| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.04 |
| Score | 0% | 61% |
If a = c = 4, b = d = 2, what is the area of this rectangle?
| 5 | |
| 48 | |
| 8 | |
| 63 |
The area of a rectangle is equal to its length x width:
a = l x w
a = a x b
a = 4 x 2
a = 8
Solve for a:
a2 + 8a + 44 = -5a + 4
| -5 or -7 | |
| 1 or -5 | |
| -5 or -8 | |
| 7 or 3 |
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 + 8a + 44 = -5a + 4
a2 + 8a + 44 - 4 = -5a
a2 + 8a + 5a + 40 = 0
a2 + 13a + 40 = 0
Next, factor the quadratic equation:
a2 + 13a + 40 = 0
(a + 5)(a + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 5) or (a + 8) must equal zero:
If (a + 5) = 0, a must equal -5
If (a + 8) = 0, a must equal -8
So the solution is that a = -5 or -8
The endpoints of this line segment are at (-2, -9) and (2, 1). What is the slope-intercept equation for this line?
| y = 3x - 3 | |
| y = \(\frac{1}{2}\)x + 2 | |
| y = 2\(\frac{1}{2}\)x - 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 -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, -9) and (2, 1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (-9.0)}{(2) - (-2)} \) = \( \frac{10}{4} \)Plugging these values into the slope-intercept equation:
y = 2\(\frac{1}{2}\)x - 4
Solve for c:
c2 + 9c + 8 = 0
| 6 or 5 | |
| 6 or 6 | |
| -1 or -8 | |
| 9 or 1 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
c2 + 9c + 8 = 0
(c + 1)(c + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 1) or (c + 8) must equal zero:
If (c + 1) = 0, c must equal -1
If (c + 8) = 0, c must equal -8
So the solution is that c = -1 or -8
A(n) __________ is two expressions separated by an equal sign.
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formula |
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equation |
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expression |
An equation is two expressions separated by an equal sign. The key to solving equations is to 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.