Answer:

Step-by-step explanation:
![volume = \frac{4}{3} \pi {r}^{3} \\ \\ 288\pi = \frac{4}{3} \pi {r}^{3} \\ \\ 3(288\pi) = 4\pi {r}^{3} \\ \\ \frac{3(288\pi)}{4\pi} = {r}^{3} \\ \\ 216 = {r}^{3} \\ \\ r = \sqrt[3]{216} \\ r = 6](https://tex.z-dn.net/?f=volume%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20288%5Cpi%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20%5C%5C%20%20%5C%5C%203%28288%5Cpi%29%20%3D%204%5Cpi%20%7Br%7D%5E%7B3%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B3%28288%5Cpi%29%7D%7B4%5Cpi%7D%20%20%3D%20%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20216%20%3D%20%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20r%20%3D%20%20%5Csqrt%5B3%5D%7B216%7D%20%20%5C%5C%20r%20%3D%206)

Answer:
7x^2-20
Step-by-step explanation:
Answer:
2y = x + 2
Step-by-step explanation:
Looking at the graph, we can see from one point to the next (from right to left), the x-value rises by 2 and the y-value by 1;
From this we can work out the gradient between two points using the formula, i.e. the change/difference in y divided by the change/difference in x:

Joining the points gives a straight line, which means a constant gradient of ¹/₂
Use the line equation formula to get the function:
y - y₁ = m(x - x₁)
m = ¹/₂
x₁ = 0
y₁ = 1
y - 1 = ¹/₂.(x - 0)
y - 1 = ¹/₂.x
2y - 2 = x
2y = x + 2
Basically the question is asking if the proportions for the dimensions of the 2 rugs are the same, so in this case yes, since 6 X 8 can be written as 3 X 4 which if you set up a fraction you can easily multiply both the top and bottom number by 3 to get 9 X 12.