| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.40 |
| Score | 0% | 48% |
Which of the following statements about math operations is incorrect?
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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you can add 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.
The endpoints of this line segment are at (-2, 3) and (2, -9). What is the slope of this line?
| 1\(\frac{1}{2}\) | |
| -2 | |
| -3 | |
| 2\(\frac{1}{2}\) |
The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 3) and (2, -9) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-9.0) - (3.0)}{(2) - (-2)} \) = \( \frac{-12}{4} \)Find the value of a:
-3a + x = -3
-5a - 4x = 2
| 1\(\frac{8}{21}\) | |
| \(\frac{10}{19}\) | |
| \(\frac{10}{17}\) | |
| -\(\frac{10}{17}\) |
You need to find the value of a so solve the first equation in terms of x:
-3a + x = -3
x = -3 + 3a
then substitute the result (-3 - -3a) into the second equation:
-5a - 4(-3 + 3a) = 2
-5a + (-4 x -3) + (-4 x 3a) = 2
-5a + 12 - 12a = 2
-5a - 12a = 2 - 12
-17a = -10
a = \( \frac{-10}{-17} \)
a = \(\frac{10}{17}\)
For this diagram, the Pythagorean theorem states that b2 = ?
a2 - c2 |
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c - a |
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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, \(c = \sqrt{a + b}\)
Solve 7a - 3a = -9a - 6z - 5 for a in terms of z.
| -\(\frac{3}{16}\)z - \(\frac{5}{16}\) | |
| 1\(\frac{1}{3}\)z - 2 | |
| -3\(\frac{1}{2}\)z + \(\frac{1}{4}\) | |
| -z + \(\frac{2}{3}\) |
To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.
7a - 3z = -9a - 6z - 5
7a = -9a - 6z - 5 + 3z
7a + 9a = -6z - 5 + 3z
16a = -3z - 5
a = \( \frac{-3z - 5}{16} \)
a = \( \frac{-3z}{16} \) + \( \frac{-5}{16} \)
a = -\(\frac{3}{16}\)z - \(\frac{5}{16}\)