| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.30 |
| Score | 0% | 66% |
If side a = 5, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{113} \) | |
| \( \sqrt{41} \) | |
| \( \sqrt{73} \) | |
| \( \sqrt{97} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 42
c2 = 25 + 16
c2 = 41
c = \( \sqrt{41} \)
If the area of this square is 25, what is the length of one of the diagonals?
| 8\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 7\( \sqrt{2} \) | |
| 5\( \sqrt{2} \) |
To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:
a = s2
so the length of one side of the square is:
s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5
The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:
c2 = a2 + b2
c2 = 52 + 52
c2 = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)
What is the area of a circle with a radius of 4?
| 81π | |
| 16π | |
| 2π | |
| 5π |
The formula for area is πr2:
a = πr2
a = π(42)
a = 16π
The dimensions of this cylinder are height (h) = 8 and radius (r) = 1. What is the volume?
| 8π | |
| 486π | |
| 18π | |
| 50π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(12 x 8)
v = 8π
Simplify (9a)(2ab) + (2a2)(9b).
| 36a2b | |
| 121ab2 | |
| 36ab2 | |
| b2 |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
(9a)(2ab) + (2a2)(9b)
(9 x 2)(a x a x b) + (2 x 9)(a2 x b)
(18)(a1+1 x b) + (18)(a2b)
18a2b + 18a2b
36a2b