| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
The endpoints of this line segment are at (-2, 6) and (2, -4). What is the slope-intercept equation for this line?
| y = -\(\frac{1}{2}\)x + 0 | |
| y = 1\(\frac{1}{2}\)x + 4 | |
| y = -2\(\frac{1}{2}\)x + 1 | |
| y = \(\frac{1}{2}\)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 1. 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, 6) and (2, -4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-4.0) - (6.0)}{(2) - (-2)} \) = \( \frac{-10}{4} \)Plugging these values into the slope-intercept equation:
y = -2\(\frac{1}{2}\)x + 1
If the base of this triangle is 3 and the height is 8, what is the area?
| 12 | |
| 78 | |
| 91 | |
| 67\(\frac{1}{2}\) |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 3 x 8 = \( \frac{24}{2} \) = 12
If BD = 6 and AD = 13, AB = ?
| 10 | |
| 7 | |
| 14 | |
| 20 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BDWhat is 8a7 + 5a7?
| 3 | |
| a714 | |
| 13a14 | |
| 13a7 |
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.
8a7 + 5a7 = 13a7
Solve for c:
c2 - 6c - 16 = 0
| 8 or 3 | |
| 2 or -3 | |
| -2 or 8 | |
| 4 or 1 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 - 6c - 16 = 0
(c + 2)(c - 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 2) or (c - 8) must equal zero:
If (c + 2) = 0, c must equal -2
If (c - 8) = 0, c must equal 8
So the solution is that c = -2 or 8