| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
A trapezoid is a quadrilateral with one set of __________ sides.
equal length |
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equal angle |
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parallel |
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right angle |
A trapezoid is a quadrilateral with one set of parallel sides.
If side a = 4, side b = 1, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{68} \) | |
| \( \sqrt{89} \) | |
| \( \sqrt{17} \) | |
| \( \sqrt{117} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 42 + 12
c2 = 16 + 1
c2 = 17
c = \( \sqrt{17} \)
If the length of AB equals the length of BD, point B __________ this line segment.
trisects |
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midpoints |
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bisects |
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intersects |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.
Solve for a:
3a - 9 = -1 - 8a
| -\(\frac{1}{2}\) | |
| \(\frac{5}{6}\) | |
| -1\(\frac{1}{6}\) | |
| \(\frac{8}{11}\) |
To solve this equation, 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.
3a - 9 = -1 - 8a
3a = -1 - 8a + 9
3a + 8a = -1 + 9
11a = 8
a = \( \frac{8}{11} \)
a = \(\frac{8}{11}\)
The endpoints of this line segment are at (-2, 0) and (2, -2). What is the slope-intercept equation for this line?
| y = 2x + 3 | |
| y = 3x - 2 | |
| y = -\(\frac{1}{2}\)x - 1 | |
| y = -\(\frac{1}{2}\)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 -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, 0) and (2, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (0.0)}{(2) - (-2)} \) = \( \frac{-2}{4} \)Plugging these values into the slope-intercept equation:
y = -\(\frac{1}{2}\)x - 1