| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.74 |
| Score | 0% | 55% |
The dimensions of this cylinder are height (h) = 4 and radius (r) = 2. What is the surface area?
| 30π | |
| 24π | |
| 10π | |
| 66π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(22) + 2π(2 x 4)
sa = 2π(4) + 2π(8)
sa = (2 x 4)π + (2 x 8)π
sa = 8π + 16π
sa = 24π
Solve for b:
b2 - 9 = 0
| 2 or -6 | |
| -5 or -8 | |
| 3 or -3 | |
| 8 or 4 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
b2 - 9 = 0
(b - 3)(b + 3) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 3) or (b + 3) must equal zero:
If (b - 3) = 0, b must equal 3
If (b + 3) = 0, b must equal -3
So the solution is that b = 3 or -3
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
acute, obtuse |
|
obtuse, acute |
|
supplementary, vertical |
|
vertical, supplementary |
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).
Solve for c:
-8c + 4 < \( \frac{c}{-8} \)
| c < -1\(\frac{5}{37}\) | |
| c < \(\frac{32}{63}\) | |
| c < -8\(\frac{1}{10}\) | |
| c < -\(\frac{4}{7}\) |
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.
-8c + 4 < \( \frac{c}{-8} \)
-8 x (-8c + 4) < c
(-8 x -8c) + (-8 x 4) < c
64c - 32 < c
64c - 32 - c < 0
64c - c < 32
63c < 32
c < \( \frac{32}{63} \)
c < \(\frac{32}{63}\)
Simplify (7a)(3ab) - (5a2)(5b).
| 46a2b | |
| 4ab2 | |
| 100a2b | |
| -4a2b |
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.
(7a)(3ab) - (5a2)(5b)
(7 x 3)(a x a x b) - (5 x 5)(a2 x b)
(21)(a1+1 x b) - (25)(a2b)
21a2b - 25a2b
-4a2b