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College Algebra Graphs and Models 5th edition Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna - Solutions

The point at which a company's costs equal its revenues is the break-even point. In Exercises 73-76, C represents the production cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in
The amount of red meat consumed in the United States has remained fairly constant in recent years while the amount of poultry consumed has increased during those years, as shown by the data in the table below.a) Find linear regression functions r(x) and p(x) that represent red meat consumption and
The table below lists the revenue, in billions of dollars, from video rentals in video stores and with subscriptions in recent years.a) Find linear functions v(x) and s(x) that represent the revenues from video rentals in video stores and with subscriptions x years since 2005. b) Use the functions
The number of people flying to, from, and within the United States in 2009 was at its lowest level since 2004. In 2009, the number of air travelers totaled 769.6 million, a decrease of 8.2% from 2004 (Source: Bureau of Transportation Statistics, Department of Transportation). Find the number of air
Consider the function f 1x2 = x2 - 4x + 3 in Exercises. a. What are the inputs if the output is 15? b. Given an output of 8, find the corresponding inputs. c. What is the output if the input is -9?
Nancy jogs and walks to campus each day. She averages 4 km/h walking and 8 km/h jogging. The distance from home to the campus is 6 km, and she makes the trip in 1 hr. How far does she jog on each trip?
Shirts.com advertises a limited time sale, offering 1 turtleneck for $15 and 2 turtlenecks for $25. A total of 1250 turtlenecks are sold and $16,750 is taken in. How many customers ordered 2 turtlenecks?
A train leaves Union Station for Central Station, 216 km away, at 9 A.M. One hour later, a train leaves Central Station for Union Station. They meet at noon. If the second train had started at 9 A.M. and the first train at 10:30 A.M., they would still have met at noon. Find the speed of each train.
An automobile radiator contains 16 L of antifreeze and water. This mixture is 30% antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so that the final mixture will be 50% antifreeze?
Two solutions of the equation Ax + By = 1 are (3, -1) and (-4, -2). Find A and B.
You are in line at a ticket window. There are 2 more people ahead of you in line than there are behind you. In the entire line, there are three times as many people as there are behind you. How many people are ahead of you?
The Honda Civic Hybrid vehicle, powered by gasoline-electric technology, gets 49 miles per gallon (mpg) in city driving and 51 mpg in highway driving (Source: Honda.com). The car is driven 447 mi on 9 gal of gasoline. How many miles were driven in the city and how many were driven on the highway?
Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination. [6.3] a. x + 2y = 5, 2x - 5y = -8 b. 3x + 4y + 2z = 3, 5x - 2y - 13z = 3, 4x + 3y - 3z = 6
The value of 75 coins, consisting of only nickels and dimes, is $5.95. How many of each kind are there?
The Wong family invested $5000, part at 3% and the remainder at 3.5%. The annual income from both investments is $167. What is the amount invested at each rate?
A dietician must plan a breakfast menu that provides 460 Cal, 9 g of fat, and 55 mg of calcium. One plain bagel contains 200 Cal, 2 g of fat, and 29 mg of calcium. A one-tablespoon serving of cream cheese contains 100 Cal, 10 g of fat, and 24 mg of calcium. One banana contains 105 Cal, 1 g of fat,
A student has a total of 226 points on three tests. The sum of the scores on the first and second tests exceeds the score on the third test by 62. The first score exceeds the second by 6. Find the three scores.
The table below lists the number of trademarks renewed, in thousands, in the United States, represented in terms of the number of years since 2006. Years, x Number of Trademarks Renewed (in thousands) 2006, 0 .......................... 40 2007, 1 .......................... 48 2008, 2
Find each of the following, if possible. a. A + B b. -3A c. -A
The table below lists the cost per serving, in dollars, for items on four menus that are served at an elder-care facility.On a particular day, a dietician orders 32 meals from menu 1, 19 from menu 2, 43 from menu 3, and 38 from menu 4. a) Write the information in the table as a 4 Ã— 5
Write a matrix equation equivalent to this system of equations: 3x - 2y + 4z = 13, x + 5y - 3z = 7, 2x - 3y + 7z = -8.
Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation. a. 2x + 3y = 5, 3x + 5y = 11 b. 5x - y + 2z = 17, 3x + 2y - 3z = -16, 4x - 3y - z = 5
In Exercises, match the equations or inequalities with one of the graphs (a)-(h),which follow.a.b. c. d. e. f. g. h. 1. x + y = 7, 2x - y = 5 2. 3x - 5y = -8, 4x + 3y = -1 3. y = 2x - 1, 4x - 2y = 2 4. 6x - 3y = 5, y = 2x + 3 5. y ‰¤ 3x - 4
Graph this system of inequalities and find the coordinates of any vertices formed. [6.7] 2x + y ≥ 9, 4x + 3y ≥ 23, x + 3y ≥ 8, x ≥ 0, y ≥ 0
Find the maximum value and the minimum value of T = 6x + 10y subject tox + y ≤ 10,5x + 10y ≥ 50,x ≥ 2,y ≥ 0.
Aiden is taking a test that contains questions in group A worth 7 points each and questions in group B worth 12 points each. The total number of questions answered must be at least 8. If Aiden knows that group A questions take 8 min each and group B questions take 10 min each and the maximum time
Decompose into partial fractions. a. 5 / (x + 2)2 (x + 1) b. (-8x + 23) / (2x2 + 5x - 12)
Solve: 2x + y = 7, x - 2y = 6. A. x and y are both positive numbers. B. x and y are both negative numbers. C. x is positive and y is negative. D. x is negative and y is positive.
One year, Don invested a total of $40,000, part at 4%, part at 5%, and the rest at 5 ½ %. The total amount of interest received on the investments was $1990. The interest received on the 5 ½ % investments was $590 more than the interest received on the 4% investment. How much was invested at each
Cassidy solves the equation 2x + 5 = 3x - 7 by finding the point of intersection of the graphs of y1 = 2x + 5 and y2 = 3x - 7. She finds the same point when she solves the system of equations y = 2x + 5, y = 3x - 7.
For square matrices A and B, is it true, in general, that (AB) 2 = A2 B2? Explain.
Given the system of equations a1x + b1y = c1, a2x + b2y = c2, Explain why the equations are dependent or the system is inconsistent when
If the lines a1x + b1y = c1 and a2x + b2y = c2 are parallel, what can you say about the values of
Describe how the graph of a linear inequality differs from the graph of a linear equation. [
What would you say to a classmate who tells you that the partial fraction decomposition of (3x2 - 8x + 9) / ((x + 3) (x2 - 5x + 6)) is 2 / (x + 3) + (x - 1) / (x2 - 5x + 6)? Explain.
Use any method. Also determine whether the system is consistent or inconsistent and whether the equations are dependent or independent. a. 3x + 2y = 1, 2x - y = -11 b. 2x - y = 3, 2y = 4x - 6
The table below lists the cost per serving, in dollars, for items on three lunch menus served at a senior citizens' center.On a particular day, 26 Menu 1 meals, 18 Menu 2 meals, and 23 Menu 3 meals are served. a) Write the information in the table as a 3 Ã— 3 matrix M. b) Write a row
Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation. 3x + 2y + 6z = 2, x + y + 2z = 1, 2x + 2y + 5z = 3
Solve using Cramer's rule. Show your work.5x + 2y = -1,7x + 6y = 1
Find the maximum value and the minimum value of Q = 2x + 3y subject tox + y ≤ 6,2x - 3y ≥ -3,x ≥ 1,y ≥ 0.
Gracilyn's Gourmet Sweets prepares coffeecakes and cheesecakes for restaurants. In a given week, at most 100 cakes can be prepared, of which 25 coffeecakes and 15 cheesecakes are required by regular customers. The profit from each coffeecake is $8, and the profit from each cheesecake is $17. How
Decompose into partial fractions: (3x - 11) / (x2 + 2x - 3) .
Three solutions of the equation Ax - By = Cz - 8 are (2, -2, 2), (-3, -1, 1), and (4, 2, 9). Find A, B, and C.
One evening 750 tickets were sold for Shortridge Community College's spring musical. Tickets cost $3 for students and $5 for nonstudents. Total receipts were $3066. How many of each type of ticket were sold?
Latonna, Cole, and Sam can process 352 online orders per day. Latonna and Cole together can process 224 orders per day while Latonna and Sam together can process 248 orders per day. How many orders can each of them process alone?
The Winter Olympics have been held a total of 21 times on the continents of North America, Europe, and Asia. The number of European sites is 5 more than the total number of sites in North America and Asia. There are 4 more sites in North America than in Asia.
The total number of restaurant purchased meals that the average person will eat in a restaurant, in a car, or at home in a year are 170. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 14. Twenty more restaurant-purchased meals will be eaten in
The top three apple growers in the world-China, the United States, and Turkey-grew a total of about 74 billion lb of apples in a recent year. China produced 44 billion lb more than the combined production of the United States and Turkey. The United States produced twice as many pounds of apples as
The three foreign countries from which the largest number of children was adopted in 2009 were China, Ethiopia, and Russia. A total of 6864 children were adopted from these countries. The number of children adopted from China was 862 fewer than the total number adopted from Ethiopia and Russia.
One 8-oz serving each of brewed coffee, Red Bull energy drink, and Mountain Dew soda contains a total of 197 mg of caffeine. One serving of brewed coffee has 6 mg more caffeine than two servings of Mountain Dew. One serving of Red Bull contains 37 mg less caffeine than one serving each of brewed
The top three Mother's Day gifts are flowers, jewelry, and gift certificates. The total of the average amounts spent on these gifts is $53.42. The average amount spent on jewelry is $4.40 more than the average amount spent on gift certificates. Together, the average amounts spent on flowers and
Americans own a total of about 355 million fish, cats, and dogs as pets. The number of fish owned is 11 million more than the total number of cats and dogs owned, and 16 million more cats are owned than dogs. (Source: American Pet Products Manufacturers Association) How many of each type of pet do
Natural Fibers Clothing charges $4 for shipping orders of $25 or less, $8 for orders from $25.01 to $75, and $10 for orders over $75. One week, shipping charges for 600 orders totaled $4280. Eighty more orders for $25 or less were shipped than orders for more than $75. Find the number of orders
Recently, the movies The Dark Knight, Spider-Man 3, and The Twilight Saga: New Moon held the record for having the three highest-grossing weekends at the box office, with a total of $452 million. Together, Spider-Man 3 and New Moon earned $136 million more than The Dark Knight. New Moon earned $15
In a group of 100 adults, 70 say they are most likely to do spring housecleaning in March, April, or May. Of these 70, the number who cleans in April is 14 more than the total number who cleans in March and May. The total number who cleans in April and May is 2 more than three times the number who
A hospital dietician must plan a lunch menu that provides 485 Cal, 41.5 g of carbohydrates, and 35 mg of calcium. A 3-oz serving of broiled ground beef contains 245 Cal, 0 g of carbohydrates, and 9 mg of calcium. One baked potato contains 145 Cal, 34 g of carbohydrates, and 8 mg of calcium. A
A diabetic patient wishes to prepare a meal consisting of roasted chicken breast, mashed potatoes, and peas. A 3-oz serving of roasted skinless chicken breast contains 140 Cal, 27 g of protein, and 64 mg of sodium. A one-cup serving of mashed potatoes contains 160 Cal, 4 g of protein, and 636 mg of
Walter earns a year-end bonus of $5000 and puts it in 3 one-year investments that pay $243 in simple interest. Part is invested at 3%, part at 4%, and part at 6%. There is $1500 more invested at 6% than at 3%. Find the amount invested at each rate.
Natsumi receives $126 per year in simple interest from three investments. Part is invested at 2%, part at 3%, and part at 4%. There is $500 more invested at 3% than at 2%. The amount invested at 4% is three times the amount invested at 3%. Find the amount invested at each rate.
In New York City, orange juice, a raisin bagel, and a cup of coffee from Katie's Koffee Kart cost a total of $8.15. Katie posts a notice announcing that, effective the following week, the price of orange juice will increase 25% and the price of bagels will increase 20%. After the increase, the same
Martin and Eva pool their loose change to buy snacks on their coffee break. One day, they spent $6.75 on 1 carton of milk, 2 donuts, and 1 cup of coffee. The next day, they spent $8.50 on 3 donuts and 2 cups of coffee. The third day, they bought 1 carton of milk, 1 donut, and 2 cups of coffee and
The table below lists the percent of American workers who responded that they were likely to be laid off from their jobs in the coming year, represented in terms of the number of years since 1990. Year, x Percent who say Lay-off Likely 1990, 0.......................16 1997,
The table below lists the volume of nonfederal student loans, in billions of dollars, represented in terms of the number of years since 2004. Year, x Volume of student Loans (in billions) 2004, 0 ................................. $15.1 2006, 2 ...................................20.5 2008, 4
The table below lists the average size of U.S. farms, represented in terms of the number of years since 1997. Year, x Average Size of U.S. Farms (in number of acres) 1997, 0 ........................ 431 2002, 5 ......................... 441 2009, 12 ........................418 a) Fit a quadratic
The table below lists the number of books shipped by publishers, in billions, represented in terms of the number of years since 2007. Year , x Books Shipped (in billions) 2007, 0......................... 3.127 2008, 1 ......................... 3.079 2009, 2 ........................ 3.101 a) Fit a
The table below lists the U.S. unemployment rate in October for selected years. Year U.S. Unemployment Rate in October 2002 ...................... 5.7% 2004 ......................... 5.5 2005 ......................... 5.0 2008 ......................... 6.6 2010 ........................ 9.7 a) Use
Let u represent 1/x, v represent 1/y, and w represent 1/z. Solve first for u, v, and w. Then solve the following system of equations: 2/x + 2/y - 3/z = 3, 1/x - 2/y - 3/z = 9, 7/x - 2/y + 9/z = -39.
Use the following facts to find the year in which the first U.S. transcontinental railroad was completed: The sum of the digits in the year is 24. The units digit is 1 more than the hundreds digit. Both the tens and the unit's digits are multiples of three.
In Exercises, three solutions of an equation are given. Use a system of three equations in three variables to find the constants and write the equation. a. Ax + By + Cz = 12; (1, 3/4, 3), (4/3, 1, 2), and (2, 1, 1) b. y = B - Mx - Nz; (1, 1, 2), (3, 2, -6(, and (3/2, 1, 1)
In Exercises, four solutions of the equation y = ax3 + bx2 + cx + d are given. Use a system of four equations in four variables to find the constants a, b, c, and d and write the equation. a. (-2, 59), (-1, 13), (1, -1), and (2, -17) b. (-2, -39), (-1, -12), (1, -6), and (3, 16)
Write the system of equations that corresponds to the augmented matrix.a.b. c. d.
Solve the system of equations using Gaussian elimination or Gauss-Jordan elimination. Use a graphing calculator to check your answer. a. 4x + 2y = 11, 3x - y = 2 b. 2x + y = 1, 3x + 2y = -2
Use Gaussian elimination or Gauss-Jordan elimination in Exercises.a. Stamp Purchase. Otto spent $22.35 on 44¢ and 17¢ stamps. He bought a total of 60 stamps. How many of each type did he buy?b. The Coopers pay their babysitter $8 per hour before 11 P.M. and $9.50 per hour after 11 P.M.
Classify the function as linear, quadratic, cubic, quadratic, rational, exponential, or logarithmic. a. f (x) = 3x-1 b. f (x) = 3x - 1 c. f (x) = 3x - 1/x2 + 4 d. f (x) = - ¾ x4 + 9/2 x3 + 2x2 - 4 e. f (x) = ln (3x - 1)
In Exercises, three solutions of the equation y = ax2 + bx + c are given. Use a system of three equations in three variables and Gaussian elimination or Gauss-Jordan elimination to find the constants a, b, and c and write the equation. a. (-3, 12), (-1, -7), and (1, -2) b. (-1, 0), (1, -3), and (3,
Find two different row-echelon forms of
Consider the system of equations x - y + 3z = -8, 2x + 3y - z = 5, 3x + 2y + 2kz = -3k. For what value(s) of k, if any, will the system have?
Write the augmented matrix for the system of equations. a. 2x - y = 7, x + 4y = -5 b. 3x + 2y = 8, 2x - 3y = 15 c. x - 2y + 3z = 12, 2x - 4z = 8, 3y + z = 7 d. x + y - z = 7, 3y + 2z = 1, -2x - 5y = 6
The produce manager at Dugan's Market orders 40 lb of tomatoes, 20 lb of zucchini, and 30 lb of onions from a local farmer one week.a) Write a 1 Ã— 3 matrix A that represents the amount of each item ordered. b) The following week the produce manager increases her order by 10%. Find a
For the month of June, Madelyn budgets $400 for food, $160 for clothes, and $60 for entertainment. a) Write a 1 × 3 matrix B that represents the amounts budgeted for these items. b) After receiving a raise, Madelyn increases the amount budgeted for each item in July by 5%. Find a matrix R that
A 3-oz serving of roasted, skinless chicken breast contains 140 Cal, 27 g of protein, 3 g of fat, 13 mg of calcium, and 64 mg of sodium. One-half cup of potato salad contains 180 Cal, 4 g of protein, 11 g of fat, 24 mg of calcium, and 662 mg of sodium. One broccoli spear contains 50 Cal, 5 g of
One slice of cheese pizza contains 290 Cal, 15 g of protein, 9 g of fat, and 39 g of carbohydrates. One-half cup of gelatin dessert contains 70 Cal, 2 g of protein, 0 g of fat, and 17 g of carbohydrates. One cup of whole milk contains 150 Cal, 8 g of protein, 8 g of fat, and 11 g of carbohydrates.
The food service manager at a large hospital is concerned about maintaining reasonable food costs. The table below lists the cost per serving, in dollars, for items on four menus.On a particular day, a dietician orders 65 meals from menu 1, 48 from menu 2, 93 from menu 3, and 57 from menu 4. a)
A college food service manager uses a table like the one below to list the number of units of ingredients, by weight, required for various menu items.The cost per unit of each ingredient is 25 cents for flour, 34 cents for milk, 54 cents for eggs, and 83 cents for butter. a) Write the information
A manufacturer produces exterior plywood, interior plywood, and fiberboard, which are shipped to two distributors. The table below shows the number of units of each type of product that are shipped to each warehouse.a) Write the information in the table as a 3 Ã— 2 matrix M. b) Write a
Karin supplies two small campus coffee shops with homemade chocolate chip cookies, oatmeal cookies, and peanut butter cookies. The table below shows the number of each type of cookie, in dozens, that Karin sold in one week.Karin spends $4 for the ingredients for one dozen chocolate chip cookies,
In Exercise 35, suppose that the manufacturer's production costs for each unit of exterior plywood, interior plywood, and fiberboard are $20, $25, and $15, respectively. a) Write a row matrix C that represents this information. b) Use the matrices M and C to find the total production cost for the
In Exercise 36, suppose that Karin's profits on one dozen chocolate chip, oatmeal, and peanut butter cookies are $6, $4.50, and $5.20, respectively. a) Write a row matrix P that represents this information. b) Use the matrices S and P to find Karin's total profit from each coffee shop.
Write a matrix equation equivalent to the system of equations. a. 2x - 3y = 7, x + 5y = -6 b. -x + y = 3, 5x - 4y = 16 c. x + y - 2z = 6, 3x - y + z = 7, 2x + 5y - 3z = 8
In Exercises a) Find the vertex. b) Find the axis of symmetry. c) Determine whether there is a maximum or minimum value and find that value. d) Graph the function. 1. f (x) = x2 - x - 6 2. f(x) = 2x2 - 5x - 3
Determine whether B is the inverse of A.a.b. c. d.
Use a graphing calculator to find A-1, if it exists.a.b.
In Exercises, a system of equations is given, together with the inverse of the coefficient matrix. Use the inverse of the coefficient matrix to solve the system of equations.a. 11x + 3y = -4,7x + 2y = 5;b. 8x + 5y = -6, 5x + 3y = 2; c. 3x + y = 2, 2x - y + 2z = -5, x + y + z = 5;
Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation. a. 4x + 3y = 2, x - 2y = 6 b. 2x - 3y = 7, 4x + y = -7
Kayla sold a total of 145 Italian sausages and hot dogs from her curbside pushcart and collected $242.05. She sold 45 more hot dogs than sausages. How many of each did she sell?
Rubio bought 4 lab record books and 3 highlighters for $17.83. Marcus bought 3 lab record books and 2 highlighters for $13.05. Find the price of each item.
Green-Up Landscaping bought 4 tons of topsoil, 3 tons of mulch, and 6 tons of pea gravel for $2825. The next week the firm bought 5 tons of topsoil, 2 tons of mulch, and 5 tons of pea gravel for $2663. Pea gravel costs $17 less per ton than topsoil. Find the price per ton for each item.
Donna receives $230 per year in simple interest from three investments totaling $8500. Part is invested at 2.2%, part at 2.65%, and the rest at 3.05%. There is $1500 more invested at 3.05% than at 2.2%. Find the amount invested at each rate.
Use synthetic division to find the function values. a. f(x) = x3 - 6x2 + 4x - 8; find f (-2) b. f(x) = 2x4 - x3 + 5x2 + 6x - 4; find f(3)
Use the Gauss-Jordan method to find A-1, if it exists. Check your answers by using a graphing calculator to find A-1A and AA-1.a.b.

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