appendix week 3-4 math 116

Appendix Week 3-4

Answer each question.  You must show your work for each question.  If the question asks for you to explain or give a description, you must explain in addition to your work.  Each question is worth 5 points.

1.  Are the inequalities  and  equivalent? Why or why not?  Show your work and explain your answer.

3x – 4  10 – 4x                                   

                                                                                                                        

 Collect like terms.                                 Solve parenthesis first.

3x + 4x  10 + 4                                       2x – 10 6x - 18

7x  14                                                     Collect like terms.

Divide 17 by 7.                                          2x – 6x  -18 + 10

X  14/7                                                   -4x  -8

                                         

X  2                                                         Divide -8 by -4

                                                                 

                                                                X  -8/-4

                                                                

                                                                X  2

Both inequalities are the same because in the second equation the sign changes when the result of x is -4, to .

2.    The following graph shows data for a Ford Explorer driven on city streets. At what rate was the vehicle consuming gas? What is the equation of the line?  How did you determine this? Show your work and explain your answer.

Y= mx + b

 b=0

m=  

To find the value of m, I used the slope form:

(60,5)   (120, 10)

  10-5 =   5  =   1

120-60   60    12   

B= y intercept = 0

The vehicle consumes 12 miles per gallon.

3.    The yearly cost T, in thousands of dollars, of tuition and required fees at a private college (includes two- and four-year schools and does not include room and board) can be approximated by

 where n is the number of years since 1985. That is, corresponds to 1985, corresponds to 1990, and so on. Show your work and explain each answer.

Source: Statistical Abstract of the United States, 2003

a.  Find the cost of tuition in 1985, 1996, 2000, and 2004.

              In 1985, n=0. Therefore,

Tuition fees are:

In 1996, n=11. Therefore,

Tuition fees are:

In 2000, n=15. Therefore,

Tuition fees are:

In 2004, n=19. Therefore,

Tuition fees are:

    

b.  Graph the equation and then use the graph to estimate the cost of tuition in 2005.  Use the drawing tools to draw your line on the graph.

n=20, which is 2005, and then T is about 17.5.

 Cost of tuition in 2005 is about $17,500

c.   Predict the year in which the cost of tuition will be $23,000. Explain your answer.

 The cost of tuition will be $23,000 in 30 years after 1985, viz. 2015

4.    Show that the ordered pairs (-4, -3) and (-1, 3) are solutions of the equation . Then use the graph of the straight line containing the two points to determine another solution.  Show your work and explain your answer.

Let . Then

.  is a solution of the equation

Let . Then

   is a solution of the equation

Another solution, reading off the graph, is: y=0 at x = -2.5

Another solution point is: (-2.5, 0)