| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.61 |
| Score | 0% | 52% |
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
2lw x 2wh + 2lh |
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h x l x w |
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h2 x l2 x w2 |
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lw x wh + lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
Solve for a:
a2 - 6a - 27 = 0
| -5 or -7 | |
| 8 or -3 | |
| -3 or -5 | |
| -3 or 9 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
a2 - 6a - 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
The dimensions of this trapezoid are a = 6, b = 4, c = 7, d = 3, and h = 4. What is the area?
| 7\(\frac{1}{2}\) | |
| 25\(\frac{1}{2}\) | |
| 14 | |
| 18 |
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(4 + 3)(4)
a = ½(7)(4)
a = ½(28) = \( \frac{28}{2} \)
a = 14
Solve for y:
y2 - 12y + 16 = -3y - 4
| 7 or 4 | |
| 4 or 5 | |
| 4 or -9 | |
| 8 or -1 |
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 - 12y + 16 = -3y - 4
y2 - 12y + 16 + 4 = -3y
y2 - 12y + 3y + 20 = 0
y2 - 9y + 20 = 0
Next, factor the quadratic equation:
y2 - 9y + 20 = 0
(y - 4)(y - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 4) or (y - 5) must equal zero:
If (y - 4) = 0, y must equal 4
If (y - 5) = 0, y must equal 5
So the solution is that y = 4 or 5
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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same-side interior angles are complementary and equal each other |
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all acute angles 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°).