Ok Skylar what is (this)?
$100 - $61
$39 (how much you need for the price to become equal)
$15 - $12
$3 (how much cheaper it is per uniform)
$39/$3
13 uniforms is where it is equal
14 uniforms is where it is a better deal
Answer:

Step-by-step explanation:
Given is a non homogeneous second degree equation as

Auxialary equation is

Hence general solution is
x = Acos 2t + B sin 2t
Particular integral is = 
Since t has coefficient 1, we substitute

Hence full solution is

In order to multiply a matrix by another matrix, we multiply the rows in the first matrix by the columns in the other matrix (How this is done is shown below)
To determine the pairs of matrices that AB=BA, we will determine AB and BA for each of the options below.
For the first option
![A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-2%261%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-2\times5)+(1\times3)&(-2\times0)+(1\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-10+3&0+2&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&-7&2&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes5%29%2B%280%5Ctimes3%29%26%281%5Ctimes0%29%2B%280%5Ctimes%202%29%26%28-2%5Ctimes5%29%2B%281%5Ctimes3%29%26%28-2%5Ctimes0%29%2B%281%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%26-10%2B3%260%2B2%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%26-7%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(5\times1)+(0\times-2)&(5\times0)+(0\times 1)&(3\times1)+(2\times-2)&(3\times0)+(1\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-4&0+2&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&-1&2&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%285%5Ctimes1%29%2B%280%5Ctimes-2%29%26%285%5Ctimes0%29%2B%280%5Ctimes%201%29%26%283%5Ctimes1%29%2B%282%5Ctimes-2%29%26%283%5Ctimes0%29%2B%281%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%263%2B-4%260%2B2%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
∴ AB≠BA
For the second option
![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%266%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-1\times3)+(2\times6)&(-1\times0)+(2\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-3+12&0+-6&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes3%29%2B%280%5Ctimes6%29%26%281%5Ctimes0%29%2B%280%5Ctimes%20-3%29%26%28-1%5Ctimes3%29%2B%282%5Ctimes6%29%26%28-1%5Ctimes0%29%2B%282%5Ctimes-3%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%26-3%2B12%260%2B-6%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%269%26-6%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(3\times1)+(0\times-1)&(3\times0)+(0\times 2)&(6\times1)+(-3\times-1)&(6\times0)+(-3\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+3&0+-6&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283%5Ctimes1%29%2B%280%5Ctimes-1%29%26%283%5Ctimes0%29%2B%280%5Ctimes%202%29%26%286%5Ctimes1%29%2B%28-3%5Ctimes-1%29%26%286%5Ctimes0%29%2B%28-3%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%266%2B3%260%2B-6%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%269%26-6%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here AB = BA
For the third option
![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-1\times5)+(2\times3)&(-1\times0)+(2\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-5+6&0+4&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes5%29%2B%280%5Ctimes3%29%26%281%5Ctimes0%29%2B%280%5Ctimes%202%29%26%28-1%5Ctimes5%29%2B%282%5Ctimes3%29%26%28-1%5Ctimes0%29%2B%282%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%26-5%2B6%260%2B4%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%261%264%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(5\times1)+(0\times-1)&(5\times0)+(0\times 2)&(3\times1)+(2\times-1)&(3\times0)+(2\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-2&0+4&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%285%5Ctimes1%29%2B%280%5Ctimes-1%29%26%285%5Ctimes0%29%2B%280%5Ctimes%202%29%26%283%5Ctimes1%29%2B%282%5Ctimes-1%29%26%283%5Ctimes0%29%2B%282%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%263%2B-2%260%2B4%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%261%264%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here also, AB=BA
For the fourth option
![A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-2%261%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%266%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-2\times3)+(1\times6)&(-2\times0)+(1\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-6+6&0+-3&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&0&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes3%29%2B%280%5Ctimes6%29%26%281%5Ctimes0%29%2B%280%5Ctimes%20-3%29%26%28-2%5Ctimes3%29%2B%281%5Ctimes6%29%26%28-2%5Ctimes0%29%2B%281%5Ctimes-3%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%26-6%2B6%260%2B-3%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%260%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(3\times1)+(0\times-2)&(3\times0)+(0\times 1)&(6\times1)+(-3\times-2)&(6\times0)+(-3\times1)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+6&0+-3&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&12&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283%5Ctimes1%29%2B%280%5Ctimes-2%29%26%283%5Ctimes0%29%2B%280%5Ctimes%201%29%26%286%5Ctimes1%29%2B%28-3%5Ctimes-2%29%26%286%5Ctimes0%29%2B%28-3%5Ctimes1%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%266%2B6%260%2B-3%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%2612%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here, AB≠BA
Hence, it is only in the second and third options that AB = BA
and ![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5DB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Learn more on matrices multiplication here: brainly.com/question/12755004
Step-by-step explanation:
1.
Subtract the coefficient from both sides, keep 55 on the same side.

Complete the square by dividing the coefficient by two and squaring it.

Use binomial to factor the left side.

2. Solve for x.


Remeber the square root of 64 is also -8 so


So the solutions are -5 and 11