| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.33 |
| Score | 0% | 67% |
What is the circumference of a circle with a diameter of 10?
| 16π | |
| 2π | |
| 6π | |
| 10π |
The formula for circumference is circle diameter x π:
c = πd
c = 10π
If the area of this square is 9, what is the length of one of the diagonals?
| 6\( \sqrt{2} \) | |
| 3\( \sqrt{2} \) | |
| 4\( \sqrt{2} \) | |
| 2\( \sqrt{2} \) |
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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3
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 = 32 + 32
c2 = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)
Solve for x:
x2 - 8x + 7 = 0
| 6 or -7 | |
| 1 or 7 | |
| -2 or -4 | |
| 9 or 8 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
x2 - 8x + 7 = 0
(x - 1)(x - 7) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 1) or (x - 7) must equal zero:
If (x - 1) = 0, x must equal 1
If (x - 7) = 0, x must equal 7
So the solution is that x = 1 or 7
A trapezoid is a quadrilateral with one set of __________ sides.
right angle |
|
equal angle |
|
parallel |
|
equal length |
A trapezoid is a quadrilateral with one set of parallel sides.
If a = 7 and y = -2, what is the value of -5a(a - y)?
| -315 | |
| -160 | |
| -90 | |
| 32 |
To solve this equation, 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.)
-5a(a - y)
-5(7)(7 + 2)
-5(7)(9)
(-35)(9)
-315