| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
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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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).
If angle a = 70° and angle b = 60° what is the length of angle c?
| 123° | |
| 93° | |
| 50° | |
| 122° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 70° - 60° = 50°
A right angle measures:
90° |
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360° |
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180° |
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45° |
A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.
The endpoints of this line segment are at (-2, -2) and (2, 0). What is the slope-intercept equation for this line?
| y = \(\frac{1}{2}\)x + 3 | |
| y = \(\frac{1}{2}\)x - 1 | |
| y = -1\(\frac{1}{2}\)x + 0 | |
| y = 2x - 4 |
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 -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, -2) and (2, 0) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(0.0) - (-2.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)Plugging these values into the slope-intercept equation:
y = \(\frac{1}{2}\)x - 1
Solve -4b + 9b = -8b - 4y + 7 for b in terms of y.
| 3\(\frac{3}{4}\)y - 1\(\frac{1}{4}\) | |
| 1\(\frac{2}{3}\)y + 2\(\frac{2}{3}\) | |
| -\(\frac{5}{11}\)y + \(\frac{3}{11}\) | |
| -3\(\frac{1}{4}\)y + 1\(\frac{3}{4}\) |
To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.
-4b + 9y = -8b - 4y + 7
-4b = -8b - 4y + 7 - 9y
-4b + 8b = -4y + 7 - 9y
4b = -13y + 7
b = \( \frac{-13y + 7}{4} \)
b = \( \frac{-13y}{4} \) + \( \frac{7}{4} \)
b = -3\(\frac{1}{4}\)y + 1\(\frac{3}{4}\)