| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.03 |
| Score | 0% | 61% |
A(n) __________ is to a parallelogram as a square is to a rectangle.
trapezoid |
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rhombus |
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quadrilateral |
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triangle |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
For this diagram, the Pythagorean theorem states that b2 = ?
c - a |
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a2 - c2 |
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c2 - a2 |
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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, \(c = \sqrt{a + b}\)
If a = c = 5, b = d = 7, what is the area of this rectangle?
| 14 | |
| 35 | |
| 54 | |
| 48 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 5 x 7
a = 35
A(n) __________ is two expressions separated by an equal sign.
problem |
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expression |
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equation |
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formula |
An equation is two expressions separated by an equal sign. The key to solving equations is to 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.
Solve for c:
c2 - 3c - 20 = -3c - 4
| 4 or -4 | |
| 1 or -7 | |
| -5 or -6 | |
| 3 or -5 |
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 - 3c - 20 = -3c - 4
c2 - 3c - 20 + 4 = -3c
c2 - 3c + 3c - 16 = 0
c2 - 16 = 0
Next, factor the quadratic equation:
c2 - 16 = 0
(c - 4)(c + 4) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 4) or (c + 4) must equal zero:
If (c - 4) = 0, c must equal 4
If (c + 4) = 0, c must equal -4
So the solution is that c = 4 or -4