| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.11 |
| Score | 0% | 62% |
What is the circumference of a circle with a diameter of 2?
| 2π | |
| 9π | |
| 15π | |
| 32π |
The formula for circumference is circle diameter x π:
c = πd
c = 2π
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
exponents |
|
division |
|
addition |
|
pairs |
When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)
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 x:
-5x - 1 < -3 + 4x
| x < \(\frac{2}{9}\) | |
| x < -\(\frac{7}{8}\) | |
| x < 4 | |
| x < 2\(\frac{2}{3}\) |
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 < sign and the answer on the other.
-5x - 1 < -3 + 4x
-5x < -3 + 4x + 1
-5x - 4x < -3 + 1
-9x < -2
x < \( \frac{-2}{-9} \)
x < \(\frac{2}{9}\)
Solve for b:
b2 - 12b + 51 = 3b - 3
| 9 or 9 | |
| 5 or -6 | |
| 6 or 9 | |
| 6 or -1 |
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 - 12b + 51 = 3b - 3
b2 - 12b + 51 + 3 = 3b
b2 - 12b - 3b + 54 = 0
b2 - 15b + 54 = 0
Next, factor the quadratic equation:
b2 - 15b + 54 = 0
(b - 6)(b - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 6) or (b - 9) must equal zero:
If (b - 6) = 0, b must equal 6
If (b - 9) = 0, b must equal 9
So the solution is that b = 6 or 9