| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.73 |
| Score | 0% | 55% |
Solve for a:
a2 - 9a + 21 = a - 3
| 4 or 6 | |
| 7 or 1 | |
| 8 or -9 | |
| 9 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:
a2 - 9a + 21 = a - 3
a2 - 9a + 21 + 3 = a
a2 - 9a - a + 24 = 0
a2 - 10a + 24 = 0
Next, factor the quadratic equation:
a2 - 10a + 24 = 0
(a - 4)(a - 6) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 4) or (a - 6) must equal zero:
If (a - 4) = 0, a must equal 4
If (a - 6) = 0, a must equal 6
So the solution is that a = 4 or 6
On this circle, a line segment connecting point A to point D is called:
radius |
|
chord |
|
diameter |
|
circumference |
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).
What is the circumference of a circle with a diameter of 17?
| 17π | |
| 12π | |
| 7π | |
| 4π |
The formula for circumference is circle diameter x π:
c = πd
c = 17π
The endpoints of this line segment are at (-2, 0) and (2, 8). What is the slope-intercept equation for this line?
| y = -3x + 2 | |
| y = 3x + 2 | |
| y = 2x + 4 | |
| 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 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, 0) and (2, 8) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(8.0) - (0.0)}{(2) - (-2)} \) = \( \frac{8}{4} \)Plugging these values into the slope-intercept equation:
y = 2x + 4
If side a = 3, side b = 8, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{5} \) | |
| \( \sqrt{73} \) | |
| \( \sqrt{58} \) | |
| \( \sqrt{8} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 32 + 82
c2 = 9 + 64
c2 = 73
c = \( \sqrt{73} \)