| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.94 |
| Score | 0% | 59% |
The dimensions of this cylinder are height (h) = 4 and radius (r) = 4. What is the volume?
| 64π | |
| 225π | |
| 324π | |
| 45π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(42 x 4)
v = 64π
What is the circumference of a circle with a diameter of 8?
| 30π | |
| 12π | |
| 8π | |
| 19π |
The formula for circumference is circle diameter x π:
c = πd
c = 8π
What is 9a6 - 5a6?
| a612 | |
| 4 | |
| 4a6 | |
| 45a6 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
9a6 - 5a6 = 4a6
The endpoints of this line segment are at (-2, 1) and (2, 3). What is the slope-intercept equation for this line?
| y = -x + 0 | |
| y = \(\frac{1}{2}\)x + 2 | |
| y = x + 1 | |
| y = -2\(\frac{1}{2}\)x + 1 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 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, 1) and (2, 3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(3.0) - (1.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)Plugging these values into the slope-intercept equation:
y = \(\frac{1}{2}\)x + 2
For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
|
c - a |
|
a2 - c2 |
|
c2 + a2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)