Answers:
<u>5) A.) 26</u> and <u>6) D.) 30</u>
Step-by-step explanations:
<em>Question 5)</em>
For this question, we need to analyze the graph given and look at how many people scored 601 or above on the math portion. So, looking at the answers given we aren't going to have a smaller number of only 16 or 10, since they are both equal to or higher than 601. So, we need to add the amount of students that scored the 601 or higher amount.
16 + 10 = 26.
This answer matches up with the answer given of A).
<em>Question 6)</em>
For this question, it is similar except you don't add the numbers given. Instead, the question is asking for a specific amount given. So, looking at the answers given, yes 18 and 6 did score below 500, but the question asked "...scored <u>500 or below</u>?" This is a specific question telling us about the 500 or below, which is in one column. As shown in the graph, 30 students scored this specific amount, which gives us our answer of D).
I hope that this helps.
Assume the bigger number is x, since the difference is 18, another one should be x - 18
So the product will be x(x-18) = x^2 - 18x = (x-9)^2 - 81
Since the minimum of (x-9)^2 is 0, then the minimum of the product is -81
The solution for the given system of equations x + 8y = -37, 4x + 8y = -52 is ![\left[\begin{array}{ccc}&5&\\\\&4&\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%265%26%5C%5C%5C%5C%264%26%5Cend%7Barray%7D%5Cright%5D)
Given,
System of equations as,
x + 8y = -37
4x + 8y = -52
We have to solve this by using the inverse of coefficient matrix of the equivalent matrix equation.
That is,
![A=\left[\begin{array}{ccc}a&&b\\\\c&&d\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26%26b%5C%5C%5C%5Cc%26%26d%5Cend%7Barray%7D%5Cright%5D)
![A^{-1} =\frac{1}{ad -bc} \left[\begin{array}{ccc}d&&-b\\\\-c&&a\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%5Cfrac%7B1%7D%7Bad%20-bc%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26%26-b%5C%5C%5C%5C-c%26%26a%5Cend%7Barray%7D%5Cright%5D)
Now we can solve the equations.
Here we have,
x + 8y = -37
4x + 8y = -52
Now in matrix form,
![\left[\begin{array}{ccc}1&&8\\\\4&&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26%268%5C%5C%5C%5C4%26%268%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}&x&\\\\&y&\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26x%26%5C%5C%5C%5C%26y%26%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{ccc}&-37&\\\\&-52&\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26-37%26%5C%5C%5C%5C%26-52%26%5Cend%7Barray%7D%5Cright%5D)
A X B
We know that,
Therefore,
![A^{-1} = \frac{1}{(1X8)-(4X8)} \left[\begin{array}{ccc}8&&-8\\\\-4&&1\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%3D%20%5Cfrac%7B1%7D%7B%281X8%29-%284X8%29%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26%26-8%5C%5C%5C%5C-4%26%261%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{8-32} \left[\begin{array}{ccc}8&&-8\\\\-4&&1\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B8-32%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26%26-8%5C%5C%5C%5C-4%26%261%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{-24} \left[\begin{array}{ccc}8&&-8\\\\-4&&1\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B-24%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D8%26%26-8%5C%5C%5C%5C-4%26%261%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{ccc}\frac{-8}{24} &&\frac{8}{24} \\\\\frac{4}{24} &&\frac{-1}{24} \end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B-8%7D%7B24%7D%20%26%26%5Cfrac%7B8%7D%7B24%7D%20%5C%5C%5C%5C%5Cfrac%7B4%7D%7B24%7D%20%26%26%5Cfrac%7B-1%7D%7B24%7D%20%5Cend%7Barray%7D%5Cright%5D)
Then,
![\left[\begin{array}{ccc}&x&\\\\&y&\end{array}\right] =](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26x%26%5C%5C%5C%5C%26y%26%5Cend%7Barray%7D%5Cright%5D%20%3D)
![\left[\begin{array}{ccc}&\frac{37}{52} &\\\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26%5Cfrac%7B37%7D%7B52%7D%20%26%5C%5C%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{24} \left[\begin{array}{ccc}-8&&8\\\\4&&-1\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B24%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%26%268%5C%5C%5C%5C4%26%26-1%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{24} \left[\begin{array}{ccc}(-8X37)+(8X52)\\\\(4X37)+(-1X52)\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B24%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28-8X37%29%2B%288X52%29%5C%5C%5C%5C%284X37%29%2B%28-1X52%29%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{24} \left[\begin{array}{ccc}-296+416\\\\148-52\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B24%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-296%2B416%5C%5C%5C%5C148-52%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{24} \left[\begin{array}{ccc}120\\\\96\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B24%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D120%5C%5C%5C%5C96%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{ccc}\frac{120}{24} \\\\\frac{96}{24} \end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B120%7D%7B24%7D%20%5C%5C%5C%5C%5Cfrac%7B96%7D%7B24%7D%20%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{ccc}5\\\\4\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C%5C%5C4%5Cend%7Barray%7D%5Cright%5D)
That is ![\left[\begin{array}{ccc}x\\\\y\end{array}\right] =\left[\begin{array}{ccc}5\\\\4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5C%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C%5C%5C4%5Cend%7Barray%7D%5Cright%5D)
Learn more about matrix equations here: brainly.com/question/27799804
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The question is incomplete. Completed question is given below:
Solve The System Of Equations By Using The Inverse Of The Coefficient Matrix Of The Equivalent Matrix Equation.
x + 8y = -37
4x + 8y = -52
