| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.56 |
| Score | 0% | 51% |
Solve for a:
4a - 1 < \( \frac{a}{6} \)
| a < 2\(\frac{1}{4}\) | |
| a < \(\frac{6}{23}\) | |
| a < 1\(\frac{7}{9}\) | |
| a < \(\frac{1}{2}\) |
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 < sign and the answer on the other.
4a - 1 < \( \frac{a}{6} \)
6 x (4a - 1) < a
(6 x 4a) + (6 x -1) < a
24a - 6 < a
24a - 6 - a < 0
24a - a < 6
23a < 6
a < \( \frac{6}{23} \)
a < \(\frac{6}{23}\)
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
acute, obtuse |
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obtuse, acute |
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supplementary, vertical |
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vertical, supplementary |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
Which of the following is not required to define the slope-intercept equation for a line?
x-intercept |
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\({\Delta y \over \Delta x}\) |
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slope |
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y-intercept |
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.
The endpoints of this line segment are at (-2, -3) and (2, 3). What is the slope-intercept equation for this line?
| y = 1\(\frac{1}{2}\)x + 0 | |
| y = -2\(\frac{1}{2}\)x - 2 | |
| y = -3x - 3 | |
| y = 2x - 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 0. 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, -3) and (2, 3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(3.0) - (-3.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x + 0
What is the circumference of a circle with a radius of 19?
| 17π | |
| 22π | |
| 38π | |
| 18π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 19)
c = 38π