| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.05 |
| Score | 0% | 61% |
If side a = 5, side b = 3, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{85} \) | |
| \( \sqrt{26} \) | |
| \( \sqrt{34} \) | |
| \( \sqrt{50} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 32
c2 = 25 + 9
c2 = 34
c = \( \sqrt{34} \)
If a = c = 4, b = d = 5, what is the area of this rectangle?
| 28 | |
| 25 | |
| 72 | |
| 20 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 4 x 5
a = 20
On this circle, line segment CD is the:
diameter |
|
circumference |
|
radius |
|
chord |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).
The endpoints of this line segment are at (-2, -2) and (2, 6). What is the slope-intercept equation for this line?
| y = x + 0 | |
| y = 2x + 2 | |
| y = 1\(\frac{1}{2}\)x - 3 | |
| y = -1\(\frac{1}{2}\)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 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, -2) and (2, 6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(6.0) - (-2.0)}{(2) - (-2)} \) = \( \frac{8}{4} \)Plugging these values into the slope-intercept equation:
y = 2x + 2
The formula for the area of a circle is which of the following?
a = π r |
|
a = π d2 |
|
a = π d |
|
a = π r2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.