Answer:
![a = -4](https://tex.z-dn.net/?f=a%20%3D%20-4)
Step-by-step explanation:
The equation to solve for "a" is:
![(\frac{1}{9})^{a+1}=81^{a+1}*27^{2-a}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B9%7D%29%5E%7Ba%2B1%7D%3D81%5E%7Ba%2B1%7D%2A27%5E%7B2-a%7D)
The first step is to convert all of them to same bases.
9, 81, and 27, all can be expressed in base 3, lets do this:
![(\frac{1}{9})^{a+1}=81^{a+1}*27^{2-a}\\(3^{-2})^{a+1}=(3^4)^{a+1}*(3^3)^{2-a}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B9%7D%29%5E%7Ba%2B1%7D%3D81%5E%7Ba%2B1%7D%2A27%5E%7B2-a%7D%5C%5C%283%5E%7B-2%7D%29%5E%7Ba%2B1%7D%3D%283%5E4%29%5E%7Ba%2B1%7D%2A%283%5E3%29%5E%7B2-a%7D)
We can use the property:
to simplify further:
![(3^{-2})^{a+1}=(3^4)^{a+1}*(3^3)^{2-a}\\3^{-2a-2}=3^{4a+4}*3^{6-3a}](https://tex.z-dn.net/?f=%283%5E%7B-2%7D%29%5E%7Ba%2B1%7D%3D%283%5E4%29%5E%7Ba%2B1%7D%2A%283%5E3%29%5E%7B2-a%7D%5C%5C3%5E%7B-2a-2%7D%3D3%5E%7B4a%2B4%7D%2A3%5E%7B6-3a%7D)
The right side has 2 same bases multiplied, we can simplify this using the property: ![a^x * a^y = a^{x+y}](https://tex.z-dn.net/?f=a%5Ex%20%2A%20a%5Ey%20%3D%20a%5E%7Bx%2By%7D)
Thus, we have:
![3^{-2a-2}=3^{4a+4}*3^{6-3a}\\3^{-2a-2}=3^{4a+4+6-3a}}\\3^{-2a-2}=3^{a+10}](https://tex.z-dn.net/?f=3%5E%7B-2a-2%7D%3D3%5E%7B4a%2B4%7D%2A3%5E%7B6-3a%7D%5C%5C3%5E%7B-2a-2%7D%3D3%5E%7B4a%2B4%2B6-3a%7D%7D%5C%5C3%5E%7B-2a-2%7D%3D3%5E%7Ba%2B10%7D)
Now, both sides have same base, so exponents would be equal. Now lets equate and solve for "a":
![3^{-2a-2}=3^{a+10}\\-2a-2=a+10\\3a=-12\\a=-4](https://tex.z-dn.net/?f=3%5E%7B-2a-2%7D%3D3%5E%7Ba%2B10%7D%5C%5C-2a-2%3Da%2B10%5C%5C3a%3D-12%5C%5Ca%3D-4)
So,
a = -4
Answer:
Sometimes protractor scales are attached to give more precise readings. ... It reads to 5 arcminutes (5′ or 112°) and can measure angles from 0° to 360°.
Step-by-step explanation:
hope this helps, plz mark brainliest :) thanks
Answer:
12
Step-by-step explanation:
Make a number line.. Then put 1/6, 2/6, 3/6, 4/6, 5/6, and 6/6 =1
<-------0-------1/6-------2/6-------3/6-------4/6-------5/6-------1------->
Then since 1/2 is half a whole thing put 1/2 ontop of the 3/6 like...
1/2
<-------0-------1/6-------2/6-------3/6-------4/6-------5/6-------1------->
Hope this helps you! :D