| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.02 |
| Score | 0% | 60% |
Solve 9c + c = 7c + 4z + 9 for c in terms of z.
| 1\(\frac{7}{10}\)z - \(\frac{3}{10}\) | |
| -5\(\frac{1}{2}\)z + 4 | |
| \(\frac{1}{2}\)z + 1\(\frac{1}{2}\) | |
| 1\(\frac{1}{2}\)z + 4\(\frac{1}{2}\) |
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.
9c + z = 7c + 4z + 9
9c = 7c + 4z + 9 - z
9c - 7c = 4z + 9 - z
2c = 3z + 9
c = \( \frac{3z + 9}{2} \)
c = \( \frac{3z}{2} \) + \( \frac{9}{2} \)
c = 1\(\frac{1}{2}\)z + 4\(\frac{1}{2}\)
The dimensions of this cylinder are height (h) = 1 and radius (r) = 2. What is the surface area?
| 144π | |
| 12π | |
| 30π | |
| 182π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(22) + 2π(2 x 1)
sa = 2π(4) + 2π(2)
sa = (2 x 4)π + (2 x 2)π
sa = 8π + 4π
sa = 12π
If side x = 12cm, side y = 9cm, and side z = 9cm what is the perimeter of this triangle?
| 30cm | |
| 36cm | |
| 28cm | |
| 34cm |
The perimeter of a triangle is the sum of the lengths of its sides:
p = x + y + z
p = 12cm + 9cm + 9cm = 30cm
The dimensions of this cube are height (h) = 2, length (l) = 2, and width (w) = 4. What is the volume?
| 128 | |
| 42 | |
| 16 | |
| 24 |
The volume of a cube is height x length x width:
v = h x l x w
v = 2 x 2 x 4
v = 16
Factor y2 + 5y - 36
| (y - 4)(y - 9) | |
| (y + 4)(y - 9) | |
| (y - 4)(y + 9) | |
| (y + 4)(y + 9) |
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 -36 as well and sum (Inside, Outside) to equal 5. For this problem, those two numbers are -4 and 9. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 + 5y - 36
y2 + (-4 + 9)y + (-4 x 9)
(y - 4)(y + 9)