widget wonders produces widgets. they have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
the company also discovered that it cost $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
find the total cost of producing 5 widgets.

I know this is an older question, but for those who may come across this question, this is the answer I got.

The answer is $17.5.

Step-by-step explanation:

c(x) = ax^(2) + bx + c

c(3) = 15.5 = (equation)

c(7) = 23.5 = (equation)

c(12) = 56 = (equation)

The first two equations

9a + 3b + c = 15.5      | x -1

+ 49a + 7b + c = 23.5

-9a - 3b - c =-15.5

+ 49a + 7b + c = 23.5

= 40a + 4b = 8/4

= 10a + b = 2

The second and third equations

49a + 7b + c = 23.5     | x -1

+ 144a + 12b + c = 56

-49a - 7b - c = -23.5

+ 144a + 12b + c = 56

= 95a + 5b = 32.5/5

= 19a + b = 6.5

Now, we solve for a, b, and c

10a + b = 2    | x -1

+ 19a + b = 6.5

-10a - b = -2

+ 19a + b = 6.5

= 9a = 4.5/9

= a = 0.5

10(0.5) + b = 2

5 + b = 2    | -5

= b = -3

49(0.5) + 7(-3) + c = 23.5

24.5 - 21 + c = 23.5

3.5 + c = 23.5     | -3.5

c = 20

Then, plug it into the equation

c(x) = 0.5x^2 - 3x + 20

c(x) = 0.5(5)^2 - 3(5) + 20

c(x) = 12.5 - 15 + 20

c(x) = 17.5

there are no figures how am i supposed to answer this question

step-by-step explanation:

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.