| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
What is the area of a circle with a radius of 4?
| 25π | |
| 4π | |
| 16π | |
| 64π |
The formula for area is πr2:
a = πr2
a = π(42)
a = 16π
The endpoints of this line segment are at (-2, 1) and (2, 5). What is the slope-intercept equation for this line?
| y = x - 1 | |
| y = \(\frac{1}{2}\)x + 1 | |
| y = -x - 3 | |
| y = x + 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 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, 1) and (2, 5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(5.0) - (1.0)}{(2) - (-2)} \) = \( \frac{4}{4} \)Plugging these values into the slope-intercept equation:
y = x + 3
Which of the following is not required to define the slope-intercept equation for a line?
slope |
|
\({\Delta y \over \Delta x}\) |
|
x-intercept |
|
y-intercept |
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.
A coordinate grid is composed of which of the following?
all of these |
|
x-axis |
|
y-axis |
|
origin |
The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.
If side a = 1, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{5} \) | |
| \( \sqrt{65} \) | |
| \( \sqrt{50} \) | |
| \( \sqrt{34} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 12 + 72
c2 = 1 + 49
c2 = 50
c = \( \sqrt{50} \)