Answer:
![\displaystyle g^{-1}(x)=\frac{-7+2x}{x-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%5E%7B-1%7D%28x%29%3D%5Cfrac%7B-7%2B2x%7D%7Bx-2%7D)
Step-by-step explanation:
We are given the function:
![\displaystyle g(x)=-\frac{3}{x-2}+2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20g%28x%29%3D-%5Cfrac%7B3%7D%7Bx-2%7D%2B2)
Let's find the inverse of g.
Call y=g(x):
![\displaystyle y=-\frac{3}{x-2}+2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D-%5Cfrac%7B3%7D%7Bx-2%7D%2B2)
We need to solve for x. Multiply both sides by x-2 to eliminate denominators:
![y(x-2)=-3+2(x-2)](https://tex.z-dn.net/?f=y%28x-2%29%3D-3%2B2%28x-2%29)
Operate:
![yx-2y=-3+2x-4](https://tex.z-dn.net/?f=yx-2y%3D-3%2B2x-4)
Collect the x's to the left side and the rest to the right side of the equation:
![yx-2x=-3-4+2y](https://tex.z-dn.net/?f=yx-2x%3D-3-4%2B2y)
Factor the left side and operate on the right side:
![x(y-2)=-7+2y](https://tex.z-dn.net/?f=x%28y-2%29%3D-7%2B2y)
Solve for x:
![\displaystyle x=\frac{-7+2y}{y-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-7%2B2y%7D%7By-2%7D)
Interchange variables:
![\displaystyle y=\frac{-7+2x}{x-2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%3D%5Cfrac%7B-7%2B2x%7D%7Bx-2%7D)
Call y as the inverse function:
![\boxed{\displaystyle g^{-1}(x)=\frac{-7+2x}{x-2}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdisplaystyle%20g%5E%7B-1%7D%28x%29%3D%5Cfrac%7B-7%2B2x%7D%7Bx-2%7D%7D)
175,900/100 = 1759.00 x 12.5 = $21,987.50
therefore it is $21,988.00
First, you must make sure that since the length is twice as big as the length. That means that the length would be 6.8 because 3.4 x 3.4 = 6.8. Then, since a rectangle has two long sides and two short sides, you add 6.8 + 6.8 + 3.4 + 3.4, which equals 20.4(perimeter).
Your answer is 78.
Area of a triangle: 1/2 base * height
Area of a rectangle: length x width
Calculate the area of all the faces separately and add them up to solve.
Answer:
One pound of jelly beans and one pound of gummy worms candy cost $6 each
Step-by-step explanation:
Given
Let
Jelly Beans
Gummy worms
So, we have:
Brook
![J + 6G = 42](https://tex.z-dn.net/?f=J%20%2B%206G%20%3D%2042)
Ken
![5J + 4G = 54](https://tex.z-dn.net/?f=5J%20%2B%204G%20%3D%2054)
Make J the subject in the first equation
![J + 6G = 42](https://tex.z-dn.net/?f=J%20%2B%206G%20%3D%2042)
![J = 42 - 6G](https://tex.z-dn.net/?f=J%20%3D%2042%20-%206G)
Substitute
in ![5J + 4G = 54](https://tex.z-dn.net/?f=5J%20%2B%204G%20%3D%2054)
![5*[42 - 6G] + 4G = 54](https://tex.z-dn.net/?f=5%2A%5B42%20-%206G%5D%20%2B%204G%20%3D%2054)
Open bracket
![210 - 30G + 4G = 54](https://tex.z-dn.net/?f=210%20-%2030G%20%2B%204G%20%3D%2054)
![210 -26G = 54](https://tex.z-dn.net/?f=210%20-26G%20%3D%2054)
Collect like terms
![-26G = 54 - 210\\](https://tex.z-dn.net/?f=-26G%20%3D%2054%20-%20210%5C%5C)
![-26G = -156](https://tex.z-dn.net/?f=-26G%20%3D%20-156)
Divide both sides by -26
![G = 6](https://tex.z-dn.net/?f=G%20%3D%206)
Substitute
in ![J = 42 - 6G](https://tex.z-dn.net/?f=J%20%3D%2042%20-%206G)
![J = 42 - 6*6](https://tex.z-dn.net/?f=J%20%3D%2042%20-%206%2A6)
![J = 42-36](https://tex.z-dn.net/?f=J%20%3D%2042-36)
![J = 6](https://tex.z-dn.net/?f=J%20%3D%206)