| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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Solve for a:
a2 - 2a - 41 = -2a - 5
| 8 or -2 | |
| 6 or -6 | |
| 5 or -8 | |
| 9 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:
a2 - 2a - 41 = -2a - 5
a2 - 2a - 41 + 5 = -2a
a2 - 2a + 2a - 36 = 0
a2 - 36 = 0
Next, factor the quadratic equation:
a2 - 36 = 0
(a - 6)(a + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 6) or (a + 6) must equal zero:
If (a - 6) = 0, a must equal 6
If (a + 6) = 0, a must equal -6
So the solution is that a = 6 or -6
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
addition |
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division |
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exponents |
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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.)
A(n) __________ is two expressions separated by an equal sign.
equation |
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expression |
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formula |
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problem |
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.
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
2lw x 2wh + 2lh |
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h x l x w |
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h2 x l2 x w2 |
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lw x wh + lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
A quadrilateral is a shape with __________ sides.
2 |
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3 |
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5 |
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4 |
A quadrilateral is a shape with four sides. The perimeter of a quadrilateral is the sum of the lengths of its four sides.