| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.52 |
| Score | 0% | 70% |
Solve for x:
x2 - 3x - 16 = -x - 1
| -6 or -8 | |
| 8 or -2 | |
| 4 or -9 | |
| -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:
x2 - 3x - 16 = -x - 1
x2 - 3x - 16 + 1 = -x
x2 - 3x + x - 15 = 0
x2 - 2x - 15 = 0
Next, factor the quadratic equation:
x2 - 2x - 15 = 0
(x + 3)(x - 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 3) or (x - 5) must equal zero:
If (x + 3) = 0, x must equal -3
If (x - 5) = 0, x must equal 5
So the solution is that x = -3 or 5
What is 4a7 + 6a7?
| -2a14 | |
| -2 | |
| 10a7 | |
| 24a14 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
4a7 + 6a7 = 10a7
A trapezoid is a quadrilateral with one set of __________ sides.
parallel |
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right angle |
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equal angle |
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equal length |
A trapezoid is a quadrilateral with one set of parallel sides.
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
division |
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pairs |
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exponents |
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addition |
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.)
Which of the following is not true about both rectangles and squares?
the perimeter is the sum of the lengths of all four sides |
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the lengths of all sides are equal |
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the area is length x width |
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all interior angles are right angles |
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).