| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.96 |
| Score | 0% | 59% |
Which of the following statements about parallel lines with a transversal is not correct?
all of the angles formed by a transversal are called interior angles |
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all acute angles equal each other |
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angles in the same position on different parallel lines are called corresponding angles |
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same-side interior angles are complementary and equal each other |
Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).
If a = c = 3, b = d = 7, and the blue angle = 56°, what is the area of this parallelogram?
| 72 | |
| 7 | |
| 21 | |
| 54 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 3 x 7
a = 21
If a = 9, b = 7, c = 8, and d = 5, what is the perimeter of this quadrilateral?
| 29 | |
| 13 | |
| 21 | |
| 18 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 9 + 7 + 8 + 5
p = 29
The endpoints of this line segment are at (-2, 2) and (2, -6). What is the slope-intercept equation for this line?
| y = -\(\frac{1}{2}\)x + 0 | |
| y = -2\(\frac{1}{2}\)x + 4 | |
| y = 2\(\frac{1}{2}\)x + 3 | |
| y = -2x - 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
Simplify (y - 9)(y + 5)
| y2 + 4y - 45 | |
| y2 - 4y - 45 | |
| y2 - 14y + 45 | |
| y2 + 14y + 45 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y - 9)(y + 5)
(y x y) + (y x 5) + (-9 x y) + (-9 x 5)
y2 + 5y - 9y - 45
y2 - 4y - 45