| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.42 |
| Score | 0% | 48% |
The dimensions of this cube are height (h) = 4, length (l) = 1, and width (w) = 4. What is the surface area?
| 178 | |
| 98 | |
| 184 | |
| 48 |
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 1 x 4) + (2 x 4 x 4) + (2 x 1 x 4)
sa = (8) + (32) + (8)
sa = 48
Find the value of a:
8a + x = -8
-a - 4x = -7
| -1\(\frac{8}{31}\) | |
| \(\frac{19}{30}\) | |
| \(\frac{8}{33}\) | |
| \(\frac{11}{28}\) |
You need to find the value of a so solve the first equation in terms of x:
8a + x = -8
x = -8 - 8a
then substitute the result (-8 - 8a) into the second equation:
-a - 4(-8 - 8a) = -7
-a + (-4 x -8) + (-4 x -8a) = -7
-a + 32 + 32a = -7
-a + 32a = -7 - 32
31a = -39
a = \( \frac{-39}{31} \)
a = -1\(\frac{8}{31}\)
If c = 7 and z = 2, what is the value of 4c(c - z)?
| 10 | |
| 140 | |
| 30 | |
| 63 |
To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
4c(c - z)
4(7)(7 - 2)
4(7)(5)
(28)(5)
140
The endpoints of this line segment are at (-2, -9) and (2, 3). What is the slope of this line?
| -2\(\frac{1}{2}\) | |
| 3 | |
| \(\frac{1}{2}\) | |
| 1\(\frac{1}{2}\) |
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, -9) and (2, 3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(3.0) - (-9.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)Solve 6b + 6b = 9b - 5x - 1 for b in terms of x.
| \(\frac{1}{5}\)x - \(\frac{2}{5}\) | |
| x + \(\frac{1}{12}\) | |
| -\(\frac{5}{6}\)x - 1 | |
| 3\(\frac{2}{3}\)x + \(\frac{1}{3}\) |
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.
6b + 6x = 9b - 5x - 1
6b = 9b - 5x - 1 - 6x
6b - 9b = -5x - 1 - 6x
-3b = -11x - 1
b = \( \frac{-11x - 1}{-3} \)
b = \( \frac{-11x}{-3} \) + \( \frac{-1}{-3} \)
b = 3\(\frac{2}{3}\)x + \(\frac{1}{3}\)