Answer:
b = -30
Step-by-step explanation:
-b/5 - 27 = -21
~Add 27 to both sides
-1/5b = 6
~Multiply -5 to both sides
b = -30
Best of Luck!
The answer is 6⁴.
Exponent is the number of times the factor is being multiplied. For example:
x * x = x²
x * x * x = x³
x * x * x * x = x⁴
....
So:
6 * 6 * 6 *6 = 6⁴
Answer:
1. 2x + 5
2. 35 students walked
3. 1:18
Step-by-step explanation:
Answer:
Option D. 3.73
Step-by-step explanation:
we know that
![tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}](https://tex.z-dn.net/?f=tan%28x%2By%29%3D%5Cfrac%7Btan%28x%29%2Btan%28y%29%7D%7B1-tan%28x%29tan%28y%29%7D)
and
![sin^{2}(\alpha)+cos^{2}(\alpha)=1](https://tex.z-dn.net/?f=sin%5E%7B2%7D%28%5Calpha%29%2Bcos%5E%7B2%7D%28%5Calpha%29%3D1)
step 1
Find cos(X)
we have
![sin(x)=\frac{1}{2}](https://tex.z-dn.net/?f=sin%28x%29%3D%5Cfrac%7B1%7D%7B2%7D)
we know that
![sin^{2}(x)+cos^{2}(x)=1](https://tex.z-dn.net/?f=sin%5E%7B2%7D%28x%29%2Bcos%5E%7B2%7D%28x%29%3D1)
substitute
![(\frac{1}{2})^{2}+cos^{2}(x)=1](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%2Bcos%5E%7B2%7D%28x%29%3D1)
![cos^{2}(x)=1-\frac{1}{4}](https://tex.z-dn.net/?f=cos%5E%7B2%7D%28x%29%3D1-%5Cfrac%7B1%7D%7B4%7D)
![cos^{2}(x)=\frac{3}{4}](https://tex.z-dn.net/?f=cos%5E%7B2%7D%28x%29%3D%5Cfrac%7B3%7D%7B4%7D)
![cos(x)=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=cos%28x%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
step 2
Find tan(x)
![tan(x)=sin(x)/cos(x)](https://tex.z-dn.net/?f=tan%28x%29%3Dsin%28x%29%2Fcos%28x%29)
substitute
![tan(x)=1/\sqrt{3}](https://tex.z-dn.net/?f=tan%28x%29%3D1%2F%5Csqrt%7B3%7D)
step 3
Find sin(y)
we have
![cos(y)=\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=cos%28y%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
we know that
![sin^{2}(y)+cos^{2}(y)=1](https://tex.z-dn.net/?f=sin%5E%7B2%7D%28y%29%2Bcos%5E%7B2%7D%28y%29%3D1)
substitute
![sin^{2}(y)+(\frac{\sqrt{2}}{2})^{2}=1](https://tex.z-dn.net/?f=sin%5E%7B2%7D%28y%29%2B%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%5E%7B2%7D%3D1)
![sin^{2}(y)=1-\frac{2}{4}](https://tex.z-dn.net/?f=sin%5E%7B2%7D%28y%29%3D1-%5Cfrac%7B2%7D%7B4%7D)
![sin^{2}(y)=\frac{2}{4}](https://tex.z-dn.net/?f=sin%5E%7B2%7D%28y%29%3D%5Cfrac%7B2%7D%7B4%7D)
![sin(y)=\frac{\sqrt{2}}{2}](https://tex.z-dn.net/?f=sin%28y%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D)
step 4
Find tan(y)
![tan(y)=sin(y)/cos(y)](https://tex.z-dn.net/?f=tan%28y%29%3Dsin%28y%29%2Fcos%28y%29)
substitute
![tan(y)=1](https://tex.z-dn.net/?f=tan%28y%29%3D1)
step 5
Find tan(x+y)
![tan(x+y)=\frac{tan(x)+tan(y)}{1-tan(x)tan(y)}](https://tex.z-dn.net/?f=tan%28x%2By%29%3D%5Cfrac%7Btan%28x%29%2Btan%28y%29%7D%7B1-tan%28x%29tan%28y%29%7D)
substitute
![tan(x+y)=[1/\sqrt{3}+1}]/[{1-1/\sqrt{3}}]=3.73](https://tex.z-dn.net/?f=tan%28x%2By%29%3D%5B1%2F%5Csqrt%7B3%7D%2B1%7D%5D%2F%5B%7B1-1%2F%5Csqrt%7B3%7D%7D%5D%3D3.73)