| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.38 |
| Score | 0% | 68% |
The dimensions of this cube are height (h) = 9, length (l) = 8, and width (w) = 1. What is the volume?
| 72 | |
| 40 | |
| 60 | |
| 196 |
The volume of a cube is height x length x width:
v = h x l x w
v = 9 x 8 x 1
v = 72
The endpoints of this line segment are at (-2, 8) and (2, -2). What is the slope-intercept equation for this line?
| y = 3x + 4 | |
| y = -2\(\frac{1}{2}\)x + 1 | |
| y = -2\(\frac{1}{2}\)x + 3 | |
| y = 2x - 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, 8) and (2, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (8.0)}{(2) - (-2)} \) = \( \frac{-10}{4} \)Plugging these values into the slope-intercept equation:
y = -2\(\frac{1}{2}\)x + 3
Solve for a:
a2 - 11a + 14 = -a - 2
| 5 or -7 | |
| 2 or 8 | |
| 4 or -6 | |
| 4 or -1 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
a2 - 11a + 14 = -a - 2
a2 - 11a + 14 + 2 = -a
a2 - 11a + a + 16 = 0
a2 - 10a + 16 = 0
Next, factor the quadratic equation:
a2 - 10a + 16 = 0
(a - 2)(a - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 2) or (a - 8) must equal zero:
If (a - 2) = 0, a must equal 2
If (a - 8) = 0, a must equal 8
So the solution is that a = 2 or 8
A right angle measures:
360° |
|
45° |
|
90° |
|
180° |
A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.
If BD = 11 and AD = 14, AB = ?
| 2 | |
| 3 | |
| 12 | |
| 18 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BD