| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.76 |
| Score | 0% | 55% |
If side a = 5, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{74} \) | |
| \( \sqrt{58} \) | |
| \( \sqrt{53} \) | |
| \( \sqrt{90} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 72
c2 = 25 + 49
c2 = 74
c = \( \sqrt{74} \)
The endpoints of this line segment are at (-2, 4) and (2, -6). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x - 1 | |
| y = 2\(\frac{1}{2}\)x + 0 | |
| y = -3x + 2 | |
| y = -2x - 4 |
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, 4) and (2, -6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-6.0) - (4.0)}{(2) - (-2)} \) = \( \frac{-10}{4} \)Plugging these values into the slope-intercept equation:
y = -2\(\frac{1}{2}\)x - 1
What is the circumference of a circle with a diameter of 8?
| 9π | |
| 22π | |
| 8π | |
| 38π |
The formula for circumference is circle diameter x π:
c = πd
c = 8π
Solve for a:
3a - 7 > \( \frac{a}{-7} \)
| a > \(\frac{8}{19}\) | |
| a > -\(\frac{48}{53}\) | |
| a > \(\frac{2}{19}\) | |
| a > 2\(\frac{5}{22}\) |
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 - 7 > \( \frac{a}{-7} \)
-7 x (3a - 7) > a
(-7 x 3a) + (-7 x -7) > a
-21a + 49 > a
-21a + 49 - a > 0
-21a - a > -49
-22a > -49
a > \( \frac{-49}{-22} \)
a > 2\(\frac{5}{22}\)
A cylinder with a radius (r) and a height (h) has a surface area of:
π r2h |
|
4π r2 |
|
π r2h2 |
|
2(π r2) + 2π rh |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.