| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.31 |
| Score | 0% | 66% |
If side a = 1, side b = 3, what is the length of the hypotenuse of this right triangle?
| 5 | |
| \( \sqrt{65} \) | |
| \( \sqrt{10} \) | |
| \( \sqrt{40} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 12 + 32
c2 = 1 + 9
c2 = 10
c = \( \sqrt{10} \)
What is the area of a circle with a diameter of 10?
| 25π | |
| 2π | |
| 3π | |
| 36π |
The formula for area is πr2. Radius is circle \( \frac{diameter}{2} \):
r = \( \frac{d}{2} \)
r = \( \frac{10}{2} \)
r = 5
a = πr2
a = π(52)
a = 25π
Simplify 3a x 3b.
| 9\( \frac{a}{b} \) | |
| 9\( \frac{b}{a} \) | |
| 9a2b2 | |
| 9ab |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
3a x 3b = (3 x 3) (a x b) = 9ab
What is the circumference of a circle with a diameter of 19?
| 13π | |
| 10π | |
| 20π | |
| 19π |
The formula for circumference is circle diameter x π:
c = πd
c = 19π
The endpoints of this line segment are at (-2, 0) and (2, 6). What is the slope-intercept equation for this line?
| y = 3x - 3 | |
| y = -2\(\frac{1}{2}\)x - 1 | |
| y = 1\(\frac{1}{2}\)x + 3 | |
| y = 3x - 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 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, 0) and (2, 6) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(6.0) - (0.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x + 3