Step-by-step explanation:

Factor by grouping,

Complete the square, with the x variables,

Factor out 25 for the y variables

Complete the square

Simplify the perfect square trinomial

Make the right side be 1 so divide everything by 25.

Here our center is (7,2).
Answer:
3
Step-by-step explanation:
There's only 3 prizes thus meaning only 3 people can be awarded
Answer: 5, 3,
, D
<u>Step-by-step explanation:</u>
-5 < 0 so f(-5) = | -5 | = 5
-3 < 0 so f(-3) = | -3 | = 3
6 > 0 so f(6) = 
graph D <em>(since x can equal zero)</em>
m x H = ![\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%2637.5%26-12.5%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Step 1; Multiply 5 with this matrix
and we get a matrix ![\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%2610%5C%5C20%2640%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Multiply the fraction
with the matrix
and we get ![\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-%5Cfrac%7B2m%7D%7B5%7D%20%26%5Cfrac%7B4m%7D%7B5%7D%20%5C%5C%5Cfrac%7B8m%7D%7B5%7D%20%26%5Cfrac%7B16m%7D%7B5%7D%20%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Step2; Now equate corresponding values of the matrices with each other.
-5 =
and so on. By equating we get the value of m as 
Step 3; Add the matrices to get the value of matrix m.
Adding the three matrices on the RHS we get
.
Step 4; Adding the matrices on the LHS we get the resulting matrix as H +
. Equating the matrices from step 3 and 4 we get the value of H as ![\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%26-1%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Step 5; Now to find the value of m x H we need to multiply the value of
with the matrix
Step 6; Multiplying we get the matrix m x H = [ -25
]
264
132 * 2
66 * 2 * 2
33 * 2 * 2 * 2
11 * 3 * 2 * 2 * 2 <== or can also be written as 11 * 3 * 2^3