| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.20 |
| Score | 0% | 64% |
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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all of these statements are correct |
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you can subtract 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 |
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 formula for the area of a circle is which of the following?
a = π r2 |
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a = π r |
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a = π d |
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a = π d2 |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
h2 x l2 x w2 |
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2lw x 2wh + 2lh |
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lw x wh + lh |
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h x l x w |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
If side a = 8, side b = 7, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{98} \) | |
| \( \sqrt{145} \) | |
| \( \sqrt{82} \) | |
| \( \sqrt{113} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 82 + 72
c2 = 64 + 49
c2 = 113
c = \( \sqrt{113} \)
The endpoints of this line segment are at (-2, -1) and (2, -5). What is the slope-intercept equation for this line?
| y = 3x + 1 | |
| y = -x - 3 | |
| y = -2\(\frac{1}{2}\)x - 3 | |
| y = -3x + 2 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -3. 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, -1) and (2, -5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-5.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{-4}{4} \)Plugging these values into the slope-intercept equation:
y = -x - 3