| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.07 |
| Score | 0% | 61% |
Find the value of c:
9c + x = 4
-7c - 2x = 4
| 1\(\frac{1}{3}\) | |
| 1\(\frac{1}{11}\) | |
| -\(\frac{47}{48}\) | |
| -1\(\frac{39}{41}\) |
You need to find the value of c so solve the first equation in terms of x:
9c + x = 4
x = 4 - 9c
then substitute the result (4 - 9c) into the second equation:
-7c - 2(4 - 9c) = 4
-7c + (-2 x 4) + (-2 x -9c) = 4
-7c - 8 + 18c = 4
-7c + 18c = 4 + 8
11c = 12
c = \( \frac{12}{11} \)
c = 1\(\frac{1}{11}\)
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 dimensions of this cylinder are height (h) = 9 and radius (r) = 3. What is the volume?
| 9π | |
| 108π | |
| 441π | |
| 81π |
The volume of a cylinder is πr2h:
v = πr2h
v = π(32 x 9)
v = 81π
A right angle measures:
90° |
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45° |
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360° |
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180° |
A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.
The endpoints of this line segment are at (-2, 0) and (2, 8). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x - 4 | |
| y = 2x + 4 | |
| y = -3x - 4 | |
| y = x - 1 |
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 4. 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, 0) and (2, 8) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(8.0) - (0.0)}{(2) - (-2)} \) = \( \frac{8}{4} \)Plugging these values into the slope-intercept equation:
y = 2x + 4