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All Textbook Solutions for College Algebra

For the following exercises, refer to Table 12. Use the LOGISTIC regression option to find a logistic growth model of the form y=c1+aebx that best fits the data in the table.For the following exercises, refer to Table 12. Graph the logistic equation on the scatter diagram.For the following exercises, refer to Table 12. To the nearest whole number, what is the predicted carrying capacity of the model?For the following exercises, refer to Table 12. Use the intersect feature to find the value of x for which the model reaches half its carrying capacity.Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .Use a graphing utility to find an exponential regression formula f(x) and a logarithmic regression formula g(x) for the points (1.5,1.5) and (8.5,8.5). Round all numbers to 6 decimal places. Graph the points and both formulas along with the line y=x on the same axis. Make a conjecture about the relationship of the regression formulas.Verify the conjecture made in the previous exercise. Round all numbers to six decimal places when necessary.Find the inverse function f1(x) for the logistic function f(x)=c1+aebx. Show all steps.Use the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its inverse on the same axis. What are the intercepts and asymptotes of each function?Determine whether the function y=156(0.825)t represents exponential growth exponential decay, orneither. Explain The population of a herd of deer is represented bythe function A(t)=205(1.13)t , where tis given inyears. To the nearest whole number, what will theherd population be after 6 years?Find an exponential equation that passes through the points (2,2.25) and (5,60.75).Determine whether Table 1 could represent a function that is linear, exponential, or neither. If it appears to beexponential find a function that passes through the points.A retirement account is opened with an initialdeposit of 8,500 and earns 8.12 interest compounded monthly. What will the account beworth in 20 years?Hsu-Mei wants to save 5,000 for a down paymenton a car. To the nearest dollar, how much will sheneed to invest in an account now with 7.5 APR,compounded daily, in order to reach her goal in 3 years?Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?Graph the function f(x)=3.5(2)x. State the domainand range and give the y-intercept.Graph the function f(x)=4(18)x and its reflectionabout the y-axis on the same axes, andgivethey-intercept.The graph of f(x)=6.5x is reflected about the y-axis and stretched vertically by a factor of 7. What is theequation of the new function, g(x) ? State its y-intercept, domain, and range.The graph below shows transformations of the graph of f(x)=2x. What is the equation for the transformation?Rewrite log17(4913)=x as an equivalent exponentialequation.Rewrite ln(s)=t as an equivalent exponentialequation.Rewrite a25=b as an equivalent logarithmicequation.Rewrite e3.5=h as an equivalent logarithmicequation.Solve for xlog64(x)=(13) to exponential form.Evaluate log5(1125) without using a calculator.Evaluate log(0.000001) without using a calculator.Evaluate log(4.005) using a calculator. Round to thenearest thousandth.Evaluate ln(e0.8648) without using a calculator.Evaluate ln(183) using a calculator. Round to thenearest thousandth.Graph the function g(x)=log(7x+21)4.Graph the function h(x)=2ln(93x)+1.State the domain, vertical asymptote, and endbehavior of the function g(x)=ln(4x+20)17.Rewrite ln(7r11st) in expanded form.Rewrite log8(x)+log8(5)+log8(y)+log8(13) incompact form.Rewrite logm(6783) in expanded form.Rewrite ln(z)ln(x)ln(y) in compact form.Rewrite ln(1x5) as. a product.Rewrite logy(112) as a single logarithm.Use properties of logarithm to expand log(r2s11t14).Use properties of logarithms to expand ln(2bb+1b1)Condense the expression 5ln(b)+ln(c)+ln(4a)2 to a single logarithm.Condense the expression 3log7v+6log7wlog7u3 to a single logarithm.Rewrite log3(12.75) to base e.Rewrite 512x17=125 as a logarithm.Then applythe change ofbase formula to solve for x using thecommon log. Round to the nearest thousandth.Solve 2163x216x=363x+2 by rewriting each sidewith a common base.Solve 125(1625)x3=53 by rewriting each side with a common base.Use logarithms to find the exact solution for 7179x7=49. If there is no solution, write nosolution.Use logarithms to find the exact solution for 3e6n2+1=60. If there is no solution, write nosolution.Find the exact solution for 5e3x4=6. If there isno solution, write no solution.Find the exact solution for 2e5x29=56. Ifthere is no solution, write no solution.Find the exact solution for 52x3=7x+1. Ifthere isno solution, write no solution.Find the exact solution for e2xex110=0. Ifthere is no solution, write no solution.Use the definition of a logarithm to solve. 5log7(10n)=5.Use the definition of a logarithm to find the exactsolution for 9+6ln(a+3)=33.Use the one-to-one property of logarithms to find an exact solution for log8(7)+log8(4x)=log(5). If there is no solution, write no solution.Use the one-to-one property oflogarithms to findan exact solution for ln(5)+ln(5x25)=ln(56). Ifthere is no solution, write no solution.The formula for measuring sound intensity indecibels D is defined by the equation D=10log (II0), where I is the intensity of the sound in wattsper square meter and I0=1012 is the lowest level ofsound that the average person can hear. How manydecibels are emitted from a largeorchestra with asound intensity of 6.3103 watts per square meter?The population of a city is modeled by the equation P(t)=256,114e0.25t where t is measured in years. Ifthe city continues to grow at this rate, haw manyyears will it take for the population to reach onemillion?Find the inverse function f1 for the exponential function f(x)=2ex+15.Find the inverse function f1 for the logarithmicfunction f(x)=0.25log2(x3+1).For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17 each hour. To the nearest minute, what is the half-life of the drug?For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17 each hour. Write an exponential model representing the amount of the drug remaining in the patient's system after t hours. Then use the formula to find the amount of the drug that would remain in the patient's system after 24 hours. Round to the nearest hundredth of a gram.For the following exercises, use this scenario: A soup with an internal temperature of 350 Fahrenheit was taken off the stove to cool in at 71F room. After ?fteen minutes, the internal temperature of the soup was 175F. Use Newton’s Law of Cooling to write a formula that models this situation.For the following exercises, use this scenario: A soup with an internal temperature of 350 Fahrenheit was taken off the stove to cool in at 71F room. After ?fteen minutes, the internal temperature of the soup was 175F. How many minutes will it take the soup to cool to 85F?For the following exercises, use this scenario: The equation N(t)=12001+199e0.625t models the number of people in a school who have heard a rumor after t days. How many people started the rumor?For the following exercises, use this scenario: The equation N(t)=12001+199e0.625t models the number of people in a school who have heard a rumor after t days. To the nearest tenth, how many days will it be before the rumor spreads to half the carrying capacity?For the following exercises, use this scenario: The equation N(t)=12001+199e0.625t models the number of people in a school who have heard a rumor after t days. What is the carrying capacity?For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic. Find a formula for an exponential equation that goes through the points (2,100) and (0,4). Then express the formula as an equivalent equation with base e .What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is in For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to ?ve decimal places.For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to ?ve decimal places.For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to ?ve decimal places.The population of a pad of bottlenose dolphins ismodeled by the function A(t)=8(1.17)t, where tisgiven in years. To the nearest whole number, whatwill the pod population be after 3 years?Find an exponential equation that passes throughthe points (0,4) and (2,9).Drew wants to save 2,500 to go to the nextWorld Cup. To the nearest dollar, how much willhe need to invest in an account now with 6.25 APR, compounding daily, in order to reach his goalin 4 years?An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?Graph the function f(x)=5(0.5)x and its reflectionacross the y-axis on the same axes, and give they-intercept.The graph below shows transformations of thegraph of f(x)=(12)x. What is the equation for thetransformation?Rewrite log8.5(614.125)=a as an equivalentexponential equation.Rewrite e12=m as an equivalent logarithmicequation.Solve for x by converting the logarithmic equation log17(x)=2 to exponential form.Evaluate log(10,000,000) without using a calculator.Evaluate ln(0.716) using a calculator. Round to thenearest thousandth.Graph the function g(x)=log(126x)+3.State the domain, vertical asymptote, and endbehavior of the function f(x)=log5(3913x)+7.Rewrite log(17a2b) as a sum.Rewrite logt(96)logt(8) in compact form.Rewrite log8(a16) as a product.Use properties of logarithm to expand ln(y3z2x43).Condense the expression 4ln(c)+ln(d)+ln(a)3+ln(b+3)3 to a singlelogarithm Rewrite 163x5=1000 as a logarithm. Then applythe change of base formula to solve for x using thenatural log. Round to the nearest thousandth.Solve (181)x1243=(19)3x1 rewriting eachside with a common base.Use logarithm to find the exact solution for 9e10a85=41. If there is no solution, writeno solution.Find the exact solution for 10e4x+2+5=56. If thereis no solution, write no solution.Find the exact solution for 5e4x14=64. Ifthere is no solution, write no solution.Find the exact solution for 2x3=62x1. If there isno solution, write no solution.Find the exact solution for e2xex72=0. If thereis no solution, write no solution.Use the definition ofa logarithm to find the exactsolution for 4log(2n)7=11.Use the one-to-one property of logarithms to find anexact solution for log(4x210)+log(3)=log(51) If there is no solution, write no solution.The formula for measuring sound intensityin decibels D is defined by the equation D=10log(II0) where I is the intensity of the sound in watts persquare meter and I0=1012 is the lowest level of sound that the average person can hear. How manydecibels are emitted from a rock concert with a sound intensity of 4.7101 watts per square meter?A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days, thesample has decayed to 80 grams. Rounding to fivesignificant digits, write an exponential equationrepresenting this situation. To the nearest day, whatis the half-life of this substance?Write the formula found in the previous exerciseas an equivalent equation with base e. Express theexponent to five significant digits.A bottle of soda with a temperature of 71 Fahrenheit was taken off a shelf and placed ina refrigerator with an internal temperature of 35 .After ten minutes, the internal temperature of thesoda was 63F . Use Newton’s Law of cooling towrite a formula that models this situation. To thenearest degree, what will the temperature of thesoda be after one hour?The population of a wildlife habitat is modeledby the equation P(t)=3601+6.2e0.35t where t isgiven in years. How many animals were originallytransported to the habitat? How many years will ittake before the habitat reaches half its capacity?Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine whetherthe data from the table would likely represent a function that is linear, exponential, or logarithmic.The population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t is time inyears. To the unrest hundredth, how manyyears will it take the lake to reach 80% of its carrying capacity?For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table.Observe the shape of the scatter diagram to determine whether the data is best described by an exponential,logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models thedata. When necessary, round values to five decimal places. Determine whether the ordered pair (8, 5) is a solution to the following system. 5x4y=202x+1=3y Solve the following system of equations by graphing. 2x5y=254x+5y=35 Solve the following system of equations by substitution. x=y+34=3x2y Solve the system of equations by addition. 2x7y=23x+y=20 Solve the system of equations by addition. 2x+3y=83x+5y=10 Solve the following system of equations in two variables. 2y2x=22y2x=6 Solve the following system of equations in two variables. y2x=5-3y+6x=15 Meal tickets at the circus cost $4.00 for children and $12.00 for adults. If 1,650 meal tickets were bought for a total of $14,200, how many children and how many adults bought meal tickets?Can a system of linear equations have exactly two solutions? Explain why or why not.If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company's profit margins.If you are solving a break-even analysis and get a negative break-even point, explain what this signifies for the company?If you are solving a break-even analysis and there is no break-even point, explain what this means for the company. How should they ensure there is a break-even point?Given a system of equations, explain at least two different methods of solving that system.For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 6. 5xy=4 x+6y=2 and (4,0)For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 7. 3x5y=13 x+4y=10 and (6,1)For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 8. 3x+7y=1 2x+4y=0 and (2,3)For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 9. 2x+5y=7 2x+9y=7 and (1,1)For the following exercises, determine whether the given ordered pair is a solution to the system of equations. 10. x+8y=43 3x2y=1 and (3,5)For the following exercises, solve each system by substitution. 11. x+3y=52x+3y=4 For the following exercises, solve each system by substitution. 12. 3x2y=185x+10y=10 For the following exercises, solve each system by substitution. 13. 4x+2y=103x+9y=0 For the following exercises, solve each system by substitution. 14. 2x+4y=3.89x5y=1.3 For the following exercises, solve each system by substitution. 15. 2x+3y=1.23x6y=1.8 For the following exercises, solve each system by substitution. 16. x0.2y=110x+2y=5 For the following exercises, solve each system by substitution. 17. 3x+5y=930x+50y=90 For the following exercises, solve each system by substitution. 18. 3x+y=212x4y=8 For the following exercises, solve each system by substitution. 19. 12x+13y=16 16x+14y=9 For the following exercises, solve each system by substitution. 20. 14x+32y=11 18x+13y=3 For the following exercises, solve each system by addition. 21. 2x+5y=427x+2y=30 For the following exercises, solve each system by addition. 22. 6x5y=342x+6y=4 For the following exercises, solve each system by addition. 23. 5xy=2.64x6y=1.4 For the following exercises, solve each system by addition. 24. 7x2y=34x+5y=3.25 For the following exercises, solve each system by addition. 25. x+2y=15x10y=6 For the following exercises, solve each system by addition. 26. 7x+6y=228x24y=8 For the following exercises, solve each system by addition. 27. 56x+14y=0 18x12y=43120 For the following exercises, solve each system by addition. 28. 13x+19y=29 12x+45y=13 For the following exercises, solve each system by addition. 29. 0.2x+0.4y=0.6x2y=3 For the following exercises, solve each system by addition. 30. 0.1x+0.2y=0.65x10y=1 For the following exercises, solve each system by any method. 31. 5x+9y=16x+2y=4 For the following exercises, solve each system by any method. 32. 6x8y=0.63x+2y=0.9 For the following exercises, solve each system by any method. 33. 5x2y=2.257x4y=3 For the following exercises, solve each system by any method. 34. x512y=5512 6x+52y=552 For the following exercises, solve each system by any method. 35. 7x4y=76 2x+4y=13 For the following exercises, solve each system by any method. 36. 3x+6y=112x+4y=9 For the following exercises, solve each system by any method. 37. 73x16y=2 216x+312y=3 For the following exercises, solve each system by any method. 38. 12x+13y=13 32x+14y=18 For the following exercises, solve each system by any method. 39. 2.2x+1.3y=0.14.2x+4.2y=2.1 For the following exercises, solve each system by any method. 40. 0.1x+0.2y=20.35x0.3y=0 For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has on solution, no solution, or infinite solutions. 3xy=0.6x2y=1.3 For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has on solution, no solution, or infinite solutions. x+2y=42x4y=1 For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has on solution, no solution, or infinite solutions. x+2y=72x+6y=12 For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has on solution, no solution, or infinite solutions. 3x5y=7x2y=3 For the following exercises, graph the system of equations and state whether the system is consistent, inconsistent, or dependent and whether the system has on solution, no solution, or infinite solutions. 3x2y=59x+6y=15 For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth . 0.1x+0.2y=0.30.3x+0.5y=1 For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 0.01x+0.12y=0.620.15x+0.20y=0.52 For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 0.5x+0.3y=40.25x0.9y=0.46 For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 49. 0.15x+0.27y=0.390.34x+0.56y=1.8 For the following exercises, use the intersect function on a graphing device to solve each system. Round all answers to the nearest hundredth. 0.71x+0.92y=0.130.83x+0.05y=2.1 For the following exercises, solve each system in terms of A,B,C,D,E, and F where A-F are nonzero numbers. Note that ABandAEBD . 51. x+y=Axy=B For the following exercises, solve each system in terms of A.B,C,D,E, and F where A-F are nonzero numbers. Note that AB and AEBD . 52. x+Ay=1x+By=1 For the following exercises, solve each system in terms of A,B,C,D,E, and F where A-F are nonzero numbers. Note that AB and AEBD . 53. Ax+y=0Bx+y=1 For the following exercises, solve each system in terms of A, B,C,D,E, and F where A-F are nonzero numbers. Note that AB and AEBD . 54. Ax+By=Cx+y=1 For the following exercises, solve each system in terms of A, B,C,D,E, and F where A-F are nonzero numbers. Note that AB and AEBD . 55. Ax+By=CDx+Ey=F For the following exercises, solve for the desired quantity. 56. A stuffed animal business has a total cost of production C=12x+30 and a revenue function R=20x . Find the break-even point.For the following exercises, solve for the desired quantity. 57. A fast-food restaurant has a cost of production C(x)=11x+120 and a revenue function R(x)=5x . When does the company start to turn a profit?For the following exercises, solve for the desired quantity. 58. A cell phone factory has a cost of production C(x)=150x+10,000 and a revenue function R(x)=200x . What is the break-even point?For the following exercises, solve for the desired quantity. 59. A musician charges C(x)=64x+20,000 , where x is the total number of attendees at the concert. The venue charges $80 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold at that point?For the following exercises, solve for the desired quantity. 60. A guitar factory has a cost of production C(x)=75x+50,000 . If the company needs to break even after 150 units sold, at what price should they sell each guitar? Round up to the nearest dollar,and write the revenue function.For the following exercises, use a system of linear equations with two variables and two equations to solve. 61. Find two numbers whose sum is 28 and difference is 13.For the following exercises, use a system of linear equations with two variables and two equations to solve. 62. A number is 9 more than another number. Twice the sum of the two numbers is 10. Find the two numbers.For the following exercises, use a system of linear equations with two variables and two equations to solve. 63. The startup cost for a restaurant is $120,000, and each meal costs $10 for the restaurant to make. If each meal is then sold for $15, after how many meals does the restaurant break even?For the following exercises, use a system of linear equations with two variables and two equations to solve. 64. A moving company charges a flat rate of $150, and an additional $5 for each box. If a taxi service would charge $20 for each box, how many boxes would you need for it to be cheaper to use the moving company, and what would be the total cost?For the following exercises, use a system of linear equations with two variables and two equations to solve. 65. A total of 1,595 first- and second-year college students gathered at a pep rally. The number of freshmen exceeded the number of sophomores by 15. How many freshmen and sophomores were in attendance?For the following exercises, use a system of linear equations with two variables and two equations to solve. 66. 276 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.For the following exercises, use a system of linear equations with two variables and two equations to solve. 67. There were 130 faculty at a conference. If there were 18 more women than men attending, how many of each gender attended the conference?For the following exercises, use a system of linear equations with two variables and two equations to solve. 68. A jeep and BMW enter a highway running east- west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 7 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 306.5 miles apart. Find the speed of each car, assuming they were driven on cruise control.For the following exercises, use a system of linear equations with two variables and two equations to solve. 69. If a scientist mixed 10% saline solution with 60% saline solution to get 25 gallons of 40% saline solution, how many gallons of 10% and 60% solutions were mixed?For the following exercises, use a system of linear equations with two variables and two equations to solve. 70. An investor earned triple the profits of what she earned last year. If she made $500,000.48 total for both years, how much did she earn in profits each year?For the following exercises, use a system of linear equations with two variables and two equations to solve. 71. An investor who dabbles in real estate invested 1.1 million dollars into two land investments. On the first investment, Swan Peak, her return was a 110% increase on the money she invested. On the second investment, Riverside Community, she earned 50% over what she invested. If she earned $1 million in profits, how much did she invest in each of the land deals?For the following exercises, use a system of linear equations with two variables and two equations to solve. 72. If an investor invests a total of $25,000 into two bonds, one that pays 3% simple interest, and the other that pays 278 interest, and the investor earns $737.50 annual interest, how much was invested in each account?For the following exercises, use a system of linear equations with two variables and two equations to solve. 73. If an investor invests $23,000 into two bonds, one that pays 4% in simple interest, and the other paying 2% simple interest, and the investor earns $710.00 annual interest, how much was invested in each account?For the following exercises, use a system of linear equations with two variables and two equations to solve. 74. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?For the following exercises, use a system of linear equations with two variables and two equations to solve. 75. A store clerk sold 60 pairs of sneakers. The high-tops sold for $98.99 and the low-tops sold for $129.99. If the receipts for the two types of sales totaled $6,404.40, how many of each type of sneaker were sold?For the following exercises, use a system of linear equations with two variables and two equations to solve. 76. A concert manager counted 350 ticket receipts the day after a concert. The price for a student ticket was $12.50, and the price for an adult ticket was $16.00. The register confirms that $5,075 was taken in. How many student tickets and adult tickets were sold?For the following exercises, use a system of linear equations with two variables and two equations to solve. 77. Admission into an amusement park for 4 children and 2 adults is $116.90. For 6 children and 3 adults, the admission is $175.35. Assuming a different price for children and adults, what is the price of the child's ticket and the price of the adult ticket?Solve the system of equations in three variables. 2x+y2z=13x3yz=5x2y+3z=6 Solve the system of equations in three variables. x+y+z=2y3z=12x+y+5z=0 Solve the following system x+y+z=73x2yz=4x+6y+5z=24 Can a linear system of three equations have exactly two solutions? Explain why or why not If a given ordered triple solves the system of equations, is that solution unique? If so, explain why. If not, give an example where it is not unique.If a given ordered triple does not solve the system of equations, is there no solution? If so, explain why. If not, give an example.Using the method of addition, is there only one way to solve the system?Can you explain whether there can be only one method to solve a linear system of equations? If yes, give an example of such a system of equations. If not, explain why not.For the Following exercises, determine whether the ordered triple given is the solution to the system of equations. 6. 2x6y+6z=12x+4y+5z=1and(0,1,1)x+2y+3z=1 For the Following exercises, determine whether the ordered triple given is the solution to the system of equations. 6xy+3z=63x+5y+2z=0and(3,3.5)x+y=0 For the Following exercises, determine whether the ordered triple given is the solution to the system of equations. 6x7y+z=2xy+3z=4and(4,2,6)2x+yz=1 For the Following exercises, determine whether the ordered triple given is the solution to the system of equations. xy=0xz=5and(4,4,1)xy+z=1 For the Following exercises, determine whether the ordered triple given is the solution to the system of equations. xy+2z=35x+8y3z=4and(4,1,7)x+3y5z=5 For the following exercises, solve each system by substitution. 3x4y+2z=152x+4y+z=162x+3y+5z=20 For the following exercises, solve each system by substitution. 5x2y+3z=202x4y3z=9x+6y8z=21 For the following exercises, solve each system by substitution. 5x+2y+4z=93x+2y+z=104x3y+5z=3 For the following exercises, solve each system by substitution. 4x3y+5z=31x+2y+4z=20x+5y2z=29 For the following exercises, solve each system by substitution. 15. 5x2y+3z=44x+6y7z=13x+2yz=4 For the following exercises, solve each system by substitution. 16. 4x+6y+9z=05x+2y6z=37x4y+3z=3 For the following exercises, solve each system by substitution. 17. 2xy+3z=175x+4y2z=462y+5z=7 For the following exercises, solve each system by substitution. 5x6y+3z=50x+4y=102xz=10 For the following exercises, solve each system by Gaussian elimination. 2x+3y6z=14x6y+12z=2x+2y+5z=10 For the following exercises, solve each system by Gaussian elimination. 4x+6y2z=86x+9y3z=122x3y+z=4 For the following exercises, solve each system by Gaussian elimination. 21. 2x+3y4z=53x+2y+z=11x+5y+3z=4 For the following exercises, solve each system by Gaussian elimination. 10x+2y14z=8x2y4z=112x6y+6z=12 For the following exercises, solve each system by Gaussian elimination. 23. x+y+z=142y+3z=1416y24z=112 For the following exercises, solve each system by Gaussian elimination. 5x3y+4z=14x+2y3z=0x+5y+7z=11 For the following exercises, solve each system by Gaussian elimination. x+y+z=02xy+3z=0xz=0 For the following exercises, solve each system by Gaussian elimination. 3x+2y5z=65x4y+3z=124x+5y2z=15 For the following exercises, solve each system by Gaussian elimination. x+y+z=02xy+3z=0xz=1 For the following exercises, solve each system by Gaussian elimination. 3x12yz=124x+z=3x+32y=52 For the following exercises, solve each system by Gaussian elimination. 6x5y+6z=3815x12y+35z=14x32yz=74 For the following exercises, solve each system by Gaussian elimination. 12x15y+25z=131014x25y15z=72012x34y12z=54 For the following exercises, solve each system by Gaussian elimination. 13x12y14z=3412x14y12z=214x34y12z=12 For the following exercises, solve each system by Gaussian elimination. 12x14y+34z=014x110y+25z=218x+15y18z=2 For the following exercises, solve each system by Gaussian elimination. 45x78y+12z=145x34y+13z=825x78y+12z=5 For the following exercises, solve each system by Gaussian elimination. 13x18y+16z=4323x78y+13z=23313x58y+56z=0 For the following exercises, solve each system by Gaussian elimination. 14x54y+52z=512x53y+54z=551213x13y+13z=53 For the following exercises, solve each system by Gaussian elimination. 140x+160y+180z=110012x13y14z=1538x+312y+316z=320 For the following exercises, solve each system by Gaussian elimination. 0.1x0.2y+0.3z=20.5x0.1y+0.4z=80.7x0.2y+0.3z=8 For the following exercises, solve each system by Gaussian elimination. 0.2x+0.1y0.3z=0.20.8x+0.4y1.2z=0.11.6x+0.8y2.4z=0.2 For the following exercises, solve each system by Gaussian elimination. 1.1x+0.7y3.1z=1.792.1x+0.5y1.6z=0.130.5x+0.4y0.5z=0.07 For the following exercises, solve each system by Gaussian elimination. 0.5x0.5y+0.5z=100.2x0.2y+0.2z=40.1x0.1y+0.1z=2 For the following exercises, solve each system by Gaussian elimination. 0.1x+0.2y+0.3z=0.370.1x0.2y0.3z=0.270.5x0.1y0.3z=0.03 For the following exercises, solve each system by Gaussian elimination. 0.5x0.5y0.3z=0.130.4x0.1y0.3z=0.110.2x0.8y0.9z=0.32 For the following exercises, solve each system by Gaussian elimination. 43. 0.5x+0.2y0.3z=10.4x0.6y+0.7z=0.80.3x0.1y0.9z=0.6 For the following exercises, solve each system by Gaussian elimination. 44. 0.3x+0.3y+0.5z=0.60.4x+0.4y+0.4z=1.80.4x+0.2y+0.1z=1.6 For the following exercises, solve each system by Gaussian elimination. 45. 0.8x+0.8y+0.8z=2.40.3x0.5y+0.2z=00.1x+0.2y+0.3z=0.6 For the following exercises, solve the system for x, y, and z. 46. x+y+z=3x12+y32+z+12=0x23+y+43+z33=23 For the following exercises, solve the system for x, y, and z. 47. 5x3yz+12=126x+y92+2z=3x+824y+z=4 For the following exercises, solve the system for x, y, and z. 48. x+47y16+z+23=1x24+y+18z+812=0x+63y+23+z+42=3 For the following exercises, solve the system for x, y, and z. 49. x36+y+22z33=2x+24+y52+z+42=1x+62y32+z+1=9 For the following exercises, solve the system for x, y, and z. 50. x13+y+34+z+26=14x+3y2z=110.02x+0.015y0.01z=0.065 Three even numbers sum up to 108. The smaller is half the larger and the middle number is 34 the larger. What are the three numbers?Three numbers sum up to 147. The smallest number is half the middle number, which is half the largest number. What are the three numbers?At a family reunion, there were only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and grandparents were in attendance?An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than one-half the number of cats, and there are 20 more cats than dogs, how many of each animal are at the shelter?Your roommate, Sarah, offered to buy groceries for you and your other roommate. The total bill was $82. She forgot to save the individual receipts but remembered that your groceries were $0.05 cheaper than half of her groceries, and that your other roommate's groceries were $2.10 more than your groceries. How much was each of your share of the groceries?Your roommate, John, offered to buy household supplies for you and your other roommate. You live near the border of three states, each of which has a different sales tax. The total amount of money spent was $100.75. Your supplies were bought with 5% tax, John's with 8% tax, and your third roommate's with 9% sales tax. The total amount of money spent without taxes is $93.50. If your supplies before tax were $1 more than half of what your third roommate's supplies were before tax, how much did each of you spend? Give your answer both with and without taxes.Three coworkers work for the same employer. Their jobs are warehouse manager, office manager, and truck driver. The sum of the annual salaries of the warehouse manager and office manager is $82,000. The office manager makes $4,000 more than the truck driver annually. The annual salaries of the warehouse manager and the truck driver total $78,000. What is the annual salary of each of the co-workers?At a carnival, $2,914.25 in receipts were taken at the end of the day. The cost of a child's ticket was $20.50, an adult ticket was $29.75, and a senior citizen ticket was $15.25. There were twice as many senior citizens as adults in attendance, and 20 more children than senior citizens. How many children, adult, and senior citizen tickets were sold?A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50. The tickets were priced at $20 for student tickets, $22.50 for children, and $29 for adult tickets. If the band sold twice as many adult as children tickets, how many of each type was sold?In a bag, a child has 325 coins worth $19.50. There were three types of coins: pennies, nickels, and dimes. If the bag contained the same number of nickels as dimes, how many of each type of coin was in the bag?Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 8%, the Jeep by 5%, and the Toyota by 12%. If the price of last year's Jeep was $7,000 less than the price of last year's BMW, what was the price of each of the three cars last year?A recent college graduate took advantage of his business education and invested in three investments immediately after graduating. He invested $80,500 into three accounts, one that paid 4% simple interest, one that paid 4% simple interest, one that paid 318 simple interest, and one that paid 212 simple interest. He earned $2,670 interest at the end of one year. If the amount of the money invested in the second account was four times the amount invested in the third account, how much was invested in each account?You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,000 in interest. If you invest four times the money into the account that pays 3% compared to 2%, how much did you invest in each account?You inherit one hundred thousand dollars. You invest it all in three accounts for one year. The first account pays 4% compounded annually, the second account pays 3% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $3,650 in interest. If you invest five times the money in the account that pays 4% compared to 3%, how much did you invest in each account?The top three countries in oil consumption in a certain year are as follows: the United States, Japan, and China. In millions of barrels per day, the three top countries consumed 39.8% of the world's consumed oil. The United States consumed 0.7% more than four times China's consumption. The United States consumed 5% more than triple Japan's consumption. What percent of the world oil consumption did the United States, Japan, and China consume?[27]The top three countries in oil production in the same year are Saudi Arabia, the United States, and Russia. In millions of barrels per day, the top three countries produced 31.4% of the world's produced oil. Saudi Arabia and the United States combined for 22.1% of the world's production, and Saudi Arabia produced 2% more oil than Russia. What percent of the world oil production did Saudi Arabia, the United States, and Russia produce?[28]The top three sources of oil imports for the United States in the same year were Saudi Arabia, Mexico, and Canada. The three top countries accounted for 47% of oil imports. The United States imported 1.8% more from Saudi Arabia than they did from Mexico, and 1.7% more from Saudi Arabia than they did from Canada. What percent of the United States oil imports were from these three countries?[29]The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for 64% of the United States oil production. The Gulf of Mexico and Texas combined for 47% of oil production. Texas produced 3% more than Alaska. What percent of United States oil production came from these regions?At one time, in the United States, 398 species of animals were on the endangered species list. The top groups were mammals, birds, and fish, which comprised 55% of the endangered species. Birds accounted for 0.7% more than fish, and fish accounted for 1.5% more than mammals. What percent of the endangered species came from mammals, birds, and fish?Meat consumption in the United States can be broken into three categories: red meat, poultry, and fish. If fish makes up 4% less than one-quarter of poultry consumption, and red meat consumption is 18.2% higher than poultry consumption, what are the percentages of meat consumption?Solve the given system of equations by substitution. 3xy=22x2y=0 Solve the given system of equations by substitution. x2+y2=10x3y=10 Find the solution set for the given system of nonlinear equations. 4x2+y2=13x2+y2=10 Graph the given system of inequalities. yx21xy1 Explain whether a system of two nonlinear equations can have exactly two solutions. What about exactly three? If not, explain why not. If so, give an example of such a system, in graph form, and explain why your choice gives two or three answers.When graphing an inequality, explain why we only need to test one point to determine whether an entire region is the solution?When you graph a system of inequalities, will there always be a feasible region? If so, explain why. If not, give an example of a graph of inequalities that does not have a feasible region. Why does it not have a feasible region?If you graph a revenue and cost function, explain how to determine in what regions there is profit.If you perform your break-even analysis and there is more than one solution, explain how you would determine which x-values are profit and which are not.For the following exercises, solve the system of nonlinear equations using substitution. x+y=4x2+y2=9 For the following exercises, solve the system of nonlinear equations using substitution. y=x3x2+y2=9 For the following exercises, solve the system of nonlinear equations using substitution. y=xx2+y2=9 For the following exercises, solve the system of nonlinear equations using substitution. y=xx2+y2=9 For the following exercises, solve the system of nonlinear equations using substitution. x=2x2y2=9 For the following exercises, solve the system of nonlinear equations using elimination. 4x29y2=364x2+9y2=36 For the following exercises, solve the system of nonlinear equations using elimination. x2+y2=25x2y2=1 For the following exercises, solve the system of nonlinear equations using elimination. 2x2+4y2=42x24y2=25x10 For the following exercises, solve the system of nonlinear equations using elimination. y2x2=93x2+2y2=8 For the following exercises, solve the system of nonlinear equations using elimination. x2+y2+116=2500y=2x2 For the following exercises, use any method to solve the system of nonlinear equations. 16. 2x2+y=56xy=9 For the following exercises, use any method to solve the system of nonlinear equations. 17. x2+y=2x+y=2 For the following exercises, use any method to solve the system of nonlinear equations. 18. x2+y2=1y=20x21 For the following exercises, use any method to solve the system of nonlinear equations. 19. x2+y2=1y=x2 For the following exercises, use any method to solve the system of nonlinear equations. 20. 2x3x2=yy=12x For the following exercises, use any method to solve the system of nonlinear equations. 21. 9x2+25y2=225(x6)2+y2=1 For the following exercises, use any method to solve the system of nonlinear equations. 22. x4x2=yx2+y=0 For the following exercises, use any method to solve the system of nonlinear equations. 23. 2x3x2=yx2+y=0 For the following exercises, use any method to solve the nonlinear system. x2+y2=9y=3x2

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