| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
What is the circumference of a circle with a radius of 3?
| 26π | |
| 1π | |
| 16π | |
| 6π |
The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:
c = πd
c = π(2 * r)
c = π(2 * 3)
c = 6π
Solve for z:
z2 + 9z - 9 = 5z - 4
| 5 or -7 | |
| 1 or -3 | |
| 1 or -5 | |
| -2 or -8 |
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:
z2 + 9z - 9 = 5z - 4
z2 + 9z - 9 + 4 = 5z
z2 + 9z - 5z - 5 = 0
z2 + 4z - 5 = 0
Next, factor the quadratic equation:
z2 + 4z - 5 = 0
(z - 1)(z + 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 1) or (z + 5) must equal zero:
If (z - 1) = 0, z must equal 1
If (z + 5) = 0, z must equal -5
So the solution is that z = 1 or -5
Which types of triangles will always have at least two sides of equal length?
isosceles and right |
|
equilateral and isosceles |
|
equilateral, isosceles and right |
|
equilateral and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
The dimensions of this cylinder are height (h) = 1 and radius (r) = 3. What is the volume?
| 9π | |
| 6π | |
| 16π | |
| 448π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(32 x 1)
v = 9π
Factor y2 - 10y + 16
| (y - 8)(y - 2) | |
| (y - 8)(y + 2) | |
| (y + 8)(y - 2) | |
| (y + 8)(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 16 as well and sum (Inside, Outside) to equal -10. For this problem, those two numbers are -8 and -2. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 10y + 16
y2 + (-8 - 2)y + (-8 x -2)
(y - 8)(y - 2)