| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.65 |
| Score | 0% | 53% |
Solve for z:
z2 - 13z + 36 = 0
| 1 or -5 | |
| 4 or 9 | |
| 5 or -6 | |
| 4 or -1 |
The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:
z2 - 13z + 36 = 0
(z - 4)(z - 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (z - 4) or (z - 9) must equal zero:
If (z - 4) = 0, z must equal 4
If (z - 9) = 0, z must equal 9
So the solution is that z = 4 or 9
The endpoints of this line segment are at (-2, -2) and (2, 4). What is the slope-intercept equation for this line?
| y = 1\(\frac{1}{2}\)x + 2 | |
| y = -2\(\frac{1}{2}\)x - 1 | |
| y = 1\(\frac{1}{2}\)x + 1 | |
| y = 2\(\frac{1}{2}\)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 1. 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, -2) and (2, 4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(4.0) - (-2.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x + 1
Solve for z:
8z - 4 > -7 - 7z
| z > -2\(\frac{1}{3}\) | |
| z > -\(\frac{1}{5}\) | |
| z > \(\frac{2}{3}\) | |
| z > \(\frac{3}{7}\) |
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 > sign and the answer on the other.
8z - 4 > -7 - 7z
8z > -7 - 7z + 4
8z + 7z > -7 + 4
15z > -3
z > \( \frac{-3}{15} \)
z > -\(\frac{1}{5}\)
A(n) __________ is to a parallelogram as a square is to a rectangle.
trapezoid |
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rhombus |
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quadrilateral |
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triangle |
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
When two lines intersect, adjacent angles are __________ (they add up to 180°) and angles across from either other are __________ (they're equal).
supplementary, vertical |
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acute, obtuse |
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obtuse, acute |
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vertical, supplementary |
Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).