| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.67 |
| Score | 0% | 53% |
Which of the following is not true about both rectangles and squares?
the lengths of all sides are equal |
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the area is length x width |
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the perimeter is the sum of the lengths of all four sides |
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all interior angles are right angles |
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).
The dimensions of this cube are height (h) = 1, length (l) = 3, and width (w) = 6. What is the surface area?
| 150 | |
| 54 | |
| 146 | |
| 180 |
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 3 x 6) + (2 x 6 x 1) + (2 x 3 x 1)
sa = (36) + (12) + (6)
sa = 54
The endpoints of this line segment are at (-2, -6) and (2, 0). What is the slope-intercept equation for this line?
| y = 2x - 1 | |
| y = 3x - 2 | |
| y = 1\(\frac{1}{2}\)x - 3 | |
| y = \(\frac{1}{2}\)x - 3 |
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 -3. 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, -6) and (2, 0) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(0.0) - (-6.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x - 3
If a = c = 7, b = d = 9, and the blue angle = 67°, what is the area of this parallelogram?
| 63 | |
| 8 | |
| 56 | |
| 20 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 7 x 9
a = 63
The endpoints of this line segment are at (-2, 7) and (2, 1). What is the slope of this line?
| 3 | |
| -\(\frac{1}{2}\) | |
| -1\(\frac{1}{2}\) | |
| 2\(\frac{1}{2}\) |
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, 7) and (2, 1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (7.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)