| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.95 |
| Score | 0% | 59% |
If AD = 14 and BD = 5, AB = ?
| 3 | |
| 12 | |
| 15 | |
| 9 |
The entire length of this line is represented by AD which is AB + BD:
AD = AB + BD
Solving for AB:AB = AD - BDSolve for c:
c2 + c - 7 = -2c + 3
| 8 or 7 | |
| 2 or -5 | |
| 9 or -8 | |
| -5 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:
c2 + c - 7 = -2c + 3
c2 + c - 7 - 3 = -2c
c2 + c + 2c - 10 = 0
c2 + 3c - 10 = 0
Next, factor the quadratic equation:
c2 + 3c - 10 = 0
(c - 2)(c + 5) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 5) must equal zero:
If (c - 2) = 0, c must equal 2
If (c + 5) = 0, c must equal -5
So the solution is that c = 2 or -5
What is the circumference of a circle with a diameter of 14?
| 28π | |
| 6π | |
| 9π | |
| 14π |
The formula for circumference is circle diameter x π:
c = πd
c = 14π
The endpoints of this line segment are at (-2, -4) and (2, 2). What is the slope of this line?
| 3 | |
| 2\(\frac{1}{2}\) | |
| 2 | |
| 1\(\frac{1}{2}\) |
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, 2) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(2.0) - (-4.0)}{(2) - (-2)} \) = \( \frac{6}{4} \)Factor y2 - 6y + 8
| (y + 4)(y + 2) | |
| (y + 4)(y - 2) | |
| (y - 4)(y - 2) | |
| (y - 4)(y + 2) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 8 as well and sum (Inside, Outside) to equal -6. For this problem, those two numbers are -4 and -2. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 6y + 8
y2 + (-4 - 2)y + (-4 x -2)
(y - 4)(y - 2)