 9.1: solve each system of linear equations by substitution.
 9.2: solve each system of linear equations by substitution.
 9.3: solve each system of linear equations by substitution.
 9.4: solve each system of linear equations by substitution.
 9.5: solve each system of linear equations by substitution.
 9.6: solve each system of linear equations by substitution.
 9.7: solve each system of linear equations by substitution.
 9.8: solve each system of linear equations by substitution.
 9.9: solve each system of linear equations by substitution.
 9.10: solve each system of linear equations by substitution.
 9.11: solve each system of linear equations by substitution.
 9.12: solve each system of linear equations by substitution.
 9.13: solve each system of linear equations by substitution.
 9.14: solve each system of linear equations by substitution.
 9.15: solve each system of linear equations by substitution.
 9.16: solve each system of linear equations by substitution.
 9.17: solve each system of linear equations by substitution.
 9.18: solve each system of linear equations by substitution.
 9.19: solve each system of linear equations by substitution.
 9.20: solve each system of linear equations by substitution.
 9.21: solve each system of linear equations by substitution.
 9.22: solve each system of linear equations by substitution.
 9.23: solve each system of linear equations by substitution.
 9.24: solve each system of linear equations by elimination.
 9.25: solve each system of linear equations by elimination.
 9.26: solve each system of linear equations by elimination.
 9.27: solve each system of linear equations by elimination.
 9.28: solve each system of linear equations by elimination.
 9.29: solve each system of linear equations by elimination.
 9.30: solve each system of linear equations by elimination.
 9.31: solve each system of linear equations by elimination.
 9.32: solve each system of linear equations by elimination.
 9.33: solve each system of linear equations by elimination.
 9.34: solve each system of linear equations by elimination.
 9.35: solve each system of linear equations by elimination.
 9.36: solve each system of linear equations by elimination.
 9.37: solve each system of linear equations by elimination.
 9.38: solve each system of linear equations by elimination.
 9.39: solve each system of linear equations by elimination.
 9.40: solve each system of linear equations by elimination.
 9.41: solve each system of linear equations by elimination.
 9.42: solve each system of linear equations by elimination.
 9.43: solve each system of linear equations by elimination.
 9.44: match the systems of equations with the graphs.
 9.45: match the systems of equations with the graphs.
 9.46: match the systems of equations with the graphs.
 9.47: solve each system of linear equations by graphing.
 9.48: solve each system of linear equations by graphing.
 9.49: solve each system of linear equations by graphing.
 9.50: solve each system of linear equations by graphing.
 9.51: solve each system of linear equations by graphing.
 9.52: solve each system of linear equations by graphing.
 9.53: solve each system of linear equations by graphing.
 9.54: solve each system of linear equations by graphing.
 9.55: Environment.Approximately 2 million dry erase markers are disposed ...
 9.56: Pharmacy.A pharmacy technician receives an order for 454 grams of a...
 9.57: Event Planning.You are in charge of event planning for a major corp...
 9.58: Health Club Management.A tness club has a budget of $915 to purchas...
 9.59: Mixture. In chemistry lab, Stephanie has to make a 37 milliliter so...
 9.60: Mixture.A mechanic has 340 gallons of gasoline and 10 gallons of oi...
 9.61: Salary Comparison. Upon graduation with a degree in management of i...
 9.62: Salary Comparison. Two types of residential real estate agents are:...
 9.63: Gas Mileage.A Honda Accord gets approximately 26 mpg on the highway...
 9.64: Wireless Plans.AT&T is offering a 600minute peak plan with free mo...
 9.65: Distance/Rate/Time.A direct ight on Delta Air Lines from Atlanta to...
 9.66: Distance/Rate/Time.A private pilot ies a Cessna 172 on a trip that ...
 9.67: Investment Portfolio. Leticia has been tracking two volatile stocks...
 9.68: Investment Portfolio.Toby split his savings into two different inve...
 9.69: BreakEven Analysis.A company produces CD players for a unit cost o...
 9.70: Managing a Lemonade Stand.An elementaryschoolage child wants to h...
 9.71: explain the mistake that is made. Solve the system of equations by ...
 9.72: explain the mistake that is made. Solve the system of equations by ...
 9.73: explain the mistake that is made. Solve the system of equations by ...
 9.74: explain the mistake that is made. Solve the system of equations by ...
 9.75: determine whether each statement is true or false.A system of equat...
 9.76: determine whether each statement is true or false. A system of equa...
 9.77: determine whether each statement is true or false. If two lines do ...
 9.78: determine whether each statement is true or false. The system of eq...
 9.79: The point (2, 3) is a solution to the system of equations Ax By 29 ...
 9.80: If you graph the lines x 50y 100 x 48y 98 they appear to be paralle...
 9.81: Energy Drinks.A nutritionist wishes to market a new vitaminenriche...
 9.82: Easter Eggs.A family is coloring Easter eggs and wants to make two ...
 9.83: Use a graphing utility to graph the two equations y 1.25x 17.5 and ...
 9.84: Use a graphing utility to graph the two equations y 14.76x 19.43 an...
 9.85: Use a graphing utility to graph the two equations and determine the...
 9.86: Use a graphing utility to graph the two equations and determine the...
 9.87: Use a graphing utility to graph the two equations and . Approximate...
 9.88: Use a graphing utility to graph the two equations and . Approximate...
 9.1: solve each system of linear equations.
 9.2: solve each system of linear equations.
 9.3: solve each system of linear equations.
 9.4: solve each system of linear equations.
 9.5: solve each system of linear equations.
 9.6: solve each system of linear equations.
 9.7: solve each system of linear equations.
 9.8: solve each system of linear equations.
 9.9: solve each system of linear equations.
 9.10: solve each system of linear equations.
 9.11: solve each system of linear equations.
 9.12: solve each system of linear equations.
 9.13: solve each system of linear equations.
 9.14: solve each system of linear equations.
 9.15: solve each system of linear equations.
 9.16: solve each system of linear equations.
 9.17: solve each system of linear equations.
 9.18: solve each system of linear equations.
 9.19: solve each system of linear equations.
 9.20: solve each system of linear equations.
 9.21: solve each system of linear equations.
 9.22: solve each system of linear equations.
 9.23: solve each system of linear equations.
 9.24: solve each system of linear equations.
 9.25: solve each system of linear equations.
 9.26: solve each system of linear equations.
 9.27: solve each system of linear equations.
 9.28: solve each system of linear equations.
 9.29: solve each system of linear equations.
 9.30: solve each system of linear equations.
 9.31: Business.A small company has an assembly line that produces three t...
 9.32: Business.A small company has an assembly line that produces three t...
 9.33: Football. On September 1, 2007, the Appalachian State Mountaineers ...
 9.34: Basketball. On April 4, 2004, the University of Connecticut Huskies...
 9.35: rely on a selection of Subway sandwiches whose nutrition informatio...
 9.36: rely on a selection of Subway sandwiches whose nutrition informatio...
 9.37: involve vertical motion and the effect of gravity on an object. Bec...
 9.38: involve vertical motion and the effect of gravity on an object. Bec...
 9.39: Data CurveFitting. The number of minutes that an average person of...
 9.40: Data CurveFitting. The average age when a woman gets married began...
 9.41: Money. Tara and Lamar decide to place $20,000 of their savings into...
 9.42: Money.Tara talks Lamar into putting less money in the money market ...
 9.43: Ski Production.A company produces three types of skis: regular mode...
 9.44: Automobile Production.An automobile manufacturing company produces ...
 9.45: Computer versus Man. The Seattle Times reported a story on November...
 9.46: Brain versus Computer. Can the human brain perform more calculation...
 9.47: explain the mistake that is made.Solve the system of equations. Equ...
 9.48: explain the mistake that is made.Solve the system of equations. Equ...
 9.49: determine whether each statement is true or false.A system of linea...
 9.50: determine whether each statement is true or false.A system of linea...
 9.51: determine whether each statement is true or false. Geometry. The ci...
 9.52: determine whether each statement is true or false.Geometry. The cir...
 9.53: A fourthdegree polynomial, f(x) ax4 bx3 cx2 dx e, with a 0, can be...
 9.54: A copy machine accepts nickels, dimes, and quarters. After 1 hour, ...
 9.55: solve the system of linear equations.
 9.56: solve the system of linear equations.
 9.57: solve the system of linear equations.
 9.58: solve the system of linear equations.
 9.59: employ a graphing calculator to solve the system of linear equation...
 9.60: employ a graphing calculator to solve the system of linear equation...
 9.61: Some graphing calculators and graphing utilities have the ability t...
 9.62: Some graphing calculators and graphing utilities have the ability t...
 9.63: employ a graphing calculator to solve the system of equations.
 9.64: employ a graphing calculator to solve the system of equations.
 9.1: match the rational expression (16) with the form of the partialfra...
 9.2: match the rational expression (16) with the form of the partialfra...
 9.3: match the rational expression (16) with the form of the partialfra...
 9.4: match the rational expression (16) with the form of the partialfra...
 9.5: match the rational expression (16) with the form of the partialfra...
 9.6: match the rational expression (16) with the form of the partialfra...
 9.7: write the form of the partialfraction decomposition. Do not solve ...
 9.8: write the form of the partialfraction decomposition. Do not solve ...
 9.9: write the form of the partialfraction decomposition. Do not solve ...
 9.10: write the form of the partialfraction decomposition. Do not solve ...
 9.11: write the form of the partialfraction decomposition. Do not solve ...
 9.12: write the form of the partialfraction decomposition. Do not solve ...
 9.13: write the form of the partialfraction decomposition. Do not solve ...
 9.14: write the form of the partialfraction decomposition. Do not solve ...
 9.15: nd the partialfraction decomposition for each rational function.
 9.16: nd the partialfraction decomposition for each rational function.
 9.17: nd the partialfraction decomposition for each rational function.
 9.18: nd the partialfraction decomposition for each rational function.
 9.19: nd the partialfraction decomposition for each rational function.
 9.20: nd the partialfraction decomposition for each rational function.
 9.21: nd the partialfraction decomposition for each rational function.
 9.22: nd the partialfraction decomposition for each rational function.
 9.23: nd the partialfraction decomposition for each rational function.
 9.24: nd the partialfraction decomposition for each rational function.
 9.25: nd the partialfraction decomposition for each rational function.
 9.26: nd the partialfraction decomposition for each rational function.
 9.27: nd the partialfraction decomposition for each rational function.
 9.28: nd the partialfraction decomposition for each rational function.
 9.29: nd the partialfraction decomposition for each rational function.
 9.30: nd the partialfraction decomposition for each rational function.
 9.31: nd the partialfraction decomposition for each rational function.
 9.32: nd the partialfraction decomposition for each rational function.
 9.33: nd the partialfraction decomposition for each rational function.
 9.34: nd the partialfraction decomposition for each rational function.
 9.35: nd the partialfraction decomposition for each rational function.
 9.36: nd the partialfraction decomposition for each rational function.
 9.37: nd the partialfraction decomposition for each rational function.
 9.38: nd the partialfraction decomposition for each rational function.
 9.39: nd the partialfraction decomposition for each rational function.
 9.40: nd the partialfraction decomposition for each rational function.
 9.41: Optics. The relationship between the distance of an object to a len...
 9.42: Sums. Find the partialfraction decomposition of and apply it to nd...
 9.43: explain the mistake that is made.Find the partialfraction decompos...
 9.44: explain the mistake that is made.Find the partialfraction decompos...
 9.45: determine whether each statement is true or false. Partialfraction...
 9.46: determine whether each statement is true or false. The degree of th...
 9.47: nd the partialfraction decomposition.
 9.48: nd the partialfraction decomposition.
 9.49: nd the partialfraction decomposition.
 9.50: nd the partialfraction decomposition.
 9.51: nd the partialfraction decomposition.
 9.52: nd the partialfraction decomposition.
 9.53: Use a graphing utility to graph and in the same viewing rectangle. ...
 9.54: Use a graphing utility to graph and in the same viewing rectangle. ...
 9.55: Use a graphing utility to graph and in the same viewing rectangle. ...
 9.56: Use a graphing utility to graph and in the same viewing rectangle. ...
 9.57: Use a graphing utility to graph and in the same viewing rectangle. ...
 9.58: Use a graphing utility to graph and in the same viewing rectangle. ...
 9.1: match the linear inequality with the correct graph.
 9.2: match the linear inequality with the correct graph.
 9.3: match the linear inequality with the correct graph.
 9.4: match the linear inequality with the correct graph.
 9.5: graph each linear inequality. y x 1
 9.6: graph each linear inequality. y x 1
 9.7: graph each linear inequality. y x
 9.8: graph each linear inequality. y x
 9.9: graph each linear inequality. y 3x 2
 9.10: graph each linear inequality. y 2x 3
 9.11: graph each linear inequality. y 2x 1
 9.12: graph each linear inequality. y 3x 2
 9.13: graph each linear inequality. 3x 4y 2
 9.14: graph each linear inequality. 2x 3y 6
 9.15: graph each linear inequality. 5x 3y
 9.16: graph each linear inequality. 4x 5y 20
 9.17: graph each linear inequality. 4x 2y 6
 9.18: graph each linear inequality. 6x 3y
 9.19: graph each linear inequality. 6x 4y 12
 9.20: graph each linear inequality. 5x 2y 10
 9.21: graph each system of inequalities or indicate that the system has n...
 9.22: graph each system of inequalities or indicate that the system has n...
 9.23: graph each system of inequalities or indicate that the system has n...
 9.24: graph each system of inequalities or indicate that the system has n...
 9.25: graph each system of inequalities or indicate that the system has n...
 9.26: graph each system of inequalities or indicate that the system has n...
 9.27: graph each system of inequalities or indicate that the system has n...
 9.28: graph each system of inequalities or indicate that the system has n...
 9.29: graph each system of inequalities or indicate that the system has n...
 9.30: graph each system of inequalities or indicate that the system has n...
 9.31: graph each system of inequalities or indicate that the system has n...
 9.32: graph each system of inequalities or indicate that the system has n...
 9.33: graph each system of inequalities or indicate that the system has n...
 9.34: graph each system of inequalities or indicate that the system has n...
 9.35: graph each system of inequalities or indicate that the system has n...
 9.36: graph each system of inequalities or indicate that the system has n...
 9.37: graph each system of inequalities or indicate that the system has n...
 9.38: graph each system of inequalities or indicate that the system has n...
 9.39: graph each system of inequalities or indicate that the system has n...
 9.40: graph each system of inequalities or indicate that the system has n...
 9.41: graph each system of inequalities or indicate that the system has n...
 9.42: graph each system of inequalities or indicate that the system has n...
 9.43: graph each system of inequalities or indicate that the system has n...
 9.44: graph each system of inequalities or indicate that the system has n...
 9.45: graph each system of inequalities or indicate that the system has n...
 9.46: graph each system of inequalities or indicate that the system has n...
 9.47: graph each system of inequalities or indicate that the system has n...
 9.48: graph each system of inequalities or indicate that the system has n...
 9.49: Area. Find the area enclosed by the system of inequalities.
 9.50: Area. Find the area enclosed by the system of inequalities.
 9.51: Area.Find the area enclosed 10 by the system of linear inequalities...
 9.52: Area. Find the area enclosed by the system of linear inequalities (...
 9.53: Hurricanes.After backtobacktobacktoback hurricanes (Charley, ...
 9.54: Hurricanes. Repeat Exercise 53 with a smaller truck and different s...
 9.55: Health.A diet must be designed to provide at least 275 units of cal...
 9.56: Health.A diet must be designed to provide at least 350 units of cal...
 9.57: Business.A manufacturer produces two types of computer mouse: USB w...
 9.58: Business.A manufacturer produces two types of mechanical pencil lea...
 9.59: employ the following supply and demand equations:. Consumer Surplus...
 9.60: employ the following supply and demand equations:Producer Surplus.W...
 9.61: employ the following supply and demand equations:Consumer Surplus. ...
 9.62: employ the following supply and demand equations:Producer Surplus. ...
 9.63: explain the mistake that is made.Graph the inequality y 2x 1. Solut...
 9.64: explain the mistake that is made. Graph the inequality y 2x 1. Solu...
 9.65: determine whether each statement is true or false. A linear inequal...
 9.66: determine whether each statement is true or false.A dashed curve is...
 9.67: determine whether each statement is true or false. A solid curve is...
 9.68: determine whether each statement is true or false. A system of line...
 9.69: For the system of linear inequalities, assume a, b, c, and d are re...
 9.70: For the system of linear inequalities, assume a, b, c, and d are re...
 9.71: Use the following system of linear inequalities If a and b are posi...
 9.72: Use the following system of linear inequalities If a and b are nega...
 9.73: use a graphing utility to graph the following inequalities. 4x 2y 6...
 9.74: use a graphing utility to graph the following inequalities. 6x 3y 9...
 9.75: use a graphing utility to graph each system of inequalities or indi...
 9.76: use a graphing utility to graph each system of inequalities or indi...
 9.1: nd the value of the objective function at each of the vertices. Wha...
 9.2: nd the value of the objective function at each of the vertices. Wha...
 9.3: nd the value of the objective function at each of the vertices. Wha...
 9.4: nd the value of the objective function at each of the vertices. Wha...
 9.5: minimize or maximize each objective function subject to the constra...
 9.6: minimize or maximize each objective function subject to the constra...
 9.7: minimize or maximize each objective function subject to the constra...
 9.8: minimize or maximize each objective function subject to the constra...
 9.9: minimize or maximize each objective function subject to the constra...
 9.10: minimize or maximize each objective function subject to the constra...
 9.11: minimize or maximize each objective function subject to the constra...
 9.12: minimize or maximize each objective function subject to the constra...
 9.13: Hurricanes.After the 2004 backtobacktobacktoback hurricanes i...
 9.14: Hurricanes. After Hurricane Charley devastated central Florida unex...
 9.15: Computer Business.A computer science major and a business major dec...
 9.16: Computer Business. Repeat Exercise 15 if the two students are able ...
 9.17: Passenger Ratio. The Eurostar is a highspeed train that travels be...
 9.18: Passenger Ratio. Repeat Exercise 17. This time, assume that there h...
 9.19: Production.A manufacturer of skis produces two models: a regular sk...
 9.20: Donut Inventory.A wellknown donut store makes two popular types of...
 9.21: Maximize the objective function z 2x y subject to the following con...
 9.22: Identify the vertices. (0, 2), (0, 0), (1, 1)The maximum, 3, is loc...
 9.23: determine whether each statement is true or false.An objective func...
 9.24: determine whether each statement is true or false.An objective func...
 9.25: Maximize the objective function z 2x y subject to the conditions, w...
 9.26: Maximize the objective function z x 2y subject to the conditions, w...
 9.27: employ a graphing utility to determine the region of feasible solut...
 9.28: employ a graphing utility to determine the region of feasible solut...
 9.29: employ a graphing utility to determine the region of feasible solut...
 9.30: employ a graphing utility to determine the region of feasible solut...
 9.31: employ a graphing utility to determine the region of feasible solut...
 9.32: employ a graphing utility to determine the region of feasible solut...
 9.1: Solve each system of linear equations.
 9.2: Solve each system of linear equations.
 9.3: Solve each system of linear equations.
 9.4: Solve each system of linear equations.
 9.5: Solve each system of linear equations.
 9.6: Solve each system of linear equations.
 9.7: Solve each system of linear equations.
 9.8: Solve each system of linear equations.
 9.9: Solve each system of linear equations.
 9.10: Solve each system of linear equations.
 9.11: Solve each system of linear equations.
 9.12: Solve each system of linear equations.
 9.13: Solve each system of linear equations.
 9.14: Solve each system of linear equations.
 9.15: Solve each system of linear equations.
 9.16: Solve each system of linear equations.
 9.17: Match each system of equations with its graph.
 9.18: Match each system of equations with its graph.
 9.19: Match each system of equations with its graph.
 9.20: Match each system of equations with its graph.
 9.21: Chemistry. In chemistry lab,Alexandra needs to make a 42 milliliter...
 9.22: Gas Mileage.A Nissan Sentra gets approximately 32 mpg on the highwa...
 9.23: Solve each system of linear equations.
 9.24: Solve each system of linear equations.
 9.25: Solve each system of linear equations.
 9.26: Solve each system of linear equations.
 9.27: Fitting a Curve to Data. The average number of ights on a commercia...
 9.28: Investment Portfolio. Danny and Paula decide to invest $20,000 of t...
 9.29: Write the form of each partialfraction decomposition. Do not solve...
 9.30: Write the form of each partialfraction decomposition. Do not solve...
 9.31: Write the form of each partialfraction decomposition. Do not solve...
 9.32: Write the form of each partialfraction decomposition. Do not solve...
 9.33: Write the form of each partialfraction decomposition. Do not solve...
 9.34: Write the form of each partialfraction decomposition. Do not solve...
 9.35: Write the form of each partialfraction decomposition. Do not solve...
 9.36: Write the form of each partialfraction decomposition. Do not solve...
 9.37: Find the partialfraction decomposition for each rational function.
 9.38: Find the partialfraction decomposition for each rational function.
 9.39: Find the partialfraction decomposition for each rational function.
 9.40: Find the partialfraction decomposition for each rational function.
 9.41: Find the partialfraction decomposition for each rational function.
 9.42: Find the partialfraction decomposition for each rational function.
 9.43: Find the partialfraction decomposition for each rational function.
 9.44: Find the partialfraction decomposition for each rational function.
 9.45: Graph each linear inequality. y 2x 3
 9.46: Graph each linear inequality. y x 4
 9.47: Graph each linear inequality. 2x 4y 5
 9.48: Graph each linear inequality. 5x 2y 4
 9.49: Graph each linear inequality. y 3x 2
 9.50: Graph each linear inequality. y x 2
 9.51: Graph each linear inequality. 3x 8y 16
 9.52: Graph each linear inequality. 4x 9y 18
 9.53: Graph each system of inequalities or indicate that the system has n...
 9.54: Graph each system of inequalities or indicate that the system has n...
 9.55: Graph each system of inequalities or indicate that the system has n...
 9.56: Graph each system of inequalities or indicate that the system has n...
 9.57: Graph each system of inequalities or indicate that the system has n...
 9.58: Graph each system of inequalities or indicate that the system has n...
 9.59: Minimize or maximize the objective function subject to the constrai...
 9.60: Minimize or maximize the objective function subject to the constrai...
 9.61: Minimize or maximize the objective function subject to the constrai...
 9.62: Minimize or maximize the objective function subject to the constrai...
 9.63: Minimize or maximize the objective function subject to the constrai...
 9.64: Minimize or maximize the objective function subject to the constrai...
 9.65: refer to the following: An art student decides to handpaint coaste...
 9.66: refer to the following: An art student decides to handpaint coaste...
 9.67: Use a graphing utility to graph the two equations 0.4x 0.3y 0.1 and...
 9.68: Use a graphing utility to graph the two equations and . Find the so...
 9.69: employ a graphing calculator to solve the system of equations. 5x 3...
 9.70: employ a graphing calculator to solve the system of equations. 2x 1...
 9.71: Apply a graphing utility to graph and in the same viewing rectangle...
 9.72: Use a graphing utility to graphand in the same viewingrectangle. Is...
 9.73: use a graphing utility to graph each system of inequalities or indi...
 9.74: use a graphing utility to graph each system of inequalities or indi...
 9.75: Maximize z 6.2x 1.5y subject to: 4x 3y 5.4 2x 4.5y 6.3 3x y 10.7
 9.76: Minimize z 1.6x 2.8y subject to: y 3.2x 4.8 x 2 y 3.2x 4.8
 9.1: Solve each system of linear equations.
 9.2: Solve each system of linear equations.
 9.3: Solve each system of linear equations.
 9.4: Solve each system of linear equations.
 9.5: Solve each system of linear equations.
 9.6: Solve each system of linear equations.
 9.7: Solve each system of linear equations.
 9.8: Solve each system of linear equations.
 9.9: Write each rational expression as a sum of partial fractions.
 9.10: Write each rational expression as a sum of partial fractions.
 9.11: Write each rational expression as a sum of partial fractions.
 9.12: Write each rational expression as a sum of partial fractions.
 9.13: Write each rational expression as a sum of partial fractions.
 9.14: Write each rational expression as a sum of partial fractions.
 9.15: Graph the inequalities. 2x y 6
 9.16: Graph the inequalities. 4x y 8
 9.17: graph the system of inequalities.
 9.18: graph the system of inequalities.
 9.19: graph the system of inequalities.
 9.20: graph the system of inequalities.
 9.21: Minimize the function z 5x 7y, subject to the constraints:
 9.22: Find the maximum value of the objective function z 3x 6y, given the...
 9.23: Stock Investment. On starting a new job, Cameron gets a $30,000 sig...
 9.24: Ranch.A rancher buys a rectangular parcel of property that is 245,0...
 9.25: Employ a graphing calculator to solve the system of equations. 5x 3...
 9.26: Minimize z x 1.2y subject to: 3.2x y 15.9 0.4x y 0.3 x 1.0
 9.1: Simplify .
 9.2: Perform the operation and write in standard form: (5 7i) (11 9i).
 9.3: Solve for x and give any excluded values:
 9.4: Solve for the radius r: A r2.
 9.5: Solve and express the solution in interval notation:
 9.6: Calculate the distance and midpoint between the line segment joinin...
 9.7: Write an equation of a line in slopeintercept form that passes thro...
 9.8: Use interval notation to express the domain of the function .
 9.9: Find the average rate of change for ,from x 2 to x 4.
 9.10: Sketch the graph of the function and identify all transformations.
 9.11: Evaluate g(f(1)) for f(x) and
 9.12: Find the inverse of the function
 9.13: Find the quadratic function that has the vertex (0, 7) and goes thr...
 9.14: Find all of the real zeros and state the multiplicity of the functi...
 9.15: List the possible rational zeros and test to determine all rational...
 9.16: Factor the polynomial P(x) 4x4 4x3 13x2 18x 5 as a product of linea...
 9.17: Graph the exponential function f(x) 5x 1; state the yintercept, th...
 9.18: How much money should be put in a savings account now that earns 5....
 9.19: Graph the function f(x) ln(x 1) 3 using transformation techniques.
 9.20: Evaluate log4.7 8.9 using the changeofbase formula. Round the ans...
 9.21: Solve the equation for x. Round the answers to three decimal places.
 9.22: At a coffee shop, one order of 4 tall coffees and 6 donuts is $14.1...
 9.23: Solve the system of linear equations.
 9.24: Find the partialfraction decomposition for the rationalexpression
 9.25: Graph the system of linear inequalities.
 9.26: Employ a graphing calculator to solve the system of equations. 2x 9...
 9.27: Apply a graphing utility to graph and in the same viewing rectangle...
Solutions for Chapter 9: Systems of Linear Equations and Inequalities
Full solutions for Algebra and Trigonometry  3rd Edition
ISBN: 9780470648032
Solutions for Chapter 9: Systems of Linear Equations and Inequalities
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Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Iterative method.
A sequence of steps intended to approach the desired solution.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.