| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.50 |
| Score | 0% | 50% |
Which of the following statements about parallel lines with a transversal is not correct?
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 |
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all acute angles equal each other |
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all of the angles formed by a transversal are called interior angles |
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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slope |
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x-intercept |
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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.
Solve for c:
c2 - 18c + 45 = -4c - 3
| 5 or 5 | |
| -2 or -5 | |
| 4 or -6 | |
| 6 or 8 |
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 - 18c + 45 = -4c - 3
c2 - 18c + 45 + 3 = -4c
c2 - 18c + 4c + 48 = 0
c2 - 14c + 48 = 0
Next, factor the quadratic equation:
c2 - 14c + 48 = 0
(c - 6)(c - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 6) or (c - 8) must equal zero:
If (c - 6) = 0, c must equal 6
If (c - 8) = 0, c must equal 8
So the solution is that c = 6 or 8
Simplify (y + 6)(y - 3)
| y2 - 3y - 18 | |
| y2 - 9y + 18 | |
| y2 + 9y + 18 | |
| y2 + 3y - 18 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y + 6)(y - 3)
(y x y) + (y x -3) + (6 x y) + (6 x -3)
y2 - 3y + 6y - 18
y2 + 3y - 18
Solve for c:
4c + 7 = 2 + 5c
| 8 | |
| 2\(\frac{1}{4}\) | |
| 5 | |
| -1\(\frac{1}{4}\) |
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 equal sign and the answer on the other.
4c + 7 = 2 + 5c
4c = 2 + 5c - 7
4c - 5c = 2 - 7
-c = -5
c = \( \frac{-5}{-1} \)
c = 5