To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 4)(y - 2)
(y x y) + (y x -2) + (-4 x y) + (-4 x -2)
y² - 2y - 4y + 8
y² - 6y + 8

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 6 + 1 + 2 + 7
p = 16

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -1) and (2, 1) so the slope becomes:

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

x² + x + 4 = -2x + 2
x² + x + 4 - 2 = -2x
x² + x + 2x + 2 = 0
x² + 3x + 2 = 0

Next, factor the quadratic equation:

x² + 3x + 2 = 0
(x + 1)(x + 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 1) or (x + 2) must equal zero:

If (x + 1) = 0, x must equal -1
If (x + 2) = 0, x must equal -2

So the solution is that x = -1 or -2

You need to find the value of a so solve the first equation in terms of z:

2a + z = -9
z = -9 - 2a

then substitute the result (-9 - 2a) into the second equation:

5a + 5(-9 - 2a) = -5
5a + (5 x -9) + (5 x -2a) = -5
5a - 45 - 10a = -5
5a - 10a = -5 + 45
-5a = 40
a = \( \frac{40}{-5} \)
a = -8