| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.37 |
| Score | 0% | 67% |
The dimensions of this trapezoid are a = 5, b = 5, c = 7, d = 6, and h = 4. What is the area?
| 10 | |
| 8 | |
| 12 | |
| 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(5 + 6)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22
Breaking apart a quadratic expression into a pair of binomials is called:
deconstructing |
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factoring |
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normalizing |
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squaring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
The dimensions of this cylinder are height (h) = 4 and radius (r) = 3. What is the surface area?
| 196π | |
| 42π | |
| 198π | |
| 6π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(32) + 2π(3 x 4)
sa = 2π(9) + 2π(12)
sa = (2 x 9)π + (2 x 12)π
sa = 18π + 24π
sa = 42π
If the area of this square is 9, what is the length of one of the diagonals?
| 4\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3
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 = 32 + 32
c2 = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
division |
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addition |
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exponents |
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pairs |
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)