| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.84 |
| Score | 0% | 57% |
The endpoints of this line segment are at (-2, 2) and (2, 6). What is the slope-intercept equation for this line?
| y = 2x + 0 | |
| y = x + 4 | |
| y = -2x + 1 | |
| y = 2\(\frac{1}{2}\)x + 0 |
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 4. 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 = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(6.0) - (2.0)}{(2) - (-2)} \) = \( \frac{4}{4} \)Plugging these values into the slope-intercept equation:
y = x + 4
Which of the following statements about parallel lines with a transversal is not correct?
all acute angles equal each other |
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all of the angles formed by a transversal are called interior angles |
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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°).
On this circle, line segment AB is the:
chord |
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circumference |
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radius |
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diameter |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
Which of the following expressions contains exactly two terms?
binomial |
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polynomial |
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monomial |
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quadratic |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
Solve for x:
x2 + 5x - 7 = 5x + 2
| 3 or -9 | |
| 6 or 4 | |
| -2 or -4 | |
| 3 or -3 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
x2 + 5x - 7 = 5x + 2
x2 + 5x - 7 - 2 = 5x
x2 + 5x - 5x - 9 = 0
x2 - 9 = 0
Next, factor the quadratic equation:
x2 - 9 = 0
(x - 3)(x + 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 3) or (x + 3) must equal zero:
If (x - 3) = 0, x must equal 3
If (x + 3) = 0, x must equal -3
So the solution is that x = 3 or -3