| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
If side a = 9, side b = 3, what is the length of the hypotenuse of this right triangle?
| 5 | |
| \( \sqrt{40} \) | |
| \( \sqrt{90} \) | |
| \( \sqrt{117} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 92 + 32
c2 = 81 + 9
c2 = 90
c = \( \sqrt{90} \)
Simplify 5a x 9b.
| 45\( \frac{b}{a} \) | |
| 45ab | |
| 14ab | |
| 45\( \frac{a}{b} \) |
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.
5a x 9b = (5 x 9) (a x b) = 45ab
The dimensions of this cylinder are height (h) = 5 and radius (r) = 7. What is the surface area?
| 90π | |
| 168π | |
| 144π | |
| 196π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(72) + 2π(7 x 5)
sa = 2π(49) + 2π(35)
sa = (2 x 49)π + (2 x 35)π
sa = 98π + 70π
sa = 168π
The endpoints of this line segment are at (-2, -2) and (2, 10). What is the slope of this line?
| 3 | |
| -3 | |
| 1 | |
| -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, 10) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(10.0) - (-2.0)}{(2) - (-2)} \) = \( \frac{12}{4} \)Solve for z:
-9z + 6 > 8 + 9z
| z > -\(\frac{1}{9}\) | |
| z > 3 | |
| z > \(\frac{1}{9}\) | |
| z > -\(\frac{1}{3}\) |
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.
-9z + 6 > 8 + 9z
-9z > 8 + 9z - 6
-9z - 9z > 8 - 6
-18z > 2
z > \( \frac{2}{-18} \)
z > -\(\frac{1}{9}\)