Answer: ok what is it
Step-by-step explanation:
I'll be using the following properties about exponents:
![a^b \times a^c=a^{b+c}](https://tex.z-dn.net/?f=a%5Eb%20%5Ctimes%20a%5Ec%3Da%5E%7Bb%2Bc%7D)
![a^b \div a^c=a^{b-c}](https://tex.z-dn.net/?f=a%5Eb%20%5Cdiv%20a%5Ec%3Da%5E%7Bb-c%7D)
![(a^b)^c=a^{bc}](https://tex.z-dn.net/?f=%28a%5Eb%29%5Ec%3Da%5E%7Bbc%7D)
where a, b, and c are some positive integers
Part a:
![8^5 \times 8^4 = 8^{5+4}=8^9](https://tex.z-dn.net/?f=8%5E5%20%5Ctimes%208%5E4%20%3D%208%5E%7B5%2B4%7D%3D8%5E9)
Part b:
![3^{11} \times 3 = 3^{11} \times 3^{1} = 3^{11+1} = 3^{12}](https://tex.z-dn.net/?f=3%5E%7B11%7D%20%5Ctimes%203%20%3D%203%5E%7B11%7D%20%5Ctimes%203%5E%7B1%7D%20%3D%203%5E%7B11%2B1%7D%20%3D%203%5E%7B12%7D)
Part c:
![9^3 \times 9^7 = 9^{3+7}=9^{10}](https://tex.z-dn.net/?f=9%5E3%20%5Ctimes%209%5E7%20%3D%209%5E%7B3%2B7%7D%3D9%5E%7B10%7D)
Part d:
![7^7 \div 7 = 7^7 \div 7^1 = 7^{7-1}=7^6](https://tex.z-dn.net/?f=7%5E7%20%5Cdiv%207%20%3D%207%5E7%20%5Cdiv%207%5E1%20%3D%207%5E%7B7-1%7D%3D7%5E6)
Part e:
![12^{10} \div 12^5 = 12^{10-5}=12^5](https://tex.z-dn.net/?f=12%5E%7B10%7D%20%5Cdiv%2012%5E5%20%3D%2012%5E%7B10-5%7D%3D12%5E5)
Part f:
![(6^3)^6 = 6^{6 \times 3} = 6^{18}](https://tex.z-dn.net/?f=%286%5E3%29%5E6%20%3D%206%5E%7B6%20%5Ctimes%203%7D%20%3D%206%5E%7B18%7D)
These should be all the answers. Let me know if you need any clarifications, thanks!
Hi!
For this question, you want to find the volume of each aquarium. To find volume, just multiply all the dimensions dogether.
For the small aquarium: 3 * 1.5 * 2 = 9 feet cubed
For the large aquarium: 6 * 3 * 4 = 72 feet cubed
Therefore, no, he is not correct, as the large aquarium holds 8 times as much water as the small one. Option D is correct.
If you would like a faster way to do this, if you look at the two dimensions, you'll see each dimension for the large aquarium is two times the respective dimensions of the small one. Since there are three dimensions, and each is two times larger, you can just do 2 * 2 * 2 to get 8 times, as the dimensions are all multiplied with one another.
Hope this helped!
Answer:
b.
It's too short. Write at least 20 characters to explain it well
Answer:
D.
The length of the granite must be less than 120 inches.
Step-by-step explanation:
Let x inches be the widht of the section. If the length is 3 times the width, then the length is 3x inches.
The perimeter of the rectangle is
![P=2(\text{width + length})](https://tex.z-dn.net/?f=P%3D2%28%5Ctext%7Bwidth%20%2B%20length%7D%29)
Hence,
![P=2(x+3x)=2\cdot 4x=8x](https://tex.z-dn.net/?f=P%3D2%28x%2B3x%29%3D2%5Ccdot%204x%3D8x)
The perimeter of the section must be less than 320 inches, so
![8x](https://tex.z-dn.net/?f=8x%3C320%5C%5C%20%5C%5Cx%3C40%5C%5C%20%5C%5C3x%3C120)