| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.39 |
| Score | 0% | 68% |
Which of the following is not true about both rectangles and squares?
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 |
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the area is length x width |
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 6a x 8b.
| 14ab | |
| 48\( \frac{a}{b} \) | |
| 48ab | |
| 48a2b2 |
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.
6a x 8b = (6 x 8) (a x b) = 48ab
Which of the following statements about math operations is incorrect?
you can add monomials that have the same variable and the same exponent |
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you can multiply monomials that have different variables and different exponents |
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all of these statements are correct |
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you can subtract monomials that have the same variable and the same exponent |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.
A(n) __________ is two expressions separated by an equal sign.
problem |
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expression |
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formula |
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equation |
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.
Find the value of a:
6a + x = -3
-3a - 6x = -9
| -\(\frac{19}{21}\) | |
| -\(\frac{17}{30}\) | |
| -\(\frac{9}{11}\) | |
| 2\(\frac{1}{5}\) |
You need to find the value of a so solve the first equation in terms of x:
6a + x = -3
x = -3 - 6a
then substitute the result (-3 - 6a) into the second equation:
-3a - 6(-3 - 6a) = -9
-3a + (-6 x -3) + (-6 x -6a) = -9
-3a + 18 + 36a = -9
-3a + 36a = -9 - 18
33a = -27
a = \( \frac{-27}{33} \)
a = -\(\frac{9}{11}\)