In order to multiply or divide a fraction by a mixed numeral, it is best to have them BOTH in fraction form. 1) We'll convert 1 2/5 into an improper fraction. (1×5)+2 = 7/5
Now 6/7 ÷ 7/5
2) when dividing by a fraction, it is the same to multiply by its reciprocal. So flip the second fraction and multiply them: 6/7 ÷ 7/5 = 6/7 × 5/7
3) reduce them: there is nothing on top that reduces with the bottom, so we simply multiply
4) multiply numerators, then multiply denominators and keep them in place: 6×5 = 30, 7×7 = 49
5) so our final answer is 30/49
Answer is C.9(3r-4) and 27r-36
Step-by-step explanation:
Given that:
The function to represent the growth of Neveah hair is
![f(x)=\dfrac{2x+4}{3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x%2B4%7D%7B3%7D)
where, x represents the number of months since her last hair cut.
To find:
The inverse of function and time when her hair will have grown 6 inches.
Solution:
We have,
![f(x)=\dfrac{2x+4}{3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B2x%2B4%7D%7B3%7D)
Put f(x)=y.
![y=\dfrac{2x+4}{3}](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B2x%2B4%7D%7B3%7D)
Interchange x and y.
![x=\dfrac{2y+4}{3}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B2y%2B4%7D%7B3%7D)
Isolate y.
![3x=2y+4](https://tex.z-dn.net/?f=3x%3D2y%2B4)
![3x-4=2y](https://tex.z-dn.net/?f=3x-4%3D2y)
![\dfrac{3x-4}{2}=y](https://tex.z-dn.net/?f=%5Cdfrac%7B3x-4%7D%7B2%7D%3Dy)
Put
.
![f^{-1}(x)=\dfrac{3x-4}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cdfrac%7B3x-4%7D%7B2%7D)
So, the required inverse function is
. It represents the number of months to grow her hair x inches.
She can predict when her hair will have grown 6 inches by putting x=6 in the inverse function.
Put x=6 in the inverse function.
![f^{-1}(6)=\dfrac{3(6)-4}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%3D%5Cdfrac%7B3%286%29-4%7D%7B2%7D)
![f^{-1}(6)=\dfrac{18-4}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%3D%5Cdfrac%7B18-4%7D%7B2%7D)
![f^{-1}(6)=\dfrac{14}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%3D%5Cdfrac%7B14%7D%7B2%7D)
![f^{-1}(6)=7](https://tex.z-dn.net/?f=f%5E%7B-1%7D%286%29%3D7)
Therefore, growth of her hair is 6 inches in 7 months.
It’s distributive because you multiplied the 2 to the x and the 7.
Since she is increasing by 2 pairs every month, the rate of change is 2 so the slope is 2