| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.28 |
| Score | 0% | 66% |
If a = 1, b = 8, c = 9, and d = 3, what is the perimeter of this quadrilateral?
| 23 | |
| 20 | |
| 21 | |
| 24 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 1 + 8 + 9 + 3
p = 21
Breaking apart a quadratic expression into a pair of binomials is called:
deconstructing |
|
factoring |
|
normalizing |
|
squaring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
The dimensions of this cylinder are height (h) = 8 and radius (r) = 9. What is the volume?
| 288π | |
| 648π | |
| 16π | |
| 36π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(92 x 8)
v = 648π
If the area of this square is 9, what is the length of one of the diagonals?
| 8\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) | |
| 6\( \sqrt{2} \) |
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\( \sqrt{2} \)
Solve 8b + 9b = 2b - 8x + 1 for b in terms of x.
| \(\frac{11}{14}\)x + \(\frac{4}{7}\) | |
| -2\(\frac{5}{6}\)x + \(\frac{1}{6}\) | |
| -\(\frac{5}{12}\)x - \(\frac{1}{4}\) | |
| -x + 6 |
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.
8b + 9x = 2b - 8x + 1
8b = 2b - 8x + 1 - 9x
8b - 2b = -8x + 1 - 9x
6b = -17x + 1
b = \( \frac{-17x + 1}{6} \)
b = \( \frac{-17x}{6} \) + \( \frac{1}{6} \)
b = -2\(\frac{5}{6}\)x + \(\frac{1}{6}\)