| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
A quadrilateral is a shape with __________ sides.
5 |
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2 |
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4 |
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3 |
A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.
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 y:
y2 + 13y + 42 = -y - 3
| 6 or 2 | |
| 7 or 7 | |
| 8 or 2 | |
| -5 or -9 |
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:
y2 + 13y + 42 = -y - 3
y2 + 13y + 42 + 3 = -y
y2 + 13y + y + 45 = 0
y2 + 14y + 45 = 0
Next, factor the quadratic equation:
y2 + 14y + 45 = 0
(y + 5)(y + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 5) or (y + 9) must equal zero:
If (y + 5) = 0, y must equal -5
If (y + 9) = 0, y must equal -9
So the solution is that y = -5 or -9
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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same-side interior angles are complementary and equal each other |
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angles in the same position on different parallel lines are called corresponding 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°).
Solve for z:
z2 + z - 12 = 0
| -4 or -5 | |
| 8 or 2 | |
| -1 or -3 | |
| 3 or -4 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
z2 + z - 12 = 0
(z - 3)(z + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 3) or (z + 4) must equal zero:
If (z - 3) = 0, z must equal 3
If (z + 4) = 0, z must equal -4
So the solution is that z = 3 or -4