7y = 8x -14
Let's make x the subject of the formula
8x = 7y + 14
x = (7y + 14)/8
Substitute the value of y (y = 6)
x = (7(6) + 14)/8 = 7
Answer:
![r = 0.01](https://tex.z-dn.net/?f=r%20%3D%200.01)
Step-by-step explanation:
In order to find r we have to square both sides of the equation
![0.1 = \sqrt{r} \\ {0.1}^{2} = { \sqrt{r} }^{2}](https://tex.z-dn.net/?f=0.1%20%3D%20%20%5Csqrt%7Br%7D%20%5C%5C%20%20%7B0.1%7D%5E%7B2%7D%20%20%3D%20%20%7B%20%5Csqrt%7Br%7D%20%7D%5E%7B2%7D%20)
The *square root* sign cancels out the *squared* sign therefore:
![{0.1}^{2} = r \\ 0.01 = r](https://tex.z-dn.net/?f=%20%7B0.1%7D%5E%7B2%7D%20%20%3D%20r%20%5C%5C%200.01%20%3D%20r)
Answer: ![6\frac{1}{12}\ gallons](https://tex.z-dn.net/?f=6%5Cfrac%7B1%7D%7B12%7D%5C%20gallons)
Step-by-step explanation:
We can make the conversion from mixed numbers to improper fractions:
- Multiply the whole number part by the denominator of the fraction.
- Add the numerator of the fraction and the product obtained (This sum will be the new numerator).
- The denominator is the same.
Then:
![2\frac{1}{4}=\frac{(2*4)+1}{4}=\frac{9}{4}\\\\3\frac{5}{6}=\frac{(6*3)+5}{6}=\frac{23}{6}](https://tex.z-dn.net/?f=2%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B%282%2A4%29%2B1%7D%7B4%7D%3D%5Cfrac%7B9%7D%7B4%7D%5C%5C%5C%5C3%5Cfrac%7B5%7D%7B6%7D%3D%5Cfrac%7B%286%2A3%29%2B5%7D%7B6%7D%3D%5Cfrac%7B23%7D%7B6%7D)
We need to add the fractions in order to calculate the amount of paint Darren bought. Since the denominators are differente, we must find the Least Common Denominator (LCD):
![4=2*2=2^2\\\\6=2*3\\\\\\LCD=2^2*3=12](https://tex.z-dn.net/?f=4%3D2%2A2%3D2%5E2%5C%5C%5C%5C6%3D2%2A3%5C%5C%5C%5C%5C%5CLCD%3D2%5E2%2A3%3D12)
Then:
![\frac{9}{4}+\frac{23}{6}=\frac{27+46}{12}=\frac{73}{12}\ gallons](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B4%7D%2B%5Cfrac%7B23%7D%7B6%7D%3D%5Cfrac%7B27%2B46%7D%7B12%7D%3D%5Cfrac%7B73%7D%7B12%7D%5C%20gallons)
To convert this improper fraction to a mixed number:
- When you divide 73 by 12 you get a quotient of 6. This will be the whole number.
- The remainder obtained is 1. This will be the numerator of the fraction.
- The denominator does not change.
Then:
![\frac{73}{12}\ gallons=6\frac{1}{12}\ gallons](https://tex.z-dn.net/?f=%5Cfrac%7B73%7D%7B12%7D%5C%20gallons%3D6%5Cfrac%7B1%7D%7B12%7D%5C%20gallons)
13. For question 13). 4/10, 7/12, 1/2