| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.22 |
| Score | 0% | 64% |
The dimensions of this cylinder are height (h) = 6 and radius (r) = 3. What is the surface area?
| 16π | |
| 54π | |
| 168π | |
| 100π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(32) + 2π(3 x 6)
sa = 2π(9) + 2π(18)
sa = (2 x 9)π + (2 x 18)π
sa = 18π + 36π
sa = 54π
A(n) __________ is two expressions separated by an equal sign.
expression |
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problem |
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formula |
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equation |
An equation is two expressions separated by an equal sign. The key to solving equations is to repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
Solve for x:
x2 + 6x - 23 = x + 1
| 5 or -4 | |
| 6 or 2 | |
| 3 or -8 | |
| 6 or -7 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
x2 + 6x - 23 = x + 1
x2 + 6x - 23 - 1 = x
x2 + 6x - x - 24 = 0
x2 + 5x - 24 = 0
Next, factor the quadratic equation:
x2 + 5x - 24 = 0
(x - 3)(x + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 3) or (x + 8) must equal zero:
If (x - 3) = 0, x must equal 3
If (x + 8) = 0, x must equal -8
So the solution is that x = 3 or -8
What is 5a - 8a?
| 13a2 | |
| -3a2 | |
| -3a | |
| 13 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
5a - 8a = -3a
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
h2 x l2 x w2 |
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h x l x w |
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2lw x 2wh + 2lh |
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lw x wh + lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.