| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.45 |
| Score | 0% | 69% |
Which of the following expressions contains exactly two terms?
polynomial |
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quadratic |
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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.
A(n) __________ is to a parallelogram as a square is to a rectangle.
trapezoid |
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rhombus |
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triangle |
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quadrilateral |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
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.
If the area of this square is 81, what is the length of one of the diagonals?
| 9\( \sqrt{2} \) | |
| 6\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{81} \) = 9
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 92 + 92
c2 = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)
If AD = 23 and BD = 20, AB = ?
| 10 | |
| 3 | |
| 2 | |
| 1 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD