| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.69 |
| Score | 0% | 54% |
Solve for a:
3a - 8 < -6 - 9a
| a < \(\frac{1}{6}\) | |
| a < \(\frac{1}{9}\) | |
| a < -\(\frac{3}{4}\) | |
| a < -\(\frac{5}{8}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.
3a - 8 < -6 - 9a
3a < -6 - 9a + 8
3a + 9a < -6 + 8
12a < 2
a < \( \frac{2}{12} \)
a < \(\frac{1}{6}\)
If c = -5 and x = -5, what is the value of 2c(c - x)?
| 0 | |
| -36 | |
| -308 | |
| 896 |
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.)
2c(c - x)
2(-5)(-5 + 5)
2(-5)(0)
(-10)(0)
0
If the base of this triangle is 6 and the height is 1, what is the area?
| 15 | |
| 63 | |
| 3 | |
| 18 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 6 x 1 = \( \frac{6}{2} \) = 3
The endpoints of this line segment are at (-2, -3) and (2, -1). What is the slope-intercept equation for this line?
| y = 2x - 1 | |
| y = \(\frac{1}{2}\)x - 2 | |
| y = -1\(\frac{1}{2}\)x - 4 | |
| y = 3x - 3 |
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, -3) and (2, -1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-1.0) - (-3.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)Plugging these values into the slope-intercept equation:
y = \(\frac{1}{2}\)x - 2
The endpoints of this line segment are at (-2, 8) and (2, -4). What is the slope of this line?
| -1\(\frac{1}{2}\) | |
| -2\(\frac{1}{2}\) | |
| 2\(\frac{1}{2}\) | |
| -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, -4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-4.0) - (8.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)