| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.58 |
| Score | 0% | 72% |
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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you can subtract monomials that have the same variable and the same exponent |
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all of these statements are correct |
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.
Solve for b:
6b - 1 < \( \frac{b}{-4} \)
| b < -\(\frac{16}{19}\) | |
| b < -\(\frac{18}{41}\) | |
| b < 1\(\frac{13}{23}\) | |
| b < \(\frac{4}{25}\) |
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.
6b - 1 < \( \frac{b}{-4} \)
-4 x (6b - 1) < b
(-4 x 6b) + (-4 x -1) < b
-24b + 4 < b
-24b + 4 - b < 0
-24b - b < -4
-25b < -4
b < \( \frac{-4}{-25} \)
b < \(\frac{4}{25}\)
If side a = 8, side b = 4, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{80} \) | |
| \( \sqrt{17} \) | |
| \( \sqrt{58} \) | |
| \( \sqrt{2} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 82 + 42
c2 = 64 + 16
c2 = 80
c = \( \sqrt{80} \)
If a = 8, b = 4, c = 5, and d = 7, what is the perimeter of this quadrilateral?
| 29 | |
| 17 | |
| 24 | |
| 26 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 8 + 4 + 5 + 7
p = 24
Which of the following is not a part of PEMDAS, the acronym for math order of operations?
pairs |
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exponents |
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division |
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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.)