Exam 4: Systems of Linear Equations and Matrices

Use the table and the given X-ray absorption diagrams to identify the composition of each of the regions marked by a letter. The number in each region shows its absorption, and the number on each X-ray beam shows the total absorption for that beam. Type Air Water Gray matter Tumor Blood Bone Absorption 0 1,000 1,020 1,030 1,050 2,000 $a = 4050$ , $b = 5130$ , $c = 8000$ , $d = 3020$

If the addition or subtraction of two linear equations results in the equation $0 = 8$ , then the graphs of those equations are parallel.

In the matrix of a system of linear equations, if one row of a matrix is a multiple of another row, then during the process of row reduction, one of those rows will eventually become all ones. Is statement

The best sports dorm on campus, Lombardi House, has won a total of 15 games this semester. Some of these games were soccer games, and the others were football games. According to the rules of the university, each win in a soccer gamer earns the winning house 4 points, whereas each win in a football game earns them 5 points. If the total number of points Lombardi House earned was 69, how many of each type of game did they win __________ soccer games and __________ football games.

Find all solutions of the given system and choose the graph of the system that shows the solutions. x+16y =5 2x+32y =12

Find the intersection of the line through $( - 6,4 )$ and $( 2,0 )$ and the line through $( - 4 , - 5 )$ and $( - 2 , - 4 )$ . ​ If the equations of the system are redundant, or if a system is inconsistent, so indicate.

The chart below shows the amount spent by three U.S. airlines to fly one available seat one mile in the fourth quarter of 2000. Airline United American SouthWest Cost 11.3 cents 11.0 cents 7.8 cents ? Suppose that, on a 3000-mile New York-Los Angeles flight, United, American and SouthWest flew a total of 150 empty seats, costing them a total of $47,430. If United had three times as many empty seats as American, how many empty seats did each of these three airlines carry on its flight United __________ American __________ SouthWest __________

In March 2002 Cisco (CSCO) stock rose from $18 to $19, and America Online-Time Warner (AOL) dropped from $34 to $33. If you invested a total of $12,000 in these stocks at the beginning of March and sold them for $11,800 at the end of March, how many shares of each stock did you buy ?

Use Gauss-Jordan row reduction to solve the given system of equations. 5x-y=29 5x+8y=38

Use Gauss-Jordan row reduction to solve the given systems of equation. x-y=6 +y+z=4 x-z=2

You own a hamburger franchise and are planning to shut down operations for the day, but you are left with 10 bread rolls, 15 defrosted beef patties, and 13 opened cheese slices. Rather than throw them out, you decide to use them to make burgers that you will sell at a discount. Plain burgers each require 1 beef patty and 1 bread roll, double cheeseburgers each require 2 beef patties, 1 bread roll, and 2 slices of cheese, and regular cheeseburgers each require 1 beef patty, 1 bread roll, and 1 slice of cheese. How many of each should you make Plain burgers: __________ Double cheeseburgers: __________ Regular cheeseburgers: __________

The Fancy French Perfume Company recently had its secret formula divulged. It turned out that it was using, as the three ingredients, rose oil, oil of fermented prunes, and alcohol. Moreover, each 18-ounce econo-size bottle contained 3 more ounces of alcohol than oil of fermented prunes, while the amount of alcohol was equal to the combined volume of the other two ingredients. How much of each ingredient did it use in an econo-size bottle Rose oil: __________ Oil of fermented prunes: __________ Alcohol: __________

In November, 2003, the four organizations ranking 5 through 8 in home Internet users in the US were eBay, the U.S. Government, Amazon, and Lycos, with a combined audience of 115 million users. Taking x to be the eBay audience in millions, y the U.S. Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that y-z=z-u x-y=3(y-u)+1 x-y+z-u=15 How large was the audience of each of the four companies in November, 2003 eBay __________ millions The U.S. Government __________ millions Amazon __________ millions Lycos __________ millions

Use Gauss-Jordan row reduction to solve the system of equations. ​ 8x+7y-2=0 5x+5y+7=0

The demand and supply functions for your college newspaper are listed in order below: q=-14,000p+5,000 q=4,000p+500 Here $p$ is the price in dollars, and $q$ represents the quantity of papers that consumers will buy, or that the paper can produce. At what equilibrium price should the newspapers be sold so that there is neither a surplus nor a shortage of papers

In 2000, total revenues from sales of recorded rock, rap, and classical music amounted to $14.5 billion. Rock music brought in twice as much revenue as rap music and 900% the revenue of classical music. How much revenues were earned in each of the three categories of recorded music (Round your answers to one decimal place.) Rock $__________ billion Rap $__________ billion Classical music $__________ billion

The demand and supply functions for your college newspaper are, respectively, $q = - 11,000 p + 4,000$ and $q = 4,000 p + 400$ , where p is the price in dollars. At what price should the newspapers be sold so that there is neither a surplus nor a shortage of papers __________ cents per paper

Find all the solutions (if any) of the given system. ​ -x+y = 3x+29y =-64 ​ If the equations of the system are redundant, or if a system is inconsistent, so indicate.

Use technology to solve the system of equations. Express all solutions as decimals, rounded to one decimal place. 1.6x+2.4y-3.2z=17.6 5.1x-6.3y+0.6z=-12.8 4.2x+3.5y+4.9z=40.4

The chart below shows the amount spent by three U.S. airlines to fly one available seat one mile in the fourth quarter of 2000. Airline Continental SkyWest SouthWest Cost 9.8 cents 20.3 cents 7.8 cents ? Suppose that, on a 2000-mile Miami-Memphis flight, Continental, SkyWest, and SouthWest flew a total of 180 empty seats, costing them a total of $54,280. If SkyWest had twice as many empty seats as SouthWest, how many empty seats did each of these three airlines carry on its flight Continental __________ SkyWest __________ SouthWest __________