Answer:
see explanation
Step-by-step explanation:
Given
3 < 5 + 6h < 10 ( subtract 5 from each interval )
- 2 < 6h < 5 ( divide each interval by 6 )
-
< h < ![\frac{5}{6}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7D)
Ok so if it’s 112 then it would be 224 because the length is double the width.
Answer:
6*5 = 30
Step-by-step explanation:
15 you split it in half as it goes down
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