A study 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 3,554 2013 3,598 2014 3,603 2015 3,655 2016 3,718 2017 3,794 The study found that the data after the year 2012 can be modeled by the function f(x) = 52.3x + 3,548, where x is the number of years since 2012 and f(x) is the total amount of salt ingested in grams. Describe the significance of 3,548. An estimate of the average grams of salt used in 2012 An estimate of the average grams of salt used in 2013 The average amount of salt in grams used in 2012 The average amount of salt in grams used in 2013

Is an estimate of the average grams of salt used in 2012

Step-by-step explanation:

Let

x ---> the number of years since 2012

f(x) ---> is the total amount of salt ingested in grams

we have

This is a linear equation in slope intercept form

where

The slope is equal to

The y-intercept or initial value is equal to

The y-intercept is the value of the function f(x) when the value of x is equal to zero

In this context, the y-intercept is the average amount of grams of salt ingested  in the year 2012

The exact value of the average amount of grams of salt ingested  in the year 2012 is 3,554 grams (see the data in the table)

Compare the exact value with the y-intercept

therefore

3,548 grams Is an estimate of the average grams of salt used in 2012

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step-by-step explanation:

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.