| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.92 |
| Score | 0% | 58% |
Solve for c:
c2 - 2c - 58 = c - 4
| -1 or -2 | |
| 8 or 4 | |
| -6 or 9 | |
| 3 or -7 |
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:
c2 - 2c - 58 = c - 4
c2 - 2c - 58 + 4 = c
c2 - 2c - c - 54 = 0
c2 - 3c - 54 = 0
Next, factor the quadratic equation:
c2 - 3c - 54 = 0
(c + 6)(c - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 6) or (c - 9) must equal zero:
If (c + 6) = 0, c must equal -6
If (c - 9) = 0, c must equal 9
So the solution is that c = -6 or 9
The endpoints of this line segment are at (-2, -4) and (2, 6). What is the slope of this line?
| 3 | |
| 2\(\frac{1}{2}\) | |
| -\(\frac{1}{2}\) | |
| \(\frac{1}{2}\) |
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, -4) and (2, 6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(6.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{10}{4} \)A quadrilateral is a shape with __________ sides.
3 |
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5 |
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2 |
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4 |
A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.
What is the area of a circle with a diameter of 8?
| 4π | |
| 8π | |
| 49π | |
| 16π |
The formula for area is πr2. Radius is circle \( \frac{diameter}{2} \):
r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr2
a = π(42)
a = 16π
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°).