| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
Solve for y:
y2 - y - 30 = 0
| 7 or 4 | |
| 3 or -7 | |
| 4 or -1 | |
| -5 or 6 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
y2 - y - 30 = 0
(y + 5)(y - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 5) or (y - 6) must equal zero:
If (y + 5) = 0, y must equal -5
If (y - 6) = 0, y must equal 6
So the solution is that y = -5 or 6
Breaking apart a quadratic expression into a pair of binomials is called:
deconstructing |
|
squaring |
|
normalizing |
|
factoring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
If a = 1, b = 6, c = 1, and d = 7, what is the perimeter of this quadrilateral?
| 20 | |
| 15 | |
| 21 | |
| 17 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 6 + 1 + 7
p = 15
Solve for z:
-7z - 1 = 3 + 7z
| \(\frac{2}{9}\) | |
| -9 | |
| 4\(\frac{1}{2}\) | |
| -\(\frac{2}{7}\) |
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 equal sign and the answer on the other.
-7z - 1 = 3 + 7z
-7z = 3 + 7z + 1
-7z - 7z = 3 + 1
-14z = 4
z = \( \frac{4}{-14} \)
z = -\(\frac{2}{7}\)
Solve for b:
-5b - 1 = \( \frac{b}{6} \)
| -5\(\frac{2}{5}\) | |
| -\(\frac{6}{31}\) | |
| -\(\frac{18}{49}\) | |
| -\(\frac{1}{4}\) |
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 equal sign and the answer on the other.
-5b - 1 = \( \frac{b}{6} \)
6 x (-5b - 1) = b
(6 x -5b) + (6 x -1) = b
-30b - 6 = b
-30b - 6 - b = 0
-30b - b = 6
-31b = 6
b = \( \frac{6}{-31} \)
b = -\(\frac{6}{31}\)