| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.10 |
| Score | 0% | 62% |
The endpoints of this line segment are at (-2, -9) and (2, 1). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x - 3 | |
| y = 2\(\frac{1}{2}\)x - 4 | |
| y = -2x + 3 | |
| y = \(\frac{1}{2}\)x + 0 |
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 x:
x2 - 6x + 25 = 5x - 5
| 6 or 1 | |
| 7 or -7 | |
| 4 or -2 | |
| 5 or 6 |
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:
x2 - 6x + 25 = 5x - 5
x2 - 6x + 25 + 5 = 5x
x2 - 6x - 5x + 30 = 0
x2 - 11x + 30 = 0
Next, factor the quadratic equation:
x2 - 11x + 30 = 0
(x - 5)(x - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (x - 5) or (x - 6) must equal zero:
If (x - 5) = 0, x must equal 5
If (x - 6) = 0, x must equal 6
So the solution is that x = 5 or 6
If angle a = 24° and angle b = 22° what is the length of angle c?
| 134° | |
| 99° | |
| 122° | |
| 92° |
The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 24° - 22° = 134°
The formula for the area of a circle is which of the following?
a = π d |
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a = π r2 |
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a = π d2 |
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a = π r |
The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)2 : a = π r2.
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).