Answer:
an apparent solution that must be rejected because it does not satisfy the original equation.
Step-by-step explanation:
Answer:
<h3>
The width (side perpedicular to the barn):
<u>x = 8 m</u></h3><h3> The lenght (side parallel to the barn):
<u>y = 16 m</u> </h3>
Step-by-step explanation:
x - the width of the barn
She has 32 m of fencing so for the lenght remain (32-2x) m of fencing:
y = 32 - 2x
Area of the fencing: A = x•y
A(x) = x•(32 - 2x)
A(x) = -2x² + 32x ← quadratic function
The maximum value of quadratic function occurs at: 
a = -2, b = 32

32-2x = 32 - 2•8 = 16
It's not reasonable to give him 4 gallons because that's way too much for a dog bowl.
The matrix should be this:
<span>
![\left[\begin{array}{ccc}2&-3\\1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%261%5Cend%7Barray%7D%5Cright%5D%20)
</span>
I say subcategory would be a good answer