Please answer all three questions and show work A 2012 repor

Please answer all three questions and show work.

A 2012 report by the Animal Pet Products Association stated Americans spent $30 billion on their pets in 2002. By 2011, that number measured $51 billion. Let y = amount (in $ billions) Americans will spend on their pets in year x, where x = 0 represents the war 2002. Which of the following linear equations could be used to predict the amount y (in $ billions) Americans spend on their pets in a given year x, where x = 0 represents the year 2002? Explain, show work. A. Use the equation from part (a) to predict the amount (in $ billions) Americans will spend on their pets in the year 2026. Round answer to nearest tenth of a billion dollars. Show work. Fill in the blanks to interpret the slope of the equation: The rate of change of pet expenditure with respect to time is billion dollars per (Include units of measurement.) Solve the system of equations using elimination by addition, substitution, or augmented matrix methods (your choice). Show work. 7x - 4y = 6 2x + 3y = 10 The feasible region shown below is bounded by lines -x + y= 1, 2x+y = 3, and y = 0. Find the coordinates of comer point A. Show work.

Solution

19.

a)Let y=mx+c

At x=0, y=30

At x=9, y=51

c=30

51=9m+30

m=21/9=2.333

Answer:c

b) in year 2026, x=2026-2002 = 24

y=2.33*24+30 = 86 billion dollars

c)

Change of rate of pet expenditure wrt time is 2.33 billion dollars per year

20.

7x-4y=6

2x+3y=10

Multiply the first equation by 3 and the second by 4

21x-12y = 18

8x+12y=40

Adding the two,

29x=58 or x=2

Substitute this in the first equation,

14-4y=6

or y=2

21.

Point A is the intersection of the lines -x+y=1 and 2x+y=3

Therefore we need the solution of the two eqns

-x+y=1

2x+y=3

Subtract the first equation from the second,

3x=2 or x=2/3

Substitute this is the second equation,

4/3+y=3

y=5/3