| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
If a = c = 3, b = d = 1, and the blue angle = 55°, what is the area of this parallelogram?
| 6 | |
| 18 | |
| 9 | |
| 3 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 3 x 1
a = 3
A cylinder with a radius (r) and a height (h) has a surface area of:
2(π r2) + 2π rh |
|
4π r2 |
|
π r2h2 |
|
π r2h |
A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r2h and the surface area is 2(π r2) + 2π rh.
The dimensions of this cube are height (h) = 4, length (l) = 4, and width (w) = 5. What is the volume?
| 54 | |
| 80 | |
| 6 | |
| 63 |
The volume of a cube is height x length x width:
v = h x l x w
v = 4 x 4 x 5
v = 80
Find the value of b:
-b + z = 1
-5b - 5z = 2
| -\(\frac{26}{35}\) | |
| -\(\frac{7}{10}\) | |
| \(\frac{2}{3}\) | |
| -\(\frac{38}{43}\) |
You need to find the value of b so solve the first equation in terms of z:
-b + z = 1
z = 1 + b
then substitute the result (1 - -1b) into the second equation:
-5b - 5(1 + b) = 2
-5b + (-5 x 1) + (-5 x b) = 2
-5b - 5 - 5b = 2
-5b - 5b = 2 + 5
-10b = 7
b = \( \frac{7}{-10} \)
b = -\(\frac{7}{10}\)
If the area of this square is 25, what is the length of one of the diagonals?
| 6\( \sqrt{2} \) | |
| 9\( \sqrt{2} \) | |
| 8\( \sqrt{2} \) | |
| 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\( \sqrt{2} \)