| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
If a = c = 5, b = d = 1, and the blue angle = 55°, what is the area of this parallelogram?
| 32 | |
| 35 | |
| 5 | |
| 49 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 5 x 1
a = 5
Breaking apart a quadratic expression into a pair of binomials is called:
squaring |
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factoring |
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normalizing |
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deconstructing |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
Which of the following statements about parallel lines with a transversal is not correct?
angles in the same position on different parallel lines are called corresponding angles |
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all of the angles formed by a transversal are called interior angles |
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all acute angles equal each other |
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same-side interior angles are complementary and equal each other |
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
vertical, supplementary |
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acute, obtuse |
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supplementary, vertical |
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obtuse, acute |
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).
Solve for a:
a2 + 2a - 3 = 0
| 1 or -3 | |
| 4 or 4 | |
| 2 or -4 | |
| 1 or -1 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
a2 + 2a - 3 = 0
(a - 1)(a + 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 1) or (a + 3) must equal zero:
If (a - 1) = 0, a must equal 1
If (a + 3) = 0, a must equal -3
So the solution is that a = 1 or -3