| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.83 |
| Score | 0% | 57% |
Solve for y:
y2 - 7y - 49 = -3y - 4
| 5 or 5 | |
| 6 or -7 | |
| -8 or -8 | |
| -5 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:
y2 - 7y - 49 = -3y - 4
y2 - 7y - 49 + 4 = -3y
y2 - 7y + 3y - 45 = 0
y2 - 4y - 45 = 0
Next, factor the quadratic equation:
y2 - 4y - 45 = 0
(y + 5)(y - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 5) or (y - 9) must equal zero:
If (y + 5) = 0, y must equal -5
If (y - 9) = 0, y must equal 9
So the solution is that y = -5 or 9
Breaking apart a quadratic expression into a pair of binomials is called:
factoring |
|
deconstructing |
|
squaring |
|
normalizing |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
If the length of AB equals the length of BD, point B __________ this line segment.
bisects |
|
midpoints |
|
intersects |
|
trisects |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.
Solve for b:
3b + 1 > \( \frac{b}{-1} \)
| b > 1\(\frac{5}{13}\) | |
| b > -\(\frac{21}{55}\) | |
| b > -1\(\frac{1}{11}\) | |
| b > -\(\frac{1}{4}\) |
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 > sign and the answer on the other.
3b + 1 > \( \frac{b}{-1} \)
-1 x (3b + 1) > b
(-1 x 3b) + (-1 x 1) > b
-3b - 1 > b
-3b - 1 - b > 0
-3b - b > 1
-4b > 1
b > \( \frac{1}{-4} \)
b > -\(\frac{1}{4}\)
What is the area of a circle with a radius of 4?
| 81π | |
| 16π | |
| 9π | |
| 7π |
The formula for area is πr2:
a = πr2
a = π(42)
a = 16π