| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.62 |
| Score | 0% | 52% |
If the base of this triangle is 7 and the height is 8, what is the area?
| 45 | |
| 44 | |
| 28 | |
| 60\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 7 x 8 = \( \frac{56}{2} \) = 28
Breaking apart a quadratic expression into a pair of binomials is called:
normalizing |
|
deconstructing |
|
squaring |
|
factoring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
The formula for the area of a circle is which of the following?
c = π r2 |
|
c = π d2 |
|
c = π r |
|
c = π d |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
Solve for c:
c2 - c - 23 = 5c + 4
| -3 or -3 | |
| 7 or 3 | |
| -5 or -7 | |
| -3 or 9 |
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:
c2 - c - 23 = 5c + 4
c2 - c - 23 - 4 = 5c
c2 - c - 5c - 27 = 0
c2 - 6c - 27 = 0
Next, factor the quadratic equation:
c2 - 6c - 27 = 0
(c + 3)(c - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 3) or (c - 9) must equal zero:
If (c + 3) = 0, c must equal -3
If (c - 9) = 0, c must equal 9
So the solution is that c = -3 or 9
Factor y2 - 8y + 7
| (y - 7)(y - 1) | |
| (y - 7)(y + 1) | |
| (y + 7)(y + 1) | |
| (y + 7)(y - 1) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 7 as well and sum (Inside, Outside) to equal -8. For this problem, those two numbers are -7 and -1. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 8y + 7
y2 + (-7 - 1)y + (-7 x -1)
(y - 7)(y - 1)