| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.18 |
| Score | 0% | 64% |
Simplify (4a)(5ab) - (9a2)(7b).
| 43ab2 | |
| 83ab2 | |
| 144a2b | |
| -43a2b |
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.
(4a)(5ab) - (9a2)(7b)
(4 x 5)(a x a x b) - (9 x 7)(a2 x b)
(20)(a1+1 x b) - (63)(a2b)
20a2b - 63a2b
-43a2b
Simplify (y - 6)(y + 1)
| y2 + 7y + 6 | |
| y2 + 5y - 6 | |
| y2 - 7y + 6 | |
| y2 - 5y - 6 |
To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:
(y - 6)(y + 1)
(y x y) + (y x 1) + (-6 x y) + (-6 x 1)
y2 + y - 6y - 6
y2 - 5y - 6
The endpoints of this line segment are at (-2, 1) and (2, -5). What is the slope-intercept equation for this line?
| y = -2\(\frac{1}{2}\)x - 1 | |
| y = -1\(\frac{1}{2}\)x - 2 | |
| y = -3x - 2 | |
| y = -1\(\frac{1}{2}\)x + 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, 1) and (2, -5) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-5.0) - (1.0)}{(2) - (-2)} \) = \( \frac{-6}{4} \)Plugging these values into the slope-intercept equation:
y = -1\(\frac{1}{2}\)x - 2
If a = 6, b = 5, c = 3, and d = 3, what is the perimeter of this quadrilateral?
| 16 | |
| 17 | |
| 22 | |
| 23 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 6 + 5 + 3 + 3
p = 17
If a = c = 6, b = d = 7, and the blue angle = 75°, what is the area of this parallelogram?
| 42 | |
| 6 | |
| 32 | |
| 3 |
The area of a parallelogram is equal to its length x width:
a = l x w
a = a x b
a = 6 x 7
a = 42