Answer:
![3n + 2 \geqslant 8](https://tex.z-dn.net/?f=3n%20%2B%202%20%5Cgeqslant%208)
Step-by-step explanation:
2 more than 3 time mean 3n+2
"is atleast 8" means it can be 8 or more so c. is right answer
Answer:
Simplifying the expression
we get ![\mathbf{108}](https://tex.z-dn.net/?f=%5Cmathbf%7B108%7D)
Step-by-step explanation:
We need to simplify the expression ![(6^{-2})(3^{-3})(3*6)^4](https://tex.z-dn.net/?f=%286%5E%7B-2%7D%29%283%5E%7B-3%7D%29%283%2A6%29%5E4)
Solving:
![(6^{-2})(3^{-3})(3*6)^4](https://tex.z-dn.net/?f=%286%5E%7B-2%7D%29%283%5E%7B-3%7D%29%283%2A6%29%5E4)
Applying exponent rule: ![a^{-m}=\frac{1}{a^m}](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Ba%5Em%7D)
![=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B%286%5E%7B2%7D%29%7D%5Cfrac%7B1%7D%7B%283%5E%7B3%7D%29%7D%2818%29%5E4%5C%5C%3D%5Cfrac%7B%2818%29%5E4%7D%7B6%5E%7B2%7D%5C%3A.%5C%3A3%5E%7B3%7D%7D%20%5C%5C)
Factors of ![18=2\times 3\times 3=2\times3^2](https://tex.z-dn.net/?f=18%3D2%5Ctimes%203%5Ctimes%203%3D2%5Ctimes3%5E2)
Factors of ![6=2\times 3](https://tex.z-dn.net/?f=6%3D2%5Ctimes%203)
Replacing terms with factors
![=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%282%5Ctimes3%5E2%29%5E4%7D%7B%282%5Ctimes%203%29%5E%7B2%7D%5C%3A.%5C%3A3%5E%7B3%7D%7D%20%5C%5C%3D%5Cfrac%7B%282%29%5E4%5Ctimes%283%5E2%29%5E4%7D%7B%282%29%5E2%5Ctimes%20%283%29%5E%7B2%7D%5C%3A.%5C%3A3%5E%7B3%7D%7D%20%5C%5C)
Using exponent rule: ![(a^m)^n=a^{m\times n}](https://tex.z-dn.net/?f=%28a%5Em%29%5En%3Da%5E%7Bm%5Ctimes%20n%7D)
![=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%282%29%5E4%5Ctimes%283%29%5E8%7D%7B%282%29%5E2%5Ctimes%20%283%29%5E%7B2%7D%5C%3A.%5C%3A3%5E%7B3%7D%7D%20%5C%5C%3D%5Cfrac%7B2%5E4%5Ctimes%203%5E8%7D%7B2%5E2%5Ctimes%203%5E%7B2%7D%5C%3A.%5C%3A3%5E%7B3%7D%7D)
Using exponent rule: ![a^m.a^n=a^{m+n}](https://tex.z-dn.net/?f=a%5Em.a%5En%3Da%5E%7Bm%2Bn%7D)
![=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%5E4%5Ctimes%203%5E8%7D%7B2%5E2%5Ctimes%203%5E%7B2%2B3%7D%7D%5C%5C%3D%5Cfrac%7B2%5E4%5Ctimes%203%5E8%7D%7B2%5E2%5Ctimes%203%5E%7B5%7D%7D)
Now using exponent rule: ![\frac{a^m}{a^n}=a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D)
![=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108](https://tex.z-dn.net/?f=%3D2%5E%7B4-2%7D%5Ctimes%203%5E%7B8-5%7D%5C%5C%3D2%5E%7B2%7D%5Ctimes%203%5E%7B3%7D%5C%5C%3D4%5Ctimes%2027%5C%5C%3D108)
So, simplifying the expression
we get ![\mathbf{108}](https://tex.z-dn.net/?f=%5Cmathbf%7B108%7D)
Tan(x)= 33/105
x = arctan(33/105)
x = 17.44718842 degrees.
Answer:
3.024 is greater.
Step-by-step explanation:
3.05 is greater because it expanded is 3.050 vs. 3.024. 3.024 is closer to 1, so it's greater.
1. D 12 2/7
2. 22 7/9 which is B hope this helps