| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.98 |
| Score | 0% | 60% |
What is the circumference of a circle with a diameter of 6?
| 8π | |
| 6π | |
| 32π | |
| 14π |
The formula for circumference is circle diameter x π:
c = πd
c = 6π
If side a = 8, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{65} \) | |
| \( \sqrt{80} \) | |
| \( \sqrt{89} \) | |
| 10 |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 82 + 42
c2 = 64 + 16
c2 = 80
c = \( \sqrt{80} \)
Solve for c:
-2c - 5 = 6 - 3c
| 11 | |
| -4\(\frac{1}{2}\) | |
| \(\frac{5}{7}\) | |
| -4 |
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.
-2c - 5 = 6 - 3c
-2c = 6 - 3c + 5
-2c + 3c = 6 + 5
c = 11
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, \(c = \sqrt{a + b}\)
Solve for z:
z2 + 5z - 14 = 0
| 2 or -5 | |
| 2 or -7 | |
| 5 or 1 | |
| 9 or 3 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
z2 + 5z - 14 = 0
(z - 2)(z + 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 2) or (z + 7) must equal zero:
If (z - 2) = 0, z must equal 2
If (z + 7) = 0, z must equal -7
So the solution is that z = 2 or -7