| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.09 |
| Score | 0% | 62% |
Solve for b:
b2 - b - 73 = -2b - 1
| 7 or -6 | |
| 8 or -9 | |
| 9 or 8 | |
| 5 or 1 |
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:
b2 - b - 73 = -2b - 1
b2 - b - 73 + 1 = -2b
b2 - b + 2b - 72 = 0
b2 + b - 72 = 0
Next, factor the quadratic equation:
b2 + b - 72 = 0
(b - 8)(b + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 8) or (b + 9) must equal zero:
If (b - 8) = 0, b must equal 8
If (b + 9) = 0, b must equal -9
So the solution is that b = 8 or -9
If angle a = 39° and angle b = 65° what is the length of angle c?
| 76° | |
| 105° | |
| 75° | |
| 82° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 39° - 65° = 76°
The endpoints of this line segment are at (-2, -5) and (2, 1). What is the slope-intercept equation for this line?
| y = -3x - 4 | |
| y = -x + 4 | |
| y = -\(\frac{1}{2}\)x - 3 | |
| 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, -5) and (2, 1) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (-5.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Plugging these values into the slope-intercept equation:
y = 1\(\frac{1}{2}\)x - 2
Breaking apart a quadratic expression into a pair of binomials is called:
factoring |
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normalizing |
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deconstructing |
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squaring |
To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.
On this circle, line segment AB is the:
diameter |
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radius |
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circumference |
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chord |
A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).