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|---|---|---|
| Questions | 5 | 5 |
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Solve -8c - 2c = -6c - 4y - 2 for c in terms of y.
| -2y + 2\(\frac{1}{3}\) | |
| -\(\frac{2}{5}\)y + 1\(\frac{1}{5}\) | |
| y + 1 | |
| \(\frac{2}{3}\)y - \(\frac{1}{12}\) |
To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.
-8c - 2y = -6c - 4y - 2
-8c = -6c - 4y - 2 + 2y
-8c + 6c = -4y - 2 + 2y
-2c = -2y - 2
c = \( \frac{-2y - 2}{-2} \)
c = \( \frac{-2y}{-2} \) + \( \frac{-2}{-2} \)
c = y + 1
The dimensions of this cylinder are height (h) = 6 and radius (r) = 2. What is the volume?
| 25π | |
| 24π | |
| 216π | |
| 75π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(22 x 6)
v = 24π
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
|
c2 - a2 |
|
c2 + a2 |
|
a2 - c2 |
The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c2) is equal to the sum of the two perpendicular sides squared (a2 + b2): c2 = a2 + b2 or, solved for c, \(c = \sqrt{a + b}\)
A cylinder with a radius (r) and a height (h) has a surface area of:
π r2h2 |
|
4π r2 |
|
π r2h |
|
2(π r2) + 2π rh |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
Factor y2 - 4y - 12
| (y - 6)(y - 2) | |
| (y - 6)(y + 2) | |
| (y + 6)(y - 2) | |
| (y + 6)(y + 2) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -12 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -6 and 2. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 4y - 12
y2 + (-6 + 2)y + (-6 x 2)
(y - 6)(y + 2)