| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
The endpoints of this line segment are at (-2, -5) and (2, -3). What is the slope-intercept equation for this line?
| y = \(\frac{1}{2}\)x - 4 | |
| y = -3x + 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, -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
If a = 9, b = 9, c = 1, and d = 5, what is the perimeter of this quadrilateral?
| 24 | |
| 23 | |
| 19 | |
| 22 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 9 + 9 + 1 + 5
p = 24
Simplify (6a)(2ab) + (3a2)(8b).
| 36a2b | |
| 36ab2 | |
| 88ab2 | |
| -12a2b |
To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.
(6a)(2ab) + (3a2)(8b)
(6 x 2)(a x a x b) + (3 x 8)(a2 x b)
(12)(a1+1 x b) + (24)(a2b)
12a2b + 24a2b
36a2b
Which types of triangles will always have at least two sides of equal length?
equilateral and isosceles |
|
isosceles and right |
|
equilateral and right |
|
equilateral, isosceles and right |
An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.
Factor y2 - 3y - 40
| (y - 8)(y + 5) | |
| (y - 8)(y - 5) | |
| (y + 8)(y + 5) | |
| (y + 8)(y - 5) |
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 -40 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -8 and 5. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 3y - 40
y2 + (-8 + 5)y + (-8 x 5)
(y - 8)(y + 5)