| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.72 |
| Score | 0% | 54% |
Solve for a:
10a + 5 = 4 + 9a
| -1 | |
| -\(\frac{1}{2}\) | |
| \(\frac{2}{3}\) | |
| \(\frac{1}{2}\) |
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.
10a + 5 = 4 + 9a
10a = 4 + 9a - 5
10a - 9a = 4 - 5
a = -1
Which of the following is not required to define the slope-intercept equation for a line?
x-intercept |
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slope |
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y-intercept |
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\({\Delta y \over \Delta x}\) |
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.
Factor y2 + 11y + 24
| (y + 3)(y - 8) | |
| (y - 3)(y + 8) | |
| (y - 3)(y - 8) | |
| (y + 3)(y + 8) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 24 as well and sum (Inside, Outside) to equal 11. For this problem, those two numbers are 3 and 8. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 + 11y + 24
y2 + (3 + 8)y + (3 x 8)
(y + 3)(y + 8)
Solve for a:
a2 + 20a + 61 = 5a + 5
| 7 or -8 | |
| -4 or -7 | |
| 4 or -8 | |
| -7 or -8 |
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:
a2 + 20a + 61 = 5a + 5
a2 + 20a + 61 - 5 = 5a
a2 + 20a - 5a + 56 = 0
a2 + 15a + 56 = 0
Next, factor the quadratic equation:
a2 + 15a + 56 = 0
(a + 7)(a + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 7) or (a + 8) must equal zero:
If (a + 7) = 0, a must equal -7
If (a + 8) = 0, a must equal -8
So the solution is that a = -7 or -8
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 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 |
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.