Acid Mixture A chemist needs 12 gallons of a 20% acid solution. The solution is to be

Fill in the blanks A system of equations that is in ________ form has a stair-step pattern with leading coefficients of 1.

Fill in the blanks A solution to a system of three linear equations in three unknowns can be written as an ________ ________, which has the form

Fill in the blanks The process used to write a system of linear equations in row-echelon form is called ________ elimination.

Fill in the blanks Interchanging two equations of a system of linear equations is a ________ ________ that produces an equivalent system.

Fill in the blanks A system of equations is called ________ if the number of equations differs from the number of variables in the system.

Fill in the blanks The equation is called the ________ equation, and it models the height of an object at time that is moving in a vertical line with a constant acceleration

In Exercises 510, use back-substitution to solve the system of linear equations.

In Exercises 510, use back-substitution to solve the system of linear equations.

In Exercises 510, use back-substitution to solve the system of linear equations.

In Exercises 510, use back-substitution to solve the system of linear equations.

In Exercises 11 and 12, perform the row operation and write the equivalent system. Add Equation 1 to Equation 2. What did this operation accomplish?

In Exercises 11 and 12, perform the row operation and write the equivalent system. Add times Equation 1 to Equation 3. What did this operation accomplish?

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 1338, solve the system of linear equations and check any solution algebraically.

In Exercises 3942, an object moving vertically is at the given heights at the specified times. Find the position equation for the object. At second, feet At seconds, feet At seconds, feet

In Exercises 3942, an object moving vertically is at the given heights at the specified times. Find the position equation for the object. At second, feet At seconds, feet At seconds, feet

In Exercises 3942, an object moving vertically is at the given heights at the specified times. Find the position equation for the object. At second, feet At seconds, feet At seconds, feet

In Exercises 3942, an object moving vertically is at the given heights at the specified times. Find the position equation for the object. At second, feet At seconds, feet At t _ 3 seconds, s _ 36 feet

In Exercises 4346, find the equation of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

In Exercises 4346, find the equation of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

In Exercises 4346, find the equation of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

In Exercises 4346, find the equation of the parabola that passes through the points. To verify your result, use a graphing utility to plot the points and graph the parabola.

In Exercises 4750, find the equation of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle.

In Exercises 4750, find the equation of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle.

In Exercises 4750, find the equation of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle.

In Exercises 4750, find the equation of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle.

Sports In Super Bowl I, on January 15, 1967, the Green Bay Packers defeated the Kansas City Chiefs by a score of 35 to 10. The total points scored came from 13 different scoring plays, which were a combination of touchdowns, extra-point kicks, and field goals, worth 6, 1, and 3 points respectively. The same number of touchdowns and extra point kicks were scored. There were six times as many touchdowns as field goals. How many touchdowns, extra-point kicks, and field goals were scored during the game? (Source: SuperBowl.com)

Sports In the 2004 Womens NCAA Final Four Championship game, the University of Connecticut Huskies defeated the University of Tennessee Lady Volunteers by a score of 70 to 61. The Huskies won by scoring a combination of two-point baskets, three-point baskets, and one-point free throws. The number of two-point baskets was two more than the number of free throws. The number of free throws was one more than two times the number of three-point baskets. What combination of scoring accounted for the Huskies 70 points? (Source: National Collegiate Athletic Association)

Finance A small corporation borrowed $775,000 to expand its clothing line. Some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Finance A small corporation borrowed $800,000 to expand its line of toys. Some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest owed was $67,000 and the amount borrowed at 8% was five times the amount borrowed at 10%? Investment Portfolio

The certificates of deposit pay 10% annually, and the municipal bonds pay 8% annually. Over a five-year period, the investor expects the blue-chip stocks to return 12% annually and the growth stocks to return 13% annually. The investor wants a combined annual return of 10% and also wants to have only one-fourth of the portfolio invested in stocks.

The certificates of deposit pay 9% annually, and the municipal bonds pay 5% annually. Over a five-year period, the investor expects the blue-chip stocks to return 12% annually and the growth stocks to return 14% annually. The investor wants a combined annual return of 10% and also wants to have only one-fourth of the portfolio invested in stocks.

Agriculture A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C. Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each fertilizer brand is needed to obtain the desired mixture?

Agriculture A mixture of 12 liters of chemical A, 16 liters of chemical B, and 26 liters of chemical C is required to kill a destructive crop insect. Commercial spray X contains 1, 2, and 2 parts, respectively, of these chemicals. Commercial spray Y contains only chemical C. Commercial spray Z contains only chemicals A and B in equal amounts. How much of each type of commercial spray is needed to get the desired mixture?

Coffee Mixture A coffee manufacturer sells a 10-pound package of coffee that consists of three flavors of coffee. Vanilla-flavored coffee costs $2 per pound, hazelnutflavored coffee costs $2.50 per pound, and mocha-flavored coffee costs $3 per pound. The package contains the same amount of hazelnut coffee as mocha coffee. The cost of the 10-pound package is $26. How many pounds of each type of coffee are in the package?

Floral Arrangements A florist is creating 10 centerpieces for a wedding. The florist can use roses that cost $2.50 each, lilies that cost $4 each, and irises that cost $2 each to make the bouquets. The customer has a budget of $300 and wants each bouquet to contain 12 flowers, with twice as many roses used as the other two types of flowers combined. How many of each type of flower should be in each centerpiece?

Advertising A health insurance company advertises on television, radio, and in the local newspaper. The marketing department has an advertising budget of $42,000 per month. A television ad costs $1000, a radio ad costs $200, and a newspaper ad costs $500. The department wants to run 60 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month?

Radio You work as a disc jockey at your college radio station. You are supposed to play 32 songs within two hours. You are to choose the songs from the latest rock, dance, and pop albums. You want to play twice as many rock songs as pop songs and four more pop songs than dance songs. How many of each type of song will you play?

Acid Mixture A chemist needs 10 liters of a 25% acid solution. The solution is to be mixed from three solutions whose concentrations are 10%, 20%, and 50%. How many liters of each solution will satisfy each condition? (a) Use 2 liters of the 50% solution. (b) Use as little as possible of the 50% solution. (c) Use as much as possible of the 50% solution.

Acid Mixture A chemist needs 12 gallons of a 20% acid solution. The solution is to be mixed from three solutions whose concentrations are 10%, 15%, and 25%. How many gallons of each solution will satisfy each condition? (a) Use 4 gallons of the 25% solution. (b) Use as little as possible of the 25% solution. (c) Use as much as possible of the 25% solution.

Electrical Network Applying Kirchhoffs Laws to the electrical network in the figure, the currents and are the solution of the system find the currents.

Pulley System A system of pulleys is loaded with 128- pound and 32-pound weights (see figure). The tensions and in the ropes and the acceleration of the 32-pound weight are found by solving the system of equations where and are measured in pounds and is measured in feet per second squared. (a) Solve this system. (b) The 32-pound weight in the pulley system is replaced by a 64-pound weight. The new pulley system will be modeled by the following system of equations. Solve this system and use your answer for the acceleration to describe what (if anything) is happening in the pulley system.

In Exercises 6770, find the least squares regression parabola for the points . . . , by solving the following system of linear equations for and Then use the regression feature of a graphing utility to confirm the result. (If you are unfamiliar with summation notation, look at the discussion in Section 9.1 or in Appendix B at the website for this text at college.hmco.com.)

In Exercises 6770, find the least squares regression parabola for the points . . . , by solving the following system of linear equations for and Then use the regression feature of a graphing utility to confirm the result. (If you are unfamiliar with summation notation, look at the discussion in Section 9.1 or in Appendix B at the website for this text at college.hmco.com.)

In Exercises 6770, find the least squares regression parabola for the points . . . , by solving the following system of linear equations for and Then use the regression feature of a graphing utility to confirm the result. (If you are unfamiliar with summation notation, look at the discussion in Section 9.1 or in Appendix B at the website for this text at college.hmco.com.)

In Exercises 6770, find the least squares regression parabola for the points . . . , by solving the following system of linear equations for and Then use the regression feature of a graphing utility to confirm the result. (If you are unfamiliar with summation notation, look at the discussion in Section 9.1 or in Appendix B at the website for this text at college.hmco.com.)

Data Analysis: Wildlife A wildlife management team studied the reproduction rates of deer in three tracts of a wildlife preserve. Each tract contained 5 acres. In each tract, the number of females and the percent of females that had offspring the following year, were recorded. The results are shown in the table. (a) Use the technique demonstrated in Exercises 6770 to set up a system of equations for the data and to find a least squares regression parabola that models the data. (b) Use a graphing utility to graph the parabola and the data in the same viewing window. (c) Use the model to create a table of estimated values of Compare the estimated values with the actual data. (d) Use the model to estimate the percent of females that had offspring when there were 170 females. (e) Use the model to estimate the number of females when 40% of the females had offspring.

Data Analysis: Stopping Distance In testing a new automobile braking system, the speed (in miles per hour) and the stopping distance (in feet) were recorded in the table. (a) Use the technique demonstrated in Exercises 6770 to set up a system of equations for the data and to find a least squares regression parabola that models the data. (b) Graph the parabola and the data on the same set of axes. (c) Use the model to estimate the stopping distance when the speed is 70 miles per hour.

Sports In Super Bowl XXXVIII, on February 1, 2004, the New England Patriots beat the Carolina Panthers by a score of 32 to 29. The total points scored came from 16 different scoring plays, which were a combination of touchdowns, extra-point kicks, two-point conversions, and field goals, worth 6, 1, 2, and 3 points, respectively. There were four times as many touchdowns as field goals and two times as many field goals as two-point conversions. How many touchdowns, extra-point kicks, two-point conversions, and field goals were scored during the game? (Source: SuperBowl.com)

Sports In the 2005 Orange Bowl, the University of Southern California won the National Championship by defeating the University of Oklahoma by a score of 55 to 19. The total points scored came from 22 different scoring plays, which were a combination of touchdowns, extrapoint kicks, field goals and safeties, worth 6, 1, 3, and 2 points respectively. The same number of touchdowns and extra-point kicks were scored, and there were three times as many field goals as safeties. How many touchdowns, extra-point kicks, field goals, and safeties were scored? (Source: ESPN.com)

In Exercises 7578, find values of and that satisfy the system. These systems arise in certain optimization problems in calculus, and is called a Lagrange multiplier.

In Exercises 7578, find values of and that satisfy the system. These systems arise in certain optimization problems in calculus, and is called a Lagrange multiplier.

In Exercises 7578, find values of and that satisfy the system. These systems arise in certain optimization problems in calculus, and is called a Lagrange multiplier.

In Exercises 7578, find values of and that satisfy the system. These systems arise in certain optimization problems in calculus, and is called a Lagrange multiplier.

True or False? In Exercises 79 and 80, determine whether the statement is true or false. Justify your answer. 79. The system The system is in row-echelon form.

True or False? In Exercises 79 and 80, determine whether the statement is true or false. Justify your answer. 79. The system If a system of three linear equations is inconsistent, then its graph has no points common to all three equations.

Think About It Are the following two systems of equations equivalent? Give reasons for your answer.

Writing When using Gaussian elimination to solve a system of linear equations, explain how you can recognize that the system has no solution. Give an example that illustrates your answer.

In Exercises 8386, find two systems of linear equations that have the ordered triple as a solution. (There are many correct answers.)

In Exercises 8386, find two systems of linear equations that have the ordered triple as a solution. (There are many correct answers.)

In Exercises 8386, find two systems of linear equations that have the ordered triple as a solution. (There are many correct answers.)

In Exercises 8386, find two systems of linear equations that have the ordered triple as a solution. (There are many correct answers.)

In Exercises 8790, solve the percent problem What is of 85?

In Exercises 8790, solve the percent problem 225 is what percent of 150?

In Exercises 8790, solve the percent problem 0.5% of what number is 400?

In Exercises 8790, solve the percent problem 48% of what number is 132?

In Exercises 9196, perform the operation and write the result in standard form.

In Exercises 9196, perform the operation and write the result in standard form.

In Exercises 9196, perform the operation and write the result in standard form.

In Exercises 9196, perform the operation and write the result in standard form.

In Exercises 9196, perform the operation and write the result in standard form.

In Exercises 9196, perform the operation and write the result in standard form.

In Exercises 97100, (a) determine the real zeros of and (b) sketch the graph of f

In Exercises 97100, (a) determine the real zeros of and (b) sketch the graph of f

In Exercises 97100, (a) determine the real zeros of and (b) sketch the graph of f

In Exercises 97100, (a) determine the real zeros of and (b) sketch the graph of f

In Exercises 101104, use a graphing utility to construct a table of values for the equation. Then sketch the graph of the equation by hand.

In Exercises 101104, use a graphing utility to construct a table of values for the equation. Then sketch the graph of the equation by hand.

In Exercises 101104, use a graphing utility to construct a table of values for the equation. Then sketch the graph of the equation by hand.

In Exercises 101104, use a graphing utility to construct a table of values for the equation. Then sketch the graph of the equation by hand.

In Exercises 105 and 106, solve the system by elimination.

In Exercises 105 and 106, solve the system by elimination.

Make a Decision To work an extended application analyzing the earnings per share for Wal-Mart Stores, Inc. from 1988 to 2003, visit this texts website at college.hmco.com. (Data Source: Wal-Mart Stores, Inc.)