| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.82 |
| Score | 0% | 56% |
The dimensions of this cube are height (h) = 6, length (l) = 2, and width (w) = 2. What is the surface area?
| 176 | |
| 48 | |
| 56 | |
| 198 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 2 x 2) + (2 x 2 x 6) + (2 x 2 x 6)
sa = (8) + (24) + (24)
sa = 56
Which of the following statements about a parallelogram is not true?
the area of a parallelogram is base x height |
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the perimeter of a parallelogram is the sum of the lengths of all sides |
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opposite sides and adjacent angles are equal |
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a parallelogram is a quadrilateral |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
If side a = 3, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{74} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{162} \) | |
| 5 |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 42
c2 = 9 + 16
c2 = 25
c = \( \sqrt{25} \)
c = 5
The endpoints of this line segment are at (-2, 2) and (2, -6). What is the slope-intercept equation for this line?
| y = 1\(\frac{1}{2}\)x - 2 | |
| y = 1\(\frac{1}{2}\)x + 0 | |
| y = -2x - 2 | |
| y = -1\(\frac{1}{2}\)x - 2 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -2. 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, 2) and (2, -6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-6.0) - (2.0)}{(2) - (-2)} \) = \( \frac{-8}{4} \)Plugging these values into the slope-intercept equation:
y = -2x - 2
A(n) __________ is two expressions separated by an equal sign.
problem |
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equation |
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formula |
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expression |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.