| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.00 |
| Score | 0% | 60% |
If side a = 9, side b = 9, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{29} \) | |
| \( \sqrt{80} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{162} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 92 + 92
c2 = 81 + 81
c2 = 162
c = \( \sqrt{162} \)
Simplify (2a)(9ab) + (7a2)(2b).
| -4ab2 | |
| 99ab2 | |
| 32a2b | |
| 99a2b |
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.
(2a)(9ab) + (7a2)(2b)
(2 x 9)(a x a x b) + (7 x 2)(a2 x b)
(18)(a1+1 x b) + (14)(a2b)
18a2b + 14a2b
32a2b
The dimensions of this cylinder are height (h) = 4 and radius (r) = 2. What is the volume?
| 16π | |
| 192π | |
| 200π | |
| 147π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(22 x 4)
v = 16π
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
supplementary, vertical |
|
vertical, supplementary |
|
acute, obtuse |
|
obtuse, acute |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).
The dimensions of this cylinder are height (h) = 8 and radius (r) = 3. What is the surface area?
| 32π | |
| 66π | |
| 64π | |
| 130π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(32) + 2π(3 x 8)
sa = 2π(9) + 2π(24)
sa = (2 x 9)π + (2 x 24)π
sa = 18π + 48π
sa = 66π