| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.89 |
| Score | 0% | 58% |
Solve for c:
c2 + c + 2 = 2c + 4
| 6 or -1 | |
| 3 or -9 | |
| 4 or -8 | |
| -1 or 2 |
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 + 2 = 2c + 4
c2 + c + 2 - 4 = 2c
c2 + c - 2c - 2 = 0
c2 - c - 2 = 0
Next, factor the quadratic equation:
c2 - c - 2 = 0
(c + 1)(c - 2) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c - 2) must equal zero:
If (c + 1) = 0, c must equal -1
If (c - 2) = 0, c must equal 2
So the solution is that c = -1 or 2
Solve for b:
4b - 7 < 3 + 9b
| b < -2 | |
| b < 1 | |
| b < -1\(\frac{1}{4}\) | |
| b < -1\(\frac{1}{8}\) |
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.
4b - 7 < 3 + 9b
4b < 3 + 9b + 7
4b - 9b < 3 + 7
-5b < 10
b < \( \frac{10}{-5} \)
b < -2
The dimensions of this trapezoid are a = 5, b = 2, c = 8, d = 2, and h = 3. What is the area?
| 13\(\frac{1}{2}\) | |
| 12 | |
| 37\(\frac{1}{2}\) | |
| 6 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(2 + 2)(3)
a = ½(4)(3)
a = ½(12) = \( \frac{12}{2} \)
a = 6
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
acute, obtuse |
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obtuse, acute |
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vertical, supplementary |
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supplementary, vertical |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
Breaking apart a quadratic expression into a pair of binomials is called:
squaring |
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normalizing |
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factoring |
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deconstructing |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.