Let
x-----> the number of hours that Candice spent doing her homework
y-----> the number of hours that Ronald spent doing his homework
we know that

convert mixed number to an improper fraction

so
-------> equation A
------> equation B
Substitute equation A in equation B

convert an improper fraction to a mixed number

therefore
<u>the answer is the option B</u>

A. -2x + 3y = -15
-2x + 2x + 3y = 2x - 15
3y = 2x - 15
3 3
y = ²/₃ - 5
A is correct.
B. y = ²/₃ - 5
B is also correct.
C. 6y = 4x - 30
6 6
y = ²/₃x - 5
C is also correct.
D. y + 3 = ²/₃(x - 3)
y + 3 = ²/₃(x) - ²/₃(3)
y + 3 = ²/₃x - 2
- 3 - 3
y = ²/₃x - 5
D is also correct.
The answer to the problem is A, B, C, and D.
Answer:
A.![2(3^{\frac{1}{3}})-\sqrt[3]{18}](https://tex.z-dn.net/?f=2%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-%5Csqrt%5B3%5D%7B18%7D)
Step-by-step explanation:
We are given that
![\frac{6-3(\sqrt[3]{6}}{\sqrt[3]{9}})](https://tex.z-dn.net/?f=%5Cfrac%7B6-3%28%5Csqrt%5B3%5D%7B6%7D%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D%29)
We have to find the quotient.
![\frac{6}{\sqrt[3]{9}}-3(\frac{\sqrt[3]{6}}{\sqrt[3]{9}})](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D-3%28%5Cfrac%7B%5Csqrt%5B3%5D%7B6%7D%7D%7B%5Csqrt%5B3%5D%7B9%7D%7D%29)
![\frac{2\times 3}{\sqrt[3]{3^2}}-3(\frac{\sqrt[3]{3\times 2}}{\sqrt[3]{3^2}})](https://tex.z-dn.net/?f=%5Cfrac%7B2%5Ctimes%203%7D%7B%5Csqrt%5B3%5D%7B3%5E2%7D%7D-3%28%5Cfrac%7B%5Csqrt%5B3%5D%7B3%5Ctimes%202%7D%7D%7B%5Csqrt%5B3%5D%7B3%5E2%7D%7D%29)

Using the property


Using the property




![2(3^{\frac{1}{3}})-2^{\frac{1}{3}}\times \sqrt[3]{3^2}](https://tex.z-dn.net/?f=2%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%20%5Csqrt%5B3%5D%7B3%5E2%7D)
![2(3^{\frac{1}{3}})-2^{\frac{1}{3}}\times \sqrt[3]{9}](https://tex.z-dn.net/?f=2%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-2%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%20%5Csqrt%5B3%5D%7B9%7D)
![2(3^{\frac{1}{3}})-\sqrt[3]{2\times 9}](https://tex.z-dn.net/?f=2%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-%5Csqrt%5B3%5D%7B2%5Ctimes%209%7D)
![2(3^{\frac{1}{3}})-\sqrt[3]{18}](https://tex.z-dn.net/?f=2%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-%5Csqrt%5B3%5D%7B18%7D)
Hence, the quotient of
is given by
![2(3^{\frac{1}{3}})-\sqrt[3]{18}](https://tex.z-dn.net/?f=2%283%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-%5Csqrt%5B3%5D%7B18%7D)
Option A is correct.