For the first one, you can reference Veritas On Demand, and see the slides on Order of Operations and you will find a detailed explanation.
The others are below:
> Page 113 (# 9)
z^2 + 14y + 45 = 0
(z+9)(z+5) = 0
so z = -9 or -5
> Page 131 (# 7 & # 8)
If all three sides are equal length, then we know it's equilateral. Since
the perimeter is 12, we can determine that each side has length 4.
The height of any equilateral triangle can be determined in the same way
-- by drawing a vertical line from the top point to the center of the
bottom edge -- this will form two 30-60-90 triangles (one on the left and
one on the right) and since we know that base of each of these is half the
base of the equilateral triangle -- in this case, 2 -- and since we know
that the hypotenuse is 4 on each of these, we know that the height is
We learn that we have two sides perpendicular to each other, which tells
us that this is a right triangle.
In a right triangle, the longest side is ALWAYS the hypotenuse. The three
sides they give us are 3, 4, and 5. Thus means the 5 is the hypotenuse, so
the height and base are 3 and 4 -- making the area 1/2 * 3 * 4 = 6.
> Page 140 (# 7 & # 8)
Circumference of the circle is 20pi.
Circumference = pi*d or 2*pi*r.
20pi = pi*d
d = 20
diameter is 14, so radius is 7.
area = pi*r^2, so pi*49
Pepperoni slices have diameter 1, so radius 1/2 and area pi*1/4 or pi/4
If there are 20 of them, then they cover 20 * pi/4, which is 5pi.
They cover 5pi out of 49pi, which is 5pi/49pi = 5/49.