| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.77 |
| Score | 0% | 55% |
If side a = 9, side b = 6, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{117} \) | |
| \( \sqrt{106} \) | |
| \( \sqrt{61} \) | |
| \( \sqrt{37} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 92 + 62
c2 = 81 + 36
c2 = 117
c = \( \sqrt{117} \)
The endpoints of this line segment are at (-2, 5) and (2, -1). What is the slope of this line?
| \(\frac{1}{2}\) | |
| -\(\frac{1}{2}\) | |
| -1\(\frac{1}{2}\) | |
| -2\(\frac{1}{2}\) |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 5) and (2, -1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-1.0) - (5.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)What is the circumference of a circle with a diameter of 19?
| 18π | |
| 15π | |
| 19π | |
| 10π |
The formula for circumference is circle diameter x π:
c = πd
c = 19π
Solve -4c - 6c = -5c + 8z + 5 for c in terms of z.
| 14z + 5 | |
| -1\(\frac{1}{3}\)z + \(\frac{1}{3}\) | |
| -3\(\frac{1}{4}\)z + 1\(\frac{1}{4}\) | |
| z - 1\(\frac{1}{2}\) |
To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.
-4c - 6z = -5c + 8z + 5
-4c = -5c + 8z + 5 + 6z
-4c + 5c = 8z + 5 + 6z
c = 14z + 5
The dimensions of this cylinder are height (h) = 9 and radius (r) = 6. What is the volume?
| 80π | |
| 324π | |
| 63π | |
| 72π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(62 x 9)
v = 324π