For a direct variation, f(x) = kx. Therefore, for f(x) = 30x, constant of variation (k) = 30.
You have to put the numbers in order and find the middle value so in this case it's-
2, 4, 4, 5, 6, 7, 8, 8, 8
The answer is $6
2 candies will be left over after you but ten in each bag.
The 3 pack cost $9.45
3 single cartons would have cost: 3 x 4.20 = $12.60
Difference in cost: 12.60 - 9.45 = $3.15
Percent savings : 3.15/ 9.45 = 0.3333
0.333 x 109 = 33.33%
Round the answer as needed
Answer: x = 4 and x = -3/2
Procedure:
1) Given: 2x^2 - 5x - 12 = 0
2) Multiply both sides by : 2(2x^2) - 2(5x) - 2(12) = 0
3) Rearrange: (2x)^2 -5(2x) - 24 = 0
4) Notice that the common factor is (2x)
5) Set the parenthesis with the common factor inside:
(2x ) (2x ) =0
6) The first sign is the same sign of the second term of the trinomial, which is negative, the second sign is the product of the signs of the second and the third terms of the polynomial, which is (-)*(-) = + (positive)
(2x - )(2x + ) = 0
7) find two numbers that sum up - 5x and its product is -24.
- 8 + 3 = - 5
(-8)(+3) = -24
=> the numbers in the factors are -8 and +3
(2x - 8) (2x + 3) = 0
That is the factored equation. Now you can solve
8) a) 2x - 8 = 0 => 2x = 8 => x = 8/2 => x = 4
b) 2x + 3 = 0 => 2x = - 3 => x = - 3/2
Answer: the two solutions are x = 4 and x = -3/2