| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.88 |
| Score | 0% | 58% |
The dimensions of this cylinder are height (h) = 7 and radius (r) = 4. What is the volume?
| 112π | |
| 64π | |
| 3π | |
| 7π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(42 x 7)
v = 112π
Order the following types of angle from least number of degrees to most number of degrees.
acute, right, obtuse |
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acute, obtuse, right |
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right, obtuse, acute |
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right, acute, obtuse |
An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.
Solve -b + 6b = -7b - z - 4 for b in terms of z.
| -1\(\frac{1}{6}\)z - \(\frac{2}{3}\) | |
| \(\frac{5}{12}\)z - \(\frac{1}{2}\) | |
| 11z + 1 | |
| -4\(\frac{1}{2}\)z - 4\(\frac{1}{2}\) |
To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.
-b + 6z = -7b - z - 4
-b = -7b - z - 4 - 6z
-b + 7b = -z - 4 - 6z
6b = -7z - 4
b = \( \frac{-7z - 4}{6} \)
b = \( \frac{-7z}{6} \) + \( \frac{-4}{6} \)
b = -1\(\frac{1}{6}\)z - \(\frac{2}{3}\)
Which of the following statements about a parallelogram is not true?
the area of a parallelogram is base x height |
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a parallelogram is a quadrilateral |
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opposite sides and adjacent angles are equal |
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the perimeter of a parallelogram is the sum of the lengths of all sides |
A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).
If the area of this square is 9, what is the length of one of the diagonals?
| \( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 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\( \sqrt{2} \)