| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.86 |
| Score | 0% | 57% |
The dimensions of this cylinder are height (h) = 5 and radius (r) = 3. What is the volume?
| 147π | |
| 125π | |
| 567π | |
| 45π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(32 x 5)
v = 45π
If the area of this square is 16, what is the length of one of the diagonals?
| 7\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| \( \sqrt{2} \) | |
| 4\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{16} \) = 4
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 = 42 + 42
c2 = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)
Solve 9a - a = 2a - 4z + 7 for a in terms of z.
| -\(\frac{3}{7}\)z + 1 | |
| -\(\frac{1}{2}\)z - \(\frac{9}{10}\) | |
| 19z + 2 | |
| z - \(\frac{1}{4}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
9a - z = 2a - 4z + 7
9a = 2a - 4z + 7 + z
9a - 2a = -4z + 7 + z
7a = -3z + 7
a = \( \frac{-3z + 7}{7} \)
a = \( \frac{-3z}{7} \) + \( \frac{7}{7} \)
a = -\(\frac{3}{7}\)z + 1
Solve for c:
3c + 2 = 1 - 4c
| -\(\frac{1}{7}\) | |
| -1 | |
| -\(\frac{2}{5}\) | |
| 1\(\frac{1}{6}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
3c + 2 = 1 - 4c
3c = 1 - 4c - 2
3c + 4c = 1 - 2
7c = -1
c = \( \frac{-1}{7} \)
c = -\(\frac{1}{7}\)
Which of the following is not true about both rectangles and squares?
all interior angles are right angles |
|
the perimeter is the sum of the lengths of all four sides |
|
the area is length x width |
|
the lengths of all sides are equal |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).