Two High Schools ordered AP Chemistry text book from the same book store. A New Hampshire school has ordered 80 copies, while a Vermont school ordered only 55 copies. The store has 70 books in its warehouses in Massachusetts and 100 books in the other warehouse in New York. Shipping one copy from Massachusetts to New Hampshire costs $2 and from Massachusetts to Vermont costs $3. Shipping from New York’s warehouse is respectively $2.5 and $1.7. How many copies should the company ship from each warehouse to each school to minimize the shipping costs on these two orders?

table 3 represents a direct variation function. : )

1260=3*6*7*10=3^2*2^2*7*5 perfect cude = 3^3*2^

step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.