Answer:
75
Step-by-step explanation:
15 divided by .20 = 75
Answer:
x = 94
Step-by-step explanation:
(86 + x)/2 = 90
86 + x = 180
x = 94
I would assume that he's using a 90° rotation.
1/10 of all take 2/5 time
10/10=10 times 1/10
so 10 times 2/5 time=20/5=4 days to finish 1 order
4 days
Answer:
The pair which are inverse of each other are:
Option: C
![f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}](https://tex.z-dn.net/?f=f%28x%29%3D11x-4%5C%20and%5C%20g%28x%29%3D%5Cdfrac%7Bx%2B4%7D%7B11%7D)
Step-by-step explanation:
Two functions f(x) and g(x) are said to be inverse of each other if:
fog(x)=gof(x)=x
i.e. the composition of two functions give identity no matter what the order is.
A)
and ![g(x)=12x-15](https://tex.z-dn.net/?f=g%28x%29%3D12x-15)
Now we calculate fog(x):
![fog(x)=f(g(x))\\\\fog(x)=f(12x-15)\\\\fog(x)=\dfrac{12x-15}{12}+15\\\\fog(x)=x-\dfrac{15}{12}+15\\\\fog(x)=x-\dfrac{55}{4}\neq x](https://tex.z-dn.net/?f=fog%28x%29%3Df%28g%28x%29%29%5C%5C%5C%5Cfog%28x%29%3Df%2812x-15%29%5C%5C%5C%5Cfog%28x%29%3D%5Cdfrac%7B12x-15%7D%7B12%7D%2B15%5C%5C%5C%5Cfog%28x%29%3Dx-%5Cdfrac%7B15%7D%7B12%7D%2B15%5C%5C%5C%5Cfog%28x%29%3Dx-%5Cdfrac%7B55%7D%7B4%7D%5Cneq%20x)
Hence, option: A is incorrect.
B)
![f(x)=\dfrac{3}{x}-10\ and\ g(x)=\dfrac{x+10}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B3%7D%7Bx%7D-10%5C%20and%5C%20g%28x%29%3D%5Cdfrac%7Bx%2B10%7D%7B2%7D)
Now we calculate fog(x):
![fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+10}{3})\\\\fog(x)=\dfrac{3}{\dfrac{x+10}{3}}-10\\\\fog(x)=\dfrac{9}{x+10}-10\neq x](https://tex.z-dn.net/?f=fog%28x%29%3Df%28g%28x%29%29%5C%5C%5C%5Cfog%28x%29%3Df%28%5Cdfrac%7Bx%2B10%7D%7B3%7D%29%5C%5C%5C%5Cfog%28x%29%3D%5Cdfrac%7B3%7D%7B%5Cdfrac%7Bx%2B10%7D%7B3%7D%7D-10%5C%5C%5C%5Cfog%28x%29%3D%5Cdfrac%7B9%7D%7Bx%2B10%7D-10%5Cneq%20x)
Hence, option: B is incorrect.
D)
![f(x)=9+\sqrt[3]{x}\ and\ g(x)=9-x^3](https://tex.z-dn.net/?f=f%28x%29%3D9%2B%5Csqrt%5B3%5D%7Bx%7D%5C%20and%5C%20g%28x%29%3D9-x%5E3)
Now we calculate fog(x):
![fog(x)=f(g(x))\\\\fog(x)=f(9-x^3)](https://tex.z-dn.net/?f=fog%28x%29%3Df%28g%28x%29%29%5C%5C%5C%5Cfog%28x%29%3Df%289-x%5E3%29)
![fog(x)=9+\sqrt[3]{9-x^3}\neq x](https://tex.z-dn.net/?f=fog%28x%29%3D9%2B%5Csqrt%5B3%5D%7B9-x%5E3%7D%5Cneq%20x)
Hence, option: D is incorrect.
C)
![f(x)=11x-4\ and\ g(x)=\dfrac{x+4}{11}](https://tex.z-dn.net/?f=f%28x%29%3D11x-4%5C%20and%5C%20g%28x%29%3D%5Cdfrac%7Bx%2B4%7D%7B11%7D)
Now we calculate fog(x):
![fog(x)=f(g(x))\\\\fog(x)=f(\dfrac{x+4}{11})](https://tex.z-dn.net/?f=fog%28x%29%3Df%28g%28x%29%29%5C%5C%5C%5Cfog%28x%29%3Df%28%5Cdfrac%7Bx%2B4%7D%7B11%7D%29)
![fog(x)=11\times (\dfrac{x+4}{11})-4\\\\fog(x)=x+4-4\\\\fog(x)=x](https://tex.z-dn.net/?f=fog%28x%29%3D11%5Ctimes%20%28%5Cdfrac%7Bx%2B4%7D%7B11%7D%29-4%5C%5C%5C%5Cfog%28x%29%3Dx%2B4-4%5C%5C%5C%5Cfog%28x%29%3Dx)
Similarly,
![gof(x)=g(f(x))\\\\gof(x)=g(11x-4)\\\\gof(x)=\dfrac{11x-4+4}{11}\\\\gof(x)=\dfrac{11x}{11}\\\\gof(x)=x](https://tex.z-dn.net/?f=gof%28x%29%3Dg%28f%28x%29%29%5C%5C%5C%5Cgof%28x%29%3Dg%2811x-4%29%5C%5C%5C%5Cgof%28x%29%3D%5Cdfrac%7B11x-4%2B4%7D%7B11%7D%5C%5C%5C%5Cgof%28x%29%3D%5Cdfrac%7B11x%7D%7B11%7D%5C%5C%5C%5Cgof%28x%29%3Dx)
Hence, option: C is the correct option.