| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
The dimensions of this cube are height (h) = 3, length (l) = 5, and width (w) = 1. What is the volume?
| 120 | |
| 10 | |
| 15 | |
| 64 |
The volume of a cube is height x length x width:
v = h x l x w
v = 3 x 5 x 1
v = 15
Solve for c:
c2 + 10c + 9 = 5c + 5
| 3 or -8 | |
| 8 or 6 | |
| -1 or -4 | |
| 4 or -4 |
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 + 10c + 9 = 5c + 5
c2 + 10c + 9 - 5 = 5c
c2 + 10c - 5c + 4 = 0
c2 + 5c + 4 = 0
Next, factor the quadratic equation:
c2 + 5c + 4 = 0
(c + 1)(c + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c + 4) must equal zero:
If (c + 1) = 0, c must equal -1
If (c + 4) = 0, c must equal -4
So the solution is that c = -1 or -4
Which of the following statements about parallel lines with a transversal is not correct?
all of the angles formed by a transversal are called interior angles |
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angles in the same position on different parallel lines are called corresponding 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°).
Which of the following statements about math operations is incorrect?
you can add monomials that have the same variable and the same exponent |
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all of these statements are correct |
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you can multiply monomials that have different variables and different exponents |
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you can subtract monomials that have the same variable and the same exponent |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.
Which of the following is not true about both rectangles and squares?
the perimeter is the sum of the lengths of all four sides |
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the area is length x width |
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all interior angles are right angles |
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the lengths of all sides are equal |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).