Answer:
6(−1/2)−2
=−3−2
=−5
Step-by-step explanation:
c(t) = t/72 represents the number of cases the coach will
need to purchase to have a total of t tennis balls.
I am hoping that this answer has
satisfied your query and it will be able to help you in your endeavor, and if
you would like, feel free to ask another question.
Answer:
<h3>Each of the given matrix equations does not represent this system of equations.</h3>
Step-by-step explanation:
![\left\{\begin{array}{ccc}2x-3=2y\\y-5x=14\end{array}\right\\\\\text{Let's convert the system of equations to form}\\\\\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{array}\right\\\\\left\{\begin{array}{ccc}2x-3=2y&(1)\\y-5x=14&(2)\end{array}\right\\\\(1)\ 2x-3=2y\qquad\text{add 3 to both sides}\\2x=2y+3\qquad\text{subtract}\ 2y\ \text{From both sides}\\\boxed{2x-2y=3}\\(2)\ y-5x=14\\\boxed{-5x+y=14}\\\\\text{We get the system of equations in the form we need.}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-3%3D2y%5C%5Cy-5x%3D14%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BLet%27s%20convert%20the%20system%20of%20equations%20to%20form%7D%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Da_1x%2Bb_1y%3Dc_1%5C%5Ca_2x%2Bb_2y%3Dc_2%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-3%3D2y%26%281%29%5C%5Cy-5x%3D14%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%281%29%5C%202x-3%3D2y%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C2x%3D2y%2B3%5Cqquad%5Ctext%7Bsubtract%7D%5C%202y%5C%20%5Ctext%7BFrom%20both%20sides%7D%5C%5C%5Cboxed%7B2x-2y%3D3%7D%5C%5C%282%29%5C%20y-5x%3D14%5C%5C%5Cboxed%7B-5x%2By%3D14%7D%5C%5C%5C%5C%5Ctext%7BWe%20get%20the%20system%20of%20equations%20in%20the%20form%20we%20need.%7D)
![\left\{\begin{array}{ccc}2x-2y=3\\-5x+y=14\end{array}\right\\\\\text{The first matrix is the matrix of coefficients at x and y.}\\\\\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\end{array}\right] \Rightarrow\left[\begin{array}{ccc}2&-2\\-5&1\end{array}\right]\\\\\text{The second matrix is the matrix:}\\\\\left[\begin{array}{ccc}x\\y\end{array}\right]\\\\\text{The third matrix is the matrix of numbers from the right side of the equation.}\\\\\left[\begin{array}{ccc}c_1\\c_2\end{array}\right]\Rightarrow\left[\begin{array}{ccc}3\\14\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-2y%3D3%5C%5C-5x%2By%3D14%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BThe%20first%20matrix%20is%20the%20matrix%20of%20coefficients%20at%20x%20and%20y.%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_1%26b_1%5C%5Ca_2%26b_2%5Cend%7Barray%7D%5Cright%5D%20%5CRightarrow%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-2%5C%5C-5%261%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Ctext%7BThe%20second%20matrix%20is%20the%20matrix%3A%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Ctext%7BThe%20third%20matrix%20is%20the%20matrix%20of%20numbers%20from%20the%20right%20side%20of%20the%20equation.%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc_1%5C%5Cc_2%5Cend%7Barray%7D%5Cright%5D%5CRightarrow%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C14%5Cend%7Barray%7D%5Cright%5D)
![\text{Therefore we have:}\\\\\left[\begin{array}{ccc}2&-2\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}3\\14\end{array}\right]](https://tex.z-dn.net/?f=%5Ctext%7BTherefore%20we%20have%3A%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-2%5C%5C-5%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C14%5Cend%7Barray%7D%5Cright%5D)
For every one boy, there is five and a half girls