A trapezoid is a quadrilateral with one set of parallel sides.

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:

b² - 16b + 32 = -5b + 4
b² - 16b + 32 - 4 = -5b
b² - 16b + 5b + 28 = 0
b² - 11b + 28 = 0

Next, factor the quadratic equation:

b² - 11b + 28 = 0
(b - 4)(b - 7) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 4) or (b - 7) must equal zero:

If (b - 4) = 0, b must equal 4
If (b - 7) = 0, b must equal 7

So the solution is that b = 4 or 7

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

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

4a + z = -1
z = -1 - 4a

then substitute the result (-1 - 4a) into the second equation:

-8a + 1(-1 - 4a) = -8
-8a + (1 x -1) + (1 x -4a) = -8
-8a - 1 - 4a = -8
-8a - 4a = -8 + 1
-12a = -7
a = \( \frac{-7}{-12} \)
a = \(\frac{7}{12}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

-5a + 2 < 6 - 9a
-5a < 6 - 9a - 2
-5a + 9a < 6 - 2
4a < 4
a < \( \frac{4}{4} \)
a < 1