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All Textbook Solutions for Algebra and Trigonometry (MindTap Course List)

25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E CONCEPTS 1-2The system of equations {2yx2=0yx=4 is graphed below. Use the graph to find the solutions of the system.2E 3E 4E 5E 6E SKILLS 3-8Substitution MethodUse the substitution method to find all solutions of the system of equations. {x+y2=02x+5y2=75 8E 9E 10E 11E SKILLS 9-14Elimination MethodUse the elimination method to find all solutions of the system of equations. {2x2+4y=13x2y2=72 SKILLS 9-14Elimination MethodUse the elimination method to find all solutions of the system of equations. {xy2+3=02x2+y24=0 14E 15E SKILLS 15-18Finding Intersection Points GraphicallyTwo equations and their graphs are given. Find the intersection points of the graphs by solving the system. {xy2=4xy=2 17E 18E SKILLS 19-32Solving Nonlinear SystemsFind all solutions of the system of equations. {y+x2=4xy+4x=16 20E 21E 22E 23E 24E SKILLS 19-32Solving Nonlinear SystemsFind all solutions of the system of equations. {x2y=16x2+4y+16=0 SKILLS 19-32Solving Nonlinear SystemsFind all solutions of the system of equations. {x+y=0y24x2=12 27E 28E 29E 30E SKILLS 19-32Solving Nonlinear SystemsFind all solutions of the system of equations. {2x3y=14x+7y=1 32E 33E 34E 35E 36E SKILLS 33-40Graphical MethodUse the graphical method to find all solutions of the system of equations, rounded to two decimal places. {x29+y218=1y=x2+6x2 38E 39E 40E 41E 42E SKILLS Plus 41-44Some Tricker SystemsFollow the hints and solve the systems. {xy=3x3y3=387Hint: Factor the left-hand side of the second equation.44E 45E 46E 47E 48E APPLICATIONS Flight of a RocketA hill is inclined so that its "slope" is 12, as shown in the figure. We introduce a coordinate system with the origin at the base of the hill and with the scales on the axes measured in meters. A rocket is fired from the base of the hill in such a way that its trajectory is the parabola y=x2+401x. At what point does the rocket strike the hillside? How far is this point from the base of the hill to the nearest centimeter?50E Global Positioning System GPS The Global Positioning System determines the location of an object from its distances to satellites in orbit around the earth. In the simplified, two-dimensional situation shown in the following figure, determine the coordinates of P from the fact that P is 26units from satellite A and 20units from satellite B.52E 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E 63E 64E 65E 66E 67E 68E 69E 70E 71E 72E APPLICATIONS Coffee BlendsA coffee merchant sells two different coffee blends. The Standard blend uses 4oz of arabica and 12oz of robusta beans per package; the Deluxe blend uses 10oz of arabica and 6oz of robusta beans per package. The merchant has 80lb of arabica and 90lb of robusta beans available. Find a system of inequalities that describes the possible number of Standard and Deluxe packages the merchant can make. Graph the solution set.74E 75E 1CC 2CC What is a system of linear equations in the variables x, y, and z?For a system of two linear equations in two variables, aHow many solutions are possible? bWhat is meant by an inconsistent system? cWhat is meant by a dependent system?What operations can be performed on a linear system to arrive at an equivalent system?aExplain how Gaussian elimination works. bUse Gaussian elimination to put the following system in triangular form, and then solve the system. System Triangular form {x+y2z=3x+2y+z=53xy+5z=1 7CC 8CC 9CC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E 20E 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E 39E 40E 41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 1CT 2CT 3CT 4CT 5CT 6CT 7CT 8CT In 212h an airplane travels 600km against the wind. It takes 50min to travel 300km with the wind. Find the speed of the wind and the speed of the airplane in still air.10CT 11CT 12CT 13CT 14CT 15CT 16CT PROBLEMS 1-4Find the maximum and minimum values of the given objective function on the indicated feasible region. M=200xy 1-4 Find the maximum and the minimum values of the given objective function on the indicated figure. N=12x+14y+40 1-4 Find the maximum and minimum values of the given objective function on the indicated feasible region. P = 140-x3y {x0y02x+y102x+4y28 4P Making FurnitureA furniture manufacturer makes wooden tables and chairs. The production process involves two basic types of labor: carpentry and finishing. A table requires 2 h of carpentry and 1 h of finishing, and a chair requires 3 h of carpentry and 12h of finishing. The profit is 35per table and 20 per chair. The manufacturers employees can supply a maximum of 108 h of carpentry work and 20 h of finishing work per day. How many tables and chairs should be made each day to maximize profit.A Housing DevelopmentA housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires 30,000 of capital and produces a profit of 4,000 when sold. A ranchstyle house requires 40,000 of capital and produces an 8,000 profit. If the contractor has 3.6million of capital on hand, how many houses of each type should she build for maximum profit? Will any of the lots be left vacant?7P Manufacturing Calculators A manufacturer of calculators produces two models: standard and scientific. Long-term demand for the two models mandates that the company manufacture at least 100 standard and 80 scientific calculators each day. However, because of limitations on production capacity, no more than 200 standard and 170 scientific calculators can be made daily. To satisfy a shopping contract, a total of at least 200 calculators must be shipped very day. aIf the production cost is 5 for a standard calculator and 7 for a scientific one, how many of each model should be produced daily to minimize this cost. bIf each standard calculator results in a 2 loss but each scientific one produces a 5 profit, how many of each model should be made easily to maximize profit.Shipping TelevisionsAn electronics discount chain has a sale on certain brand of 60-in. high-definition television set. The chain has stores in Santa Monica and El Toro and warehouses in Long Beach and Pasadena. To satisfy rush orders, 15 sets must be shipped from the warehouses to the Santa Monica store, and 19 must be shipped to the El Toro store. The cost of shipping a set is 5 from Long Beach to Santa Monica, 6 from Long Beach to El Toro, 4 from Pasadena to Santa Monica, and 5.50 from Pasadena to El Toro. If the Long Beach warehouse has 24 sets and the Pasadena warehouse has 18 sets in stock, how many sets should be shipped from each warehouse to each store to fill the orders at a minimum shipping cost?10P 11P 12P Investing in BondsA woman wishes to invest 12,000 in three types of bonds: municipal bonds paying 7 interest per year, bank certificates paying 8, and high-risk bonds paying 12. For tax reasons she wants the amount invested in municipal bonds to be at least three times the amount invested in bank certificates. To keep her level of risk manageable, she will invest no more than 2000 in high-risk bonds. How much should she invest in each type of bond to maximize her annual interest yield? Hint: Let x= amount in municipal bonds and y= amount in bank certificates. Then the high-risk bonds will be 12,000xy.14P Business StrategyA small software company publishes computer games, educational software, and utility software. Their business strategy is to market a total of 36 new programs each year, at least four of these being games. The number of utility programs published is never more than twice the number of educational programs. On average, the company makes an annual profit of 5000 on each computer game, 8000 on each educational program, and 6000 on each utility program. How many of each type of software should the company publish annually for maximum profit?Feasible RegionAll parts of this problem refer to the following feasible region and objective function. {x0xyx+2y12x+y10 P=x+4y aGraph the feasible region. bOn your graph from part a, sketch the graphs of the linear equations obtained by setting P equal to 40, 36, 32, and 28. cIf you continue to decrease the value of P, at which vertex of the feasible region will these lines first touch the feasible region? dVerify that the maximum value of P on the feasible region occurs at the vertex you chose in part c.If a system of linear equations has infinitely many solutions, then the system is called _______. If a system of linear equations has no solutions, then the system is called ______.Write the augmented matrix of the following system of equations. SystemAugmentedmatrix{x+yz=1x2z=32yz=3[]3E 4E 5E 6E 5-10 Dimension of a Matrix State the dimension of the matrix. [1235]8E 9E 10E 11E 12E 13-20 Form of a Matrix A matrix is given. a Determine whether the matrix is in row-echelon form. b Determine whether the matrix is in reduced row-echelon form. c Write the system of equations for which the given matrix is the augmented matrix. [103015]14E 15E 16E 17E 18E 13-20Form of a Matrix A matrix is given. a Determine whether the matrix is in row-echelon form. b Determine whether the matrix is in reduced row-echelon form. c Write the system of equations for which the given matrix is the augmented matrix. [13010001200000100000]20E 21E 22E 23E 24E 25-28Back-Substitution A matrix is given in row-echelon form. a Write the system of equations for which the given matrix is the augmented matrix. b Use back-substitution to solve the system. [124301270012]26E 27E 28E 29E 30E 29-38Linear Systems with One Solution The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. {x+y+z=22x3y+2z=44x+y3z=1 29-38Linear Systems with One Solution The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. {x+y+z=4x+2y+3z=172xy=7 33E 34E 35E 36E 29-38Linear Systems with One Solution The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. {2x3yz=13x+2y5z=65xyz=49 38E 39E 40E 41E 39-48Dependent or Inconsistent Linear Systems Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. {x2y+5z=32x+6y11z=13x16y+20z=26 39-48Dependent or Inconsistent Linear Systems Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. {xy+3z=34x8y+32z=242x3y+11z=4 44E 45E 46E 47E 39-48Dependent or Inconsistent Linear Systems Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. {y5z=73x+2y=123x+10z=80 SKILLS 49-64 Solving a Linear SystemsSolve the system of linear equations. {4x3y+z=82x+y3z=4xy+2z=3 50E

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