©Kathryn Bollinger, September 16, 2011 1MATH 141 Name:Exam I Review Activity1. Find the x and y-intercepts for the line 2x + 5y = 7.2. Solve the following system of equations. If the solution is parametric, give both the parametricsolution, as well as one specific solution.x + 2y = z − 33x + 5y − 6z = 103. Tom buys a camera for $500. The camera has a scrap value of $50 after 5 years. How long willit be before the camera is valued at $400 if the camera depreciates linearly?4. Solve the following matrix equation for X: AX + B = C − X5. The table below gives the an nual cr edit card sales (in thousands of dollars) at a local“mom ’n pop” store during the given years.Year2000 2002 2005 2009Sales 5.2 6.0 7.5 8.2(a) Determine the equation of the least-squares line for this data, letting x represent the numberof years since 2000. Round each coefficient/constant to four decimal places, if necessary.(b) Is the least-squares line a good rep resentation of the data? Why or why not?(c) Use your unrounded model to determine sales (to the nearest dollar) in the year 2010.(d) Use your unrounded model to determine the year when sales will first reach $10,500, assumingthis trend continues.6. Two bakeries, Breakfast Haven and S unny Bakery, make both doughnuts and kolaches. MatrixA gives the time (in minutes) to make each p roduct at each bakery. Matrix B shows the orders ofdoughnuts and kolaches two companies, C and D, place one morning.A ="BreakfastHaven SunnyBakeryDoughnuts 5 6Kolaches 10 8#B ="Doughnu ts KolachesCompanyC 50 60CompanyD 75 40#Give th e meaning of the entries, if any exists, in the matrix products, AB and BA.©Kathryn Bollinger, September 16, 2011 27. Fill in the blanks in the following sentences with either “the same” or “different”.(a) A system of two linear equations in two variables with no solution m eans the two lines haveslopes and y-intercepts.(b) A system of two linear equations in two variables with infinitely many solutions means th etwo lines have slopes and y-intercepts.8. Using the variables defined as a = the number of apples, b = the number of bananas, andc = the number of carr ots, write an equation for each of the following statements.(a) Susie bought as many carrots as apples and bananas combined.(b) Mark bought three times as many bananas as apples.(c) Bugs ate ten more carrots than he did apples.9. A book company can produce 100 books at a total cost of $800 and 150 books at a total cost of$900. The books retail for $7.50 each.(a) Exactly how many books must be mad e and sold for the company to break-even?(b) Is this amount possible for the company to “truly” break-even? Why or why not?10. Given the matrix equation below, solve for a, b, c and d."a 01 5#T+ 2"4 56 7#−1="3 bc d#11. Cookies are being sold at a fair. It is found that 50 cookies can be sold at $0.75 each, but foreach 10 cent increase in price per cookie, 5 less cookies will be bought.(a) Find the linear demand function for the cookies, p(x), where x r epresents the number of cookiessold and price is in dollars.(b) How many cookies would be taken (to the nearest cookie) if they were given away for free?(c) If the supply equation for these cookies is known to be p(x) =1100x + 0.10,find the equilibrium point for the market.12. Given the augmented matrix below, answer the questions that follow.1 0 080 1 470 −2 35(a) Is this matrix in redu ced row-echelon form?(b) Perf orm the following row operation (2R2+ R3→ R3) and give the resulting
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