| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
h2 x l2 x w2 |
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h x l x w |
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2lw x 2wh + 2lh |
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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.
The endpoints of this line segment are at (-2, 9) and (2, -3). What is the slope of this line?
| 2\(\frac{1}{2}\) | |
| -3 | |
| 1\(\frac{1}{2}\) | |
| 1 |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 9) and (2, -3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-3.0) - (9.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)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 is not true about both rectangles and squares?
the area is length x width |
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the lengths of all sides are equal |
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all interior angles are right angles |
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the perimeter is the sum of the lengths of all four sides |
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).
Solve for b:
b2 + 14b + 32 = 3b + 2
| 2 or 2 | |
| 8 or 7 | |
| -5 or -6 | |
| 7 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:
b2 + 14b + 32 = 3b + 2
b2 + 14b + 32 - 2 = 3b
b2 + 14b - 3b + 30 = 0
b2 + 11b + 30 = 0
Next, factor the quadratic equation:
b2 + 11b + 30 = 0
(b + 5)(b + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 5) or (b + 6) must equal zero:
If (b + 5) = 0, b must equal -5
If (b + 6) = 0, b must equal -6
So the solution is that b = -5 or -6