| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.48 |
| Score | 0% | 50% |
If the base of this triangle is 5 and the height is 3, what is the area?
| 7\(\frac{1}{2}\) | |
| 67\(\frac{1}{2}\) | |
| 55 | |
| 39 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 5 x 3 = \( \frac{15}{2} \) = 7\(\frac{1}{2}\)
The endpoints of this line segment are at (-2, -4) and (2, -2). What is the slope-intercept equation for this line?
| y = \(\frac{1}{2}\)x - 1 | |
| y = 2\(\frac{1}{2}\)x - 2 | |
| y = \(\frac{1}{2}\)x - 3 | |
| y = 2\(\frac{1}{2}\)x + 2 |
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 -3. 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, -4) and (2, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)Plugging these values into the slope-intercept equation:
y = \(\frac{1}{2}\)x - 3
The dimensions of this cylinder are height (h) = 9 and radius (r) = 1. What is the volume?
| 18π | |
| 9π | |
| 405π | |
| 150π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(12 x 9)
v = 9π
The dimensions of this cube are height (h) = 4, length (l) = 3, and width (w) = 3. What is the surface area?
| 76 | |
| 66 | |
| 118 | |
| 96 |
The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):
sa = 2lw + 2wh + 2lh
sa = (2 x 3 x 3) + (2 x 3 x 4) + (2 x 3 x 4)
sa = (18) + (24) + (24)
sa = 66
Solve b - 3b = -2b + 2y - 2 for b in terms of y.
| 1\(\frac{1}{8}\)y + \(\frac{1}{4}\) | |
| -\(\frac{9}{13}\)y + \(\frac{9}{13}\) | |
| -2\(\frac{1}{3}\)y + 1\(\frac{1}{6}\) | |
| 1\(\frac{2}{3}\)y - \(\frac{2}{3}\) |
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 - 3y = -2b + 2y - 2
b = -2b + 2y - 2 + 3y
b + 2b = 2y - 2 + 3y
3b = 5y - 2
b = \( \frac{5y - 2}{3} \)
b = \( \frac{5y}{3} \) + \( \frac{-2}{3} \)
b = 1\(\frac{2}{3}\)y - \(\frac{2}{3}\)