| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
Solve for y:
y2 - 7y - 11 = -y + 5
| 2 or -3 | |
| -2 or 8 | |
| 7 or -7 | |
| 3 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:
y2 - 7y - 11 = -y + 5
y2 - 7y - 11 - 5 = -y
y2 - 7y + y - 16 = 0
y2 - 6y - 16 = 0
Next, factor the quadratic equation:
y2 - 6y - 16 = 0
(y + 2)(y - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 2) or (y - 8) must equal zero:
If (y + 2) = 0, y must equal -2
If (y - 8) = 0, y must equal 8
So the solution is that y = -2 or 8
If side a = 9, side b = 5, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{106} \) | |
| \( \sqrt{74} \) | |
| \( \sqrt{68} \) | |
| 5 |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 92 + 52
c2 = 81 + 25
c2 = 106
c = \( \sqrt{106} \)
The dimensions of this trapezoid are a = 5, b = 5, c = 7, d = 7, and h = 4. What is the area?
| 18 | |
| 24 | |
| 32\(\frac{1}{2}\) | |
| 26 |
The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:
a = ½(b + d)(h)
a = ½(5 + 7)(4)
a = ½(12)(4)
a = ½(48) = \( \frac{48}{2} \)
a = 24
Which of the following expressions contains exactly two terms?
quadratic |
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polynomial |
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monomial |
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binomial |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
If the length of AB equals the length of BD, point B __________ this line segment.
bisects |
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intersects |
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midpoints |
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trisects |
A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.