| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.91 |
| Score | 0% | 58% |
The dimensions of this cylinder are height (h) = 4 and radius (r) = 3. What is the volume?
| 49π | |
| 150π | |
| 36π | |
| 175π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(32 x 4)
v = 36π
If a = c = 5, b = d = 7, and the blue angle = 79°, what is the area of this parallelogram?
| 12 | |
| 35 | |
| 15 | |
| 24 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 5 x 7
a = 35
Solve for z:
5z + 2 = 7 + z
| -\(\frac{1}{2}\) | |
| 1\(\frac{1}{4}\) | |
| 1 | |
| -1\(\frac{1}{8}\) |
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 equal sign and the answer on the other.
5z + 2 = 7 + z
5z = 7 + z - 2
5z - z = 7 - 2
4z = 5
z = \( \frac{5}{4} \)
z = 1\(\frac{1}{4}\)
If angle a = 30° and angle b = 22° what is the length of angle d?
| 121° | |
| 110° | |
| 150° | |
| 141° |
An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:
d° = b° + c°
To find angle c, remember that the sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 30° - 22° = 128°
So, d° = 22° + 128° = 150°
A shortcut to get this answer is to remember that angles around a line add up to 180°:
a° + d° = 180°
d° = 180° - a°
d° = 180° - 30° = 150°
For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
|
c2 + a2 |
|
a2 - c2 |
|
c - a |
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, \(c = \sqrt{a + b}\)