| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.53 |
| Score | 0% | 51% |
Factor y2 - 3y - 18
| (y - 6)(y + 3) | |
| (y + 6)(y + 3) | |
| (y + 6)(y - 3) | |
| (y - 6)(y - 3) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -18 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -6 and 3. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 3y - 18
y2 + (-6 + 3)y + (-6 x 3)
(y - 6)(y + 3)
Solve a - 8a = 3a - 7y - 1 for a in terms of y.
| -15y - 1 | |
| 1\(\frac{1}{3}\)y - \(\frac{5}{6}\) | |
| -8y - 9 | |
| -\(\frac{1}{2}\)y + \(\frac{1}{2}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
a - 8y = 3a - 7y - 1
a = 3a - 7y - 1 + 8y
a - 3a = -7y - 1 + 8y
-2a = y - 1
a = \( \frac{y - 1}{-2} \)
a = \( \frac{y}{-2} \) + \( \frac{-1}{-2} \)
a = -\(\frac{1}{2}\)y + \(\frac{1}{2}\)
Solve for c:
c2 - 6c + 8 = 0
| 8 or 5 | |
| 7 or 5 | |
| 2 or 4 | |
| 8 or 3 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 - 6c + 8 = 0
(c - 2)(c - 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c - 4) must equal zero:
If (c - 2) = 0, c must equal 2
If (c - 4) = 0, c must equal 4
So the solution is that c = 2 or 4
On this circle, line segment AB is the:
radius |
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circumference |
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diameter |
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chord |
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 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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angles in the same position on different parallel lines are called corresponding angles |
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all acute angles equal each other |
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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°).