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geekymuin
04.12.2020 •
Mathematics
Mr. MacArthur’s art class plans to paint a square mural on the side of the art building. The monthly art budget allows for no more than 6 quarts of paint to be purchased. The situation can be modeled by the square root function s(x), the maximum side length of the square mural if x quarts of paint are used to paint the mural. Which statement best compares and contrasts the domain and range of the mathematical function, s(x), to the reason
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Ответ:
Step-by-step explanation:
So the first step is to simply set up the problem based on what we are given. So here have two numbers, we are going to call the first number x and the second one y. With that now addressed, we can now proceed with the setup.
So the difference between the squares of the numbers is 24. So we have:
Then it says that three times the square of the first number (which we said was x) increased by the square of the second number is 76. So:
Now we can see that this is simply a system of equations and we can use elimination to solve this! We even have the setup already as the coefficients in front of our y are opposite in sign and are equal. So:
We can cancel our y squared terms out and that leaves, when we add the equations together:
We can then solve for x by diving by four and taking the square root of the result.
Therefore, x = ±5
We have both negative and positive answers because if we squared -5 or +5 they would both give us 25. So we cant rule a negative answer out yet.
So now we can plug in x = -5 or +5 to either equation to solve for y as so:
So y = ±1
In this case both negative and positive versions of our answer work (you can also double check), so we are left with:
x = ±5 and y = ±1