Dave ordered dinner for a party of 10 people. three people ordered the $4.75 chicken dinner, two people ordered the $4.95 fish dinner, and five had the beef dinner at a cost of $6.75 each. what was the average cost of each dinner at dave's party?

The average cost of each dinner at Dave's party is $5.79.

Step-by-step explanation:

Given:

Dave ordered dinner for a party of 10 people.

Three people ordered the $4.75 chicken dinner, two people ordered the $4.95 fish dinner, and five had the beef dinner at a cost of $6.75 each.

Now, to find the average cost of each dinner at Dave's party.

So, we get the total amount for the dinner:

Three people ordered the $4.75 chicken dinner.

Two people ordered the $4.95 fish dinner.

Five had the beef dinner at a cost of $6.75.

Total amount of dinner =

Now, to get the average cost of each dinner of 10 people we divide the total amount of dinner by 10:

Therefore, the average cost of each dinner at Dave's party is $5.79.

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.