5%7D%3D8%5E%7B-2%7D%3D%5Cfrac%7B1%7D%7B8%5E2%7D%3D%5Cfrac%7B1%7D%7B64%7D)
Thus, the equation becomes
![\frac{1}{64}\left(8\:^y\right)=\frac{1}{64}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B64%7D%5Cleft%288%5C%3A%5Ey%5Cright%29%3D%5Cfrac%7B1%7D%7B64%7D)
Divide both sides by 1/64
![\frac{\frac{1}{64}\left(8\:^y\right)}{\frac{1}{64}}=\frac{\frac{1}{64}}{\frac{1}{64}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7B64%7D%5Cleft%288%5C%3A%5Ey%5Cright%29%7D%7B%5Cfrac%7B1%7D%7B64%7D%7D%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B64%7D%7D%7B%5Cfrac%7B1%7D%7B64%7D%7D)
![8\:^y=1](https://tex.z-dn.net/?f=8%5C%3A%5Ey%3D1)
Solve Exponent
![8\:^y=1](https://tex.z-dn.net/?f=8%5C%3A%5Ey%3D1)
Take log of both sides
![\:log\left(8\:^y\right)\:=log\:\left(1\right)](https://tex.z-dn.net/?f=%5C%3Alog%5Cleft%288%5C%3A%5Ey%5Cright%29%5C%3A%3Dlog%5C%3A%5Cleft%281%5Cright%29)
![y\cdot \left(log\left(8\right)\right)=log\left(1\right)](https://tex.z-dn.net/?f=y%5Ccdot%20%5Cleft%28log%5Cleft%288%5Cright%29%5Cright%29%3Dlog%5Cleft%281%5Cright%29)
![y\:=\frac{log\left(1\right)}{\left(log\left(8\right)\right)}](https://tex.z-dn.net/?f=y%5C%3A%3D%5Cfrac%7Blog%5Cleft%281%5Cright%29%7D%7B%5Cleft%28log%5Cleft%288%5Cright%29%5Cright%29%7D)
![y = 0](https://tex.z-dn.net/?f=y%20%3D%200)
Therefore, the value of y = 0
If the triangle is a right triangle, the pythagorean theorem would work
since it doesn’t, the triangle is NOT A RIGHT TRIANGLE
(see attached pic for work :))
Answer:
x= 32 i think
CD= 51
Step-by-step explanation:
Answer:
Age of Mark is 25 years.
Step-by-step explanation:
Let the current age of Mark = x years
After 20 years, age of Mark=(x+20) years
10 years ago,age of Mark was (x-10) years.
In 20 years Mark will be three times as old as he was 10 years ago.
=> ![\[(x+20) = 3*(x-10)\]](https://tex.z-dn.net/?f=%5C%5B%28x%2B20%29%20%3D%203%2A%28x-10%29%5C%5D)
=> ![\[(x+20) = 3x-30\]](https://tex.z-dn.net/?f=%5C%5B%28x%2B20%29%20%3D%203x-30%5C%5D)
=> ![\[(3x-x) = 30+20\]](https://tex.z-dn.net/?f=%5C%5B%283x-x%29%20%3D%2030%2B20%5C%5D)
=> ![\[(2x) = 50\]](https://tex.z-dn.net/?f=%5C%5B%282x%29%20%3D%2050%5C%5D)
=> ![\[x = \frac{50}{2}\]](https://tex.z-dn.net/?f=%5C%5Bx%20%3D%20%5Cfrac%7B50%7D%7B2%7D%5C%5D)
=> ![\[x = 25\]](https://tex.z-dn.net/?f=%5C%5Bx%20%3D%2025%5C%5D)
Answer:
5.3, 4.3, 2.5, 1.8, 0.3, -1.4, -2.9, -3.5, -4.5, -6.2
Step-by-step explanation: