| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.48 |
| Score | 0% | 70% |
If a = 4, b = 8, c = 8, and d = 9, what is the perimeter of this quadrilateral?
| 19 | |
| 22 | |
| 21 | |
| 29 |
Perimeter is equal to the sum of the four sides:
p = a + b + c + d
p = 4 + 8 + 8 + 9
p = 29
If side a = 5, side b = 2, what is the length of the hypotenuse of this right triangle?
| \( \sqrt{130} \) | |
| \( \sqrt{29} \) | |
| \( \sqrt{17} \) | |
| \( \sqrt{68} \) |
According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:
c2 = a2 + b2
c2 = 52 + 22
c2 = 25 + 4
c2 = 29
c = \( \sqrt{29} \)
Simplify (4a)(3ab) - (5a2)(9b).
| 98a2b | |
| 57ab2 | |
| 33ab2 | |
| -33a2b |
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)(3ab) - (5a2)(9b)
(4 x 3)(a x a x b) - (5 x 9)(a2 x b)
(12)(a1+1 x b) - (45)(a2b)
12a2b - 45a2b
-33a2b
Simplify (y + 6)(y - 1)
| y2 + 7y + 6 | |
| y2 - 7y + 6 | |
| y2 + 5y - 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
Which of the following statements about math operations is incorrect?
all of these statements are correct |
|
you can multiply monomials that have different variables and different exponents |
|
you can subtract monomials that have the same variable and the same exponent |
|
you can add monomials that have the same variable and the same exponent |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.