| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
What is the circumference of a circle with a diameter of 16?
| 18π | |
| 15π | |
| 36π | |
| 16π |
The formula for circumference is circle diameter x π:
c = πd
c = 16π
This diagram represents two parallel lines with a transversal. If w° = 26, what is the value of z°?
| 150 | |
| 25 | |
| 26 | |
| 38 |
For parallel lines with a transversal, the following relationships apply:
Applying these relationships starting with w° = 26, the value of z° is 26.
Solve for y:
-3y + 6 < -3 - 2y
| y < 9 | |
| y < -2 | |
| y < -\(\frac{3}{8}\) | |
| y < -1 |
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.
-3y + 6 < -3 - 2y
-3y < -3 - 2y - 6
-3y + 2y < -3 - 6
-y < -9
y < \( \frac{-9}{-1} \)
y < 9
The endpoints of this line segment are at (-2, -5) and (2, 5). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x + 1 | |
| y = x + 4 | |
| y = -2x + 4 | |
| y = 2\(\frac{1}{2}\)x + 0 |
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 0. 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, -5) and (2, 5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(5.0) - (-5.0)}{(2) - (-2)} \) = \( \frac{10}{4} \)Plugging these values into the slope-intercept equation:
y = 2\(\frac{1}{2}\)x + 0
Solve for c:
c2 - 3c - 10 = 0
| 7 or -5 | |
| 9 or -5 | |
| 2 or -6 | |
| -2 or 5 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 - 3c - 10 = 0
(c + 2)(c - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 2) or (c - 5) must equal zero:
If (c + 2) = 0, c must equal -2
If (c - 5) = 0, c must equal 5
So the solution is that c = -2 or 5