| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.86 |
| Score | 0% | 57% |
Which of the following is not true about both rectangles and squares?
the area is length x width |
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the lengths of all sides are equal |
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all interior angles are right angles |
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the perimeter is the sum of the lengths of all four sides |
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
Simplify 8a x 2b.
| 16ab | |
| 16\( \frac{a}{b} \) | |
| 10ab | |
| 16\( \frac{b}{a} \) |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
8a x 2b = (8 x 2) (a x b) = 16ab
The formula for the area of a circle is which of the following?
c = π r |
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c = π d2 |
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c = π d |
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c = π r2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
If a = c = 8, b = d = 9, and the blue angle = 71°, what is the area of this parallelogram?
| 72 | |
| 20 | |
| 42 | |
| 24 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 8 x 9
a = 72
Solve for c:
c2 - 4c - 1 = -4c + 3
| 9 or -9 | |
| 4 or -1 | |
| -2 or -7 | |
| 2 or -2 |
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:
c2 - 4c - 1 = -4c + 3
c2 - 4c - 1 - 3 = -4c
c2 - 4c + 4c - 4 = 0
c2 - 4 = 0
Next, factor the quadratic equation:
c2 - 4 = 0
(c - 2)(c + 2) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 2) must equal zero:
If (c - 2) = 0, c must equal 2
If (c + 2) = 0, c must equal -2
So the solution is that c = 2 or -2