| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.79 |
| Score | 0% | 56% |
Solve for a:
a2 - 10a + 22 = 2a - 5
| 3 or 9 | |
| 9 or -9 | |
| 4 or 1 | |
| 5 or -8 |
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:
a2 - 10a + 22 = 2a - 5
a2 - 10a + 22 + 5 = 2a
a2 - 10a - 2a + 27 = 0
a2 - 12a + 27 = 0
Next, factor the quadratic equation:
a2 - 12a + 27 = 0
(a - 3)(a - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 9) must equal zero:
If (a - 3) = 0, a must equal 3
If (a - 9) = 0, a must equal 9
So the solution is that a = 3 or 9
A cylinder with a radius (r) and a height (h) has a surface area of:
2(π r2) + 2π rh |
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4π r2 |
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π r2h |
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π r2h2 |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
Simplify (y + 7)(y - 8)
| y2 - y - 56 | |
| y2 - 15y + 56 | |
| y2 + y - 56 | |
| y2 + 15y + 56 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 7)(y - 8)
(y x y) + (y x -8) + (7 x y) + (7 x -8)
y2 - 8y + 7y - 56
y2 - y - 56
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
supplementary, vertical |
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obtuse, acute |
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vertical, supplementary |
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acute, obtuse |
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).
Which of the following statements about a triangle is not true?
perimeter = sum of side lengths |
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exterior angle = sum of two adjacent interior angles |
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area = ½bh |
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sum of interior angles = 180° |
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.