| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.12 |
| Score | 0% | 62% |
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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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 add monomials that have the same variable and the same exponent |
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, -1) and (2, 5). What is the slope-intercept equation for this line?
| y = 3x + 0 | |
| y = -3x - 2 | |
| y = 2x - 4 | |
| y = 1\(\frac{1}{2}\)x + 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 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, -1) and (2, 5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(5.0) - (-1.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x + 2
Solve for z:
z2 - 20 = -2z + 4
| 4 or -6 | |
| -1 or -5 | |
| -4 or -9 | |
| 7 or -4 |
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
z2 - 20 = -2z + 4
z2 - 20 - 4 = -2z
z2 + + 2z - 24 = 0
z2 + 2z - 24 = 0
Next, factor the quadratic equation:
z2 + 2z - 24 = 0
(z - 4)(z + 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 4) or (z + 6) must equal zero:
If (z - 4) = 0, z must equal 4
If (z + 6) = 0, z must equal -6
So the solution is that z = 4 or -6
What is the area of a circle with a radius of 2?
| 36π | |
| 3π | |
| 4π | |
| 49π |
The formula for area is πr2:
a = πr2
a = π(22)
a = 4π
What is 8a - 5a?
| 40a2 | |
| 40a | |
| a2 | |
| 3a |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
8a - 5a = 3a