| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.62 |
| Score | 0% | 52% |
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) = 5 and radius (r) = 3. What is the surface area?
| 48π | |
| 20π | |
| 88π | |
| 130π |
The surface area of a cylinder is 2πr2 + 2πrh:
sa = 2πr2 + 2πrh
sa = 2π(32) + 2π(3 x 5)
sa = 2π(9) + 2π(15)
sa = (2 x 9)π + (2 x 15)π
sa = 18π + 30π
sa = 48π
Simplify (y - 4)(y - 6)
| y2 + 2y - 24 | |
| y2 - 2y - 24 | |
| y2 + 10y + 24 | |
| y2 - 10y + 24 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y - 4)(y - 6)
(y x y) + (y x -6) + (-4 x y) + (-4 x -6)
y2 - 6y - 4y + 24
y2 - 10y + 24
If the base of this triangle is 5 and the height is 4, what is the area?
| 21 | |
| 15 | |
| 10 | |
| 72 |
The area of a triangle is equal to ½ base x height:
a = ½bh
a = ½ x 5 x 4 = \( \frac{20}{2} \) = 10
The endpoints of this line segment are at (-2, 10) and (2, -2). What is the slope of this line?
| 2\(\frac{1}{2}\) | |
| 3 | |
| -3 | |
| -\(\frac{1}{2}\) |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 10) and (2, -2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-2.0) - (10.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)