| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
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Solve for c:
c2 + 6c - 27 = c - 3
| 6 or -7 | |
| 9 or -1 | |
| 3 or -8 | |
| 6 or 4 |
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:
c2 + 6c - 27 = c - 3
c2 + 6c - 27 + 3 = c
c2 + 6c - c - 24 = 0
c2 + 5c - 24 = 0
Next, factor the quadratic equation:
c2 + 5c - 24 = 0
(c - 3)(c + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 3) or (c + 8) must equal zero:
If (c - 3) = 0, c must equal 3
If (c + 8) = 0, c must equal -8
So the solution is that c = 3 or -8
On this circle, a line segment connecting point A to point D is called:
circumference |
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chord |
|
radius |
|
diameter |
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).
On this circle, line segment AB is the:
chord |
|
circumference |
|
diameter |
|
radius |
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).
Find the value of a:
7a + x = -7
-6a + 6x = -2
| 1\(\frac{3}{26}\) | |
| -1\(\frac{2}{3}\) | |
| -\(\frac{5}{6}\) | |
| -\(\frac{1}{23}\) |
You need to find the value of a so solve the first equation in terms of x:
7a + x = -7
x = -7 - 7a
then substitute the result (-7 - 7a) into the second equation:
-6a + 6(-7 - 7a) = -2
-6a + (6 x -7) + (6 x -7a) = -2
-6a - 42 - 42a = -2
-6a - 42a = -2 + 42
-48a = 40
a = \( \frac{40}{-48} \)
a = -\(\frac{5}{6}\)
The endpoints of this line segment are at (-2, -4) and (2, 0). What is the slope-intercept equation for this line?
| y = x - 2 | |
| y = -3x + 3 | |
| y = 2x + 0 | |
| y = 2x + 1 |
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, -4) and (2, 0) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(0.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{4}{4} \)Plugging these values into the slope-intercept equation:
y = x - 2