| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.29 |
| Score | 0% | 66% |
Solve for y:
y2 - 12y + 32 = 0
| 4 or -1 | |
| 5 or -3 | |
| 8 or 2 | |
| 4 or 8 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
y2 - 12y + 32 = 0
(y - 4)(y - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 4) or (y - 8) must equal zero:
If (y - 4) = 0, y must equal 4
If (y - 8) = 0, y must equal 8
So the solution is that y = 4 or 8
Factor y2 + 14y + 49
| (y - 7)(y - 7) | |
| (y - 7)(y + 7) | |
| (y + 7)(y - 7) | |
| (y + 7)(y + 7) |
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 49 as well and sum (Inside, Outside) to equal 14. For this problem, those two numbers are 7 and 7. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 + 14y + 49
y2 + (7 + 7)y + (7 x 7)
(y + 7)(y + 7)
A(n) __________ is two expressions separated by an equal sign.
formula |
|
equation |
|
problem |
|
expression |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
2lw x 2wh + 2lh |
|
lw x wh + lh |
|
h x l x w |
|
h2 x l2 x w2 |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
What is the circumference of a circle with a diameter of 18?
| 3π | |
| 36π | |
| 9π | |
| 18π |
The formula for circumference is circle diameter x π:
c = πd
c = 18π