| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
Solve for x:
x2 + 10x + 50 = -5x - 4
| -6 or -9 | |
| 3 or -7 | |
| -5 or -5 | |
| 1 or 1 |
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:
x2 + 10x + 50 = -5x - 4
x2 + 10x + 50 + 4 = -5x
x2 + 10x + 5x + 54 = 0
x2 + 15x + 54 = 0
Next, factor the quadratic equation:
x2 + 15x + 54 = 0
(x + 6)(x + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 6) or (x + 9) must equal zero:
If (x + 6) = 0, x must equal -6
If (x + 9) = 0, x must equal -9
So the solution is that x = -6 or -9
If a = c = 9, b = d = 8, what is the area of this rectangle?
| 72 | |
| 56 | |
| 15 | |
| 9 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 9 x 8
a = 72
Which of the following statements about a triangle is not true?
area = ½bh |
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sum of interior angles = 180° |
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exterior angle = sum of two adjacent interior angles |
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perimeter = sum of side lengths |
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.
Which of the following is not true about both rectangles and squares?
all interior angles are right angles |
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the perimeter is the sum of the lengths of all four sides |
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the lengths of all sides are equal |
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the area is length x width |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Solve for z:
2z + 3 < \( \frac{z}{2} \)
| z < \(\frac{3}{8}\) | |
| z < \(\frac{9}{80}\) | |
| z < -2 | |
| z < -\(\frac{16}{31}\) |
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 < sign and the answer on the other.
2z + 3 < \( \frac{z}{2} \)
2 x (2z + 3) < z
(2 x 2z) + (2 x 3) < z
4z + 6 < z
4z + 6 - z < 0
4z - z < -6
3z < -6
z < \( \frac{-6}{3} \)
z < -2