| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.15 |
| Score | 0% | 63% |
The dimensions of this cube are height (h) = 2, length (l) = 6, and width (w) = 4. What is the volume?
| 135 | |
| 112 | |
| 320 | |
| 48 |
The volume of a cube is height x length x width:
v = h x l x w
v = 2 x 6 x 4
v = 48
A right angle measures:
90° |
|
360° |
|
180° |
|
45° |
A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
|
c - a |
|
c2 + a2 |
|
c2 - a2 |
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, \(c = \sqrt{a + b}\)
Solve for z:
-5z + 4 = \( \frac{z}{-2} \)
| -\(\frac{4}{37}\) | |
| 1\(\frac{8}{13}\) | |
| -1\(\frac{1}{44}\) | |
| \(\frac{8}{9}\) |
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 + 4 = \( \frac{z}{-2} \)
-2 x (-5z + 4) = z
(-2 x -5z) + (-2 x 4) = z
10z - 8 = z
10z - 8 - z = 0
10z - z = 8
9z = 8
z = \( \frac{8}{9} \)
z = \(\frac{8}{9}\)
Solve for b:
b2 - 7b - 61 = -5b + 2
| -2 or -8 | |
| 8 or -9 | |
| 7 or 6 | |
| -7 or 9 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
b2 - 7b - 61 = -5b + 2
b2 - 7b - 61 - 2 = -5b
b2 - 7b + 5b - 63 = 0
b2 - 2b - 63 = 0
Next, factor the quadratic equation:
b2 - 2b - 63 = 0
(b + 7)(b - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 7) or (b - 9) must equal zero:
If (b + 7) = 0, b must equal -7
If (b - 9) = 0, b must equal 9
So the solution is that b = -7 or 9