| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.80 |
| Score | 0% | 56% |
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 add monomials that have the same variable and the same exponent |
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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.
The endpoints of this line segment are at (-2, -6) and (2, 4). What is the slope of this line?
| -1 | |
| -2 | |
| -\(\frac{1}{2}\) | |
| 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, -6) and (2, 4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(4.0) - (-6.0)}{(2) - (-2)} \) = \( \frac{10}{4} \)If side a = 6, side b = 6, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{72} \) | |
| \( \sqrt{117} \) | |
| \( \sqrt{85} \) | |
| \( \sqrt{90} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 62 + 62
c2 = 36 + 36
c2 = 72
c = \( \sqrt{72} \)
Solve for y:
y - 6 = 9 + 3y
| \(\frac{1}{7}\) | |
| 1\(\frac{1}{3}\) | |
| -7\(\frac{1}{2}\) | |
| 8 |
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 equal sign and the answer on the other.
y - 6 = 9 + 3y
y = 9 + 3y + 6
y - 3y = 9 + 6
-2y = 15
y = \( \frac{15}{-2} \)
y = -7\(\frac{1}{2}\)
Which of the following is not required to define the slope-intercept equation for a line?
\({\Delta y \over \Delta x}\) |
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x-intercept |
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y-intercept |
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slope |
A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.