| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.64 |
| Score | 0% | 53% |
Solve for b:
b2 - 1 = 0
| 1 or -1 | |
| 5 or -2 | |
| 9 or 4 | |
| 9 or -2 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 - 1 = 0
(b - 1)(b + 1) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 1) or (b + 1) must equal zero:
If (b - 1) = 0, b must equal 1
If (b + 1) = 0, b must equal -1
So the solution is that b = 1 or -1
If angle a = 45° and angle b = 68° what is the length of angle c?
| 67° | |
| 63° | |
| 87° | |
| 66° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 45° - 68° = 67°
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°).
Which of the following is not required to define the slope-intercept equation for a line?
y-intercept |
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x-intercept |
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slope |
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\({\Delta y \over \Delta x}\) |
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.
If the base of this triangle is 5 and the height is 1, what is the area?
| 2\(\frac{1}{2}\) | |
| 27\(\frac{1}{2}\) | |
| 72 | |
| 39 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 5 x 1 = \( \frac{5}{2} \) = 2\(\frac{1}{2}\)