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|---|---|---|
| Questions | 5 | 5 |
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On this circle, line segment AB is the:
circumference |
|
diameter |
|
radius |
|
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).
On this circle, line segment CD is the:
chord |
|
radius |
|
circumference |
|
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).
Solve for a:
a2 + 5a - 17 = -a - 1
| 6 or 4 | |
| 2 or -8 | |
| 6 or 1 | |
| 2 or -7 |
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 + 5a - 17 = -a - 1
a2 + 5a - 17 + 1 = -a
a2 + 5a + a - 16 = 0
a2 + 6a - 16 = 0
Next, factor the quadratic equation:
a2 + 6a - 16 = 0
(a - 2)(a + 8) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 2) or (a + 8) must equal zero:
If (a - 2) = 0, a must equal 2
If (a + 8) = 0, a must equal -8
So the solution is that a = 2 or -8
Find the value of c:
-2c + z = -2
-5c + 3z = 4
| 10 | |
| \(\frac{1}{3}\) | |
| -\(\frac{3}{7}\) | |
| -3\(\frac{8}{15}\) |
You need to find the value of c so solve the first equation in terms of z:
-2c + z = -2
z = -2 + 2c
then substitute the result (-2 - -2c) into the second equation:
-5c + 3(-2 + 2c) = 4
-5c + (3 x -2) + (3 x 2c) = 4
-5c - 6 + 6c = 4
-5c + 6c = 4 + 6
c = 10
c = \( \frac{10}{1} \)
c = 10
The endpoints of this line segment are at (-2, -5) and (2, -3). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x + 0 | |
| y = -1\(\frac{1}{2}\)x + 2 | |
| y = \(\frac{1}{2}\)x - 4 | |
| y = 3x - 3 |
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, -5) and (2, -3) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-3.0) - (-5.0)}{(2) - (-2)} \) = \( \frac{2}{4} \)Plugging these values into the slope-intercept equation:
y = \(\frac{1}{2}\)x - 4