| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.05 |
| Score | 0% | 61% |
Solve for z:
z2 - z - 17 = -4z + 1
| 3 or -6 | |
| 7 or -5 | |
| 2 or -7 | |
| 3 or 3 |
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:
z2 - z - 17 = -4z + 1
z2 - z - 17 - 1 = -4z
z2 - z + 4z - 18 = 0
z2 + 3z - 18 = 0
Next, factor the quadratic equation:
z2 + 3z - 18 = 0
(z - 3)(z + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 3) or (z + 6) must equal zero:
If (z - 3) = 0, z must equal 3
If (z + 6) = 0, z must equal -6
So the solution is that z = 3 or -6
On this circle, line segment CD is the:
circumference |
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radius |
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chord |
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diameter |
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).
A coordinate grid is composed of which of the following?
all of these |
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origin |
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y-axis |
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x-axis |
The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.
Solve for a:
a2 + a - 2 = 0
| 5 or -9 | |
| 6 or 4 | |
| 1 or -2 | |
| 8 or 6 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
a2 + a - 2 = 0
(a - 1)(a + 2) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 1) or (a + 2) must equal zero:
If (a - 1) = 0, a must equal 1
If (a + 2) = 0, a must equal -2
So the solution is that a = 1 or -2
Which of the following statements about a triangle is not true?
perimeter = sum of side lengths |
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area = ½bh |
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sum of interior angles = 180° |
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exterior angle = sum of two adjacent interior angles |
A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.