Answer:
The expression used to represent g(x) as inverse of f(x) is ![\frac{1}{5}(5x-25)+5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%285x-25%29%2B5)
Option B is correct.
Step-by-step explanation:
We are given:
![f(x)= 5x-25\\g(x)=\frac{1}{5}x+5](https://tex.z-dn.net/?f=f%28x%29%3D%205x-25%5C%5Cg%28x%29%3D%5Cfrac%7B1%7D%7B5%7Dx%2B5)
We need to find the expression that could be used to verify g(x) is the inverse of f(x).
We know that
is inverse of function
So placing value of f(x) in g(x)
![g(f(x))=\frac{1}{5}(5x-25)+5](https://tex.z-dn.net/?f=g%28f%28x%29%29%3D%5Cfrac%7B1%7D%7B5%7D%285x-25%29%2B5)
So, the expression used to represent g(x) as inverse of f(x) is ![\frac{1}{5}(5x-25)+5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B5%7D%285x-25%29%2B5)
Option B is correct.
We can also solve to prove that ![g(f(x))=x](https://tex.z-dn.net/?f=g%28f%28x%29%29%3Dx)
![g(f(x))=\frac{1}{5}(5x-25)+5\\g(f(x))=\frac{5}{5}(x-5)+5\\g(f(x))=x-5+5\\g(f(x))=x](https://tex.z-dn.net/?f=g%28f%28x%29%29%3D%5Cfrac%7B1%7D%7B5%7D%285x-25%29%2B5%5C%5Cg%28f%28x%29%29%3D%5Cfrac%7B5%7D%7B5%7D%28x-5%29%2B5%5C%5Cg%28f%28x%29%29%3Dx-5%2B5%5C%5Cg%28f%28x%29%29%3Dx)
The history museum is less that 9 4/5 miles. 9/10 means that the 9 3/4 mile is broken up into 10 equal parts and the distance to the museum is only 9 of those parts. 9 3/4 (9.8) divided by 10 equals 98/100 (.98)
98/100 x 9 = 882/100 or 8.82
Justin's house is 8.82 miles from the museum.
Answer:(6,-1)
Explanation:The slope of the line can be calculated using the following formula:
slope =
We are given that:slope = -0.75
point (x1,y1) is (-2,5)
We will use each of the given points to calculate the corresponding slope, then compare the calculated slope with the given one.
For point (6,-1):slope =
![\frac{-1-5}{6--2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-1-5%7D%7B6--2%7D%20)
= -0.75 ........> accepted choice
For point (2,8):slope =
![\frac{8-5}{2--2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8-5%7D%7B2--2%7D%20)
= 0.75 ........> rejected choice
For point (-5,1):slope =
![\frac{1-5}{-5--2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1-5%7D%7B-5--2%7D%20)
= 4/3 ........> rejected choice
For point (1,1):slope =
![\frac{1-5}{1--2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1-5%7D%7B1--2%7D%20)
= -4/3 ........> rejected choice
Therefore, the first option is the only correct one.
Hope this helps :)
The answer is going to be D