Astudy analyzed the average yearly salt intake in the united states from 2012 thru 2017. the data is summarized in the table
year
annual salt intake
(grams)
2012 3,618
2013 3,646
2014 3,680
2015 3,716
2016 3,751
2017 3,790
the study found that the data after the year 2012 can be modeled by the function f(x) = 41.8x + 3,608, where x is the numbe
amount of salt ingested in grams. describe the significance of 3,608.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

b

step-by-step explanation:

the word superfluous means unnecessary

x equals 1

step-by-step explanation:

f(4)=f(×)

x=1