| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
The dimensions of this trapezoid are a = 5, b = 4, c = 7, d = 6, and h = 3. What is the area?
| 14 | |
| 15 | |
| 9 | |
| 22 |
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(4 + 6)(3)
a = ½(10)(3)
a = ½(30) = \( \frac{30}{2} \)
a = 15
Solve for a:
a2 - 5a + 16 = 3a + 4
| 7 or 3 | |
| 8 or -9 | |
| 5 or -1 | |
| 2 or 6 |
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:
a2 - 5a + 16 = 3a + 4
a2 - 5a + 16 - 4 = 3a
a2 - 5a - 3a + 12 = 0
a2 - 8a + 12 = 0
Next, factor the quadratic equation:
a2 - 8a + 12 = 0
(a - 2)(a - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 2) or (a - 6) must equal zero:
If (a - 2) = 0, a must equal 2
If (a - 6) = 0, a must equal 6
So the solution is that a = 2 or 6
Find the value of c:
4c + z = -2
-2c - 6z = -6
| \(\frac{36}{53}\) | |
| -\(\frac{9}{11}\) | |
| 1\(\frac{3}{56}\) | |
| 3\(\frac{3}{5}\) |
You need to find the value of c so solve the first equation in terms of z:
4c + z = -2
z = -2 - 4c
then substitute the result (-2 - 4c) into the second equation:
-2c - 6(-2 - 4c) = -6
-2c + (-6 x -2) + (-6 x -4c) = -6
-2c + 12 + 24c = -6
-2c + 24c = -6 - 12
22c = -18
c = \( \frac{-18}{22} \)
c = -\(\frac{9}{11}\)
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
h x l x w |
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2lw x 2wh + 2lh |
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h2 x l2 x w2 |
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lw x wh + lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
Which of the following expressions contains exactly two terms?
quadratic |
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polynomial |
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binomial |
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monomial |
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.