Short answer: C
Let's start with the pen.
The length is x
The width is 3 more.= x + 3
Perimeter of the pen = 2L + 2W
P = 2 L + 2W
P = 2*x + 2(x + 3)
P = 2x + 2x + 6
P = 4x + 6. Leave that for now.
Area of the pen without the doghouse = x(x + 3)
Area of the pen without the doghouse = x^2 + 3x
Area with the doghouse x^2 + 3x - y = 178 (that's his running around space.
Go to the dog house for a Moment
The perimeter of the doghouse and the area are equal and we are told to make them both y.
Area = y
Perimeter = y
Combined facts.
The perimeter of the Pen is three times larger than that of the dog house.
4x + 6 = 3y
The area of the Pen - The area of the doghouse = 178
x^2 + 3x - y = 178
Now what happens is that you have to juggle these two equations so they look like your answer
x^2 + 3x - y = 178
4x + 6 = 3y Subtract 3y from both sides.
4x - 3y + 6 = 0 Subtract 6 from both sides.
4x - 3y = - 6
Answer C
A) 6x + 4x - 6 = 24 + 9x
10x - 9x = 24 + 6
x = 30
b) 25 - 4x = 15 - 3x + 10 - x
25 - 4x = 25 - 4x
Infinite Solutions.
c) 4x + 8 = 2x + 7 + 2x - 20
4x - 4x = 7 - 20 - 8
0 = - 22
No solution
(x - 4)(x^2 + 3x + 2) =
x(x^2 + 3x + 2) - 4(x^2 + 3x + 2) =
x^3 + 3x^2 + 2x - 4x^2 - 12x - 8 =
x^3 -x^2 - 10x - 8
