| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.73 |
| Score | 0% | 55% |
For this diagram, the Pythagorean theorem states that b2 = ?
c2 - a2 |
|
c - a |
|
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, \(c = \sqrt{a + b}\)
The dimensions of this cylinder are height (h) = 4 and radius (r) = 8. What is the surface area?
| 120π | |
| 192π | |
| 140π | |
| 16π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(82) + 2π(8 x 4)
sa = 2π(64) + 2π(32)
sa = (2 x 64)π + (2 x 32)π
sa = 128π + 64π
sa = 192π
If angle a = 26° and angle b = 25° what is the length of angle c?
| 89° | |
| 85° | |
| 129° | |
| 84° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 26° - 25° = 129°
Solve for c:
-7c + 6 < \( \frac{c}{9} \)
| c < -\(\frac{3}{10}\) | |
| c < 4\(\frac{1}{5}\) | |
| c < -\(\frac{25}{29}\) | |
| c < \(\frac{27}{32}\) |
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 < sign and the answer on the other.
-7c + 6 < \( \frac{c}{9} \)
9 x (-7c + 6) < c
(9 x -7c) + (9 x 6) < c
-63c + 54 < c
-63c + 54 - c < 0
-63c - c < -54
-64c < -54
c < \( \frac{-54}{-64} \)
c < \(\frac{27}{32}\)
If a = c = 7, b = d = 8, and the blue angle = 64°, what is the area of this parallelogram?
| 27 | |
| 56 | |
| 20 | |
| 12 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 7 x 8
a = 56