Algebra and Trigonometry: Real Mathematics, Real People (7th Edition)

Chapter 9

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; Solve the equation for . ; Substitute the ... more

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; Assume the amount in fund is and amount in ... more

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; Solve the equation for . ; Substitute the ... more

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No Real solution ; Solve the equation for . ; ... more

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; Solve the equation for . ; Enter the ... more

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; Let be the number of bottles.Find the total ... more

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No, because the equations have no real solutions... more

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System ; A system of equations is a group of two ... more

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Solution ; The solution of a system is an ordered ... more

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Substitution ; To solve a system of equations by ... more

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solution ; The solution is the point of ... more

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Break-even point ; Break-even point is the point ... more

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When the graph of two equations of the system does... more

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; Solve the given equation (1) for . ; Substitute... more

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; Solve the equation (1) for . ; Substitute the ... more

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, ; Solve the equation (1) for . ; Substitute the ... more

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, ; Solve the equation (1) for . ; Substitute the ... more

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; Rearrange the equation 1 for . ; Substitute the... more

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; Rearrange the equation 1 for . ; Substitute the... more

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; Rearrange the equation 1 for . ; Substitute the... more

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; Substitute the value of from equation 2 into ... more

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   ; Solve the first equation for . ; Substitute ... more

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   ; Solve the equation for . ; Substitute the ... more

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; Rearrange the equation 1 for ; Substitute the ... more

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; Rearrange the equation 1 for . ; Substitute the... more

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; Multiply the equation 1 on both sides by 10 and... more

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No solution ; Multiply the equation 1  by to both... more

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; Multiply the equation 1 by 10 and solve for... more

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; Multiply both sides of the equation 1 by 4 and ... more

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No solution ; Multiply the equation (1) by and ... more

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; Multiply the equation by and solve for . ; ... more

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4%: 20002%: 16,00  ; Let the amount funded by be... more

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6%: 10,0003%: 8,000 ; Let the amount funded by be... more

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: 3,500: 14,500 ; Let the amount funded by be ... more

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: 5,400: 12,600  ; Let the amount funded by be ... more

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, ; Solve equation (2) for . ; Substitute the ... more

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, ; Solve quation (2) for . ; Substitute the value... more

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No real solution ; Solve equation (2) for . ; ... more

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No real solution ; Solve equation (2) for . ; ... more

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, , ; Solve equation (2) for . ; Substitute the ... more

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  ; Substitute for from equation (1) into ... more

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; Solve the equation for . ; Solve the equation... more

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No solution ;  Solve the equation for . ; Solve ... more

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; Solve the equation for . ; Solve the equation... more

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; Solve the equation for . ; Solve the equation... more

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No solution ; Solve the equation for . ; Solve ... more

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; Solve the equation for . ; Solve the equation... more

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; Solve the equation for . ; Solve the equation... more

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; Solve the equation for . ; Solve the equation... more

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; Solve the equation for . ; Solve the equation... more

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; Solve the equation for . ; Solve the equation... more

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; Label the given equations. ; Rearrange the ... more

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; Label the equations. ; Rearrange the equation 1... more

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; Label the given equations. ; Rearrange equation... more

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; Label the given equations. ; Rearrange equation... more

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; Label the given equations. ; Rearrange  ... more

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; Label the given equations. ; Rearrange  ... more

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; Label the given equations. ;   ; Rearrange ... more

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; Label the given equations. ;   ; Rearrange ... more

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; Label the given equations. ; Enter the ... more

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; Label the given equations. ; Rearrange the ... more

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; Label the given equations. ; Rearrange the ... more

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; Solve both the equations for . ; Enter the ... more

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Algebraic method gives direct results by putting ... more

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No real solutionAlgebraically the method gives ... more

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Algebraic method gives direct results by putting ... more

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Algebraic method gives direct results by putting ... more

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No real solutionAlgebraic method gives direct ... more

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No real solutionAlgebraic method gives direct ... more

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Algebraic method gives direct results by putting ... more

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Algebraic method gives direct results by putting ... more

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Graphical method is a simple method to solve ... more

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Graphical method is a simple method to solve ... more

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Algebraic method gives direct results by putting ... more

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Algebraic method gives direct results by putting ... more

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No real solutionAlgebraic method gives direct ... more

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Algebraic method gives direct results by putting ... more

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192 units ; Enter the function, and into the ... more

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233,333 units  ; Enter the function, and into ... more

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3133 units ; Enter the function, and into the ... more

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1464 units ; Enter the function, and into the ... more

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; Suppose be the length of the rectangle and be... more

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; Suppose be the length of the rectangle and be... more

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; Let be the total sales.Form the system of ... more

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; Suppose be the length and be the width.Form ... more

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Base: ; height:   ; Suppose be the one side, ... more

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False, to solve a system of equations, first, by ... more

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False; There can be more than two solutions ... more

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There is no solution when , and have different ... more

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; Let a system of equations which has the ... more

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; Find the slope using the formula, of the two ... more

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; Substitute 3 for , 3 for , 10 for , and 6 for ... more

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is a vertical line and cannot be written in the ... more

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; Find the slope using the formula, of the two ... more

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Domain: all real numbers except 6Vertical ... more

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Domain: Vertical asymptote: Horizontal asymptote... more

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Domain: All real number except Vertical ... more

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Domain: All real number except Vertical ... more

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Domain: All real number  Horizontal asymptotes: ; ... more

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Domain: All real number  Horizontal asymptotes: ; ... more

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Elimination method ; Assume  Find the value of in... more

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; The coefficients of differ only in sign, ... more

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; Multiply by 5 and by to obtain like ... more

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No solutionInconsistent ; Rewrite the system of ... more

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No solution ; Multiply with 2 to obtain like ... more

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Infinitely many solutions ; Multiply by to make ... more

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; Consider,is the speed of the plane.is the speed... more

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Nothing is wrong. ; Rewrite the system of linear ... more

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MethodElimination ; The elimination method is ... more

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Equivalent ; When the system of linear equations ... more

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A system of linear equations with no solution ... more

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A system of linear equations with at least one ... more

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Yes ; If the two lines coincide with each other, ... more

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Nothing is wrong. ;   Rewrite the system of linear... more

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; Obtain the coefficients with different signs by... more

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; Perform addition of the given equations. ; ... more

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(a)Infinitely many solutionsConsistent ; Rewrite ... more

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; Obtain the coefficients with different signs by... more

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(d)No solutionInconsistent ; Rewrite the given ... more

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; Obtain the coefficients with different signs by... more

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(c)One solutionConsistent ; Rewrite the given ... more

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No solution ; Obtain the coefficients with ... more

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Infinitely many solutions ; Obtain the ... more

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; The coefficients of differ only in sign, ... more

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; The coefficients of differ only in sign, ... more

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; Multiply by 3 to obtain like coefficients of ... more

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; Obtain the coefficients with different signs by... more

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; Multiply by to obtain  like coefficients of ... more

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; Multiply by to obtain like coefficients of ... more

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; Multiply by and by 5 to obtain like ... more

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; Multiply by 2 and by 3 to obtain like ... more

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; Multiply by 4 and by 6 to obtain like ... more

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; Multiply by and by 9 to obtain like ... more

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Inconsistent ; Multiply by 5 to obtain like ... more

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; Multiply by .to obtain like coefficients of ... more

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; Multiply by 4 and by 3 to obtain like ... more

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Infinitely many solutions. ; Multiply by 2 to ... more

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(a)Infinitely many solutionsConsistent ; Graph the... more

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(d)No solutionInconsistent ; Graph the given two ... more

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(c)Exactly one solutionConsistent ; Graph the ... more

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The graph is as follows, ; Obtain the coefficients... more

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The graph is as follows, ; Obtain the coefficients... more

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Inconsistent, no solutionThe graph is as follows... more

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Infinitely many solutionsThe graph is as follows... more

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Infinitely many solutionsThe graph is as follows... more

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No solution.The graph is as follows,   ; Obtain ... more

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The graph is as follows, ; Simplify the first ... more

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The graph is as follows,  ; Simplify the first ... more

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Infinitely many solutions.The graph is as follows... more

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Inconsistent.The graph is as follows,   ; Obtain ... more

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Inconsistent.No solution.The graph is as follows... more

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Infinitely many solutionsThe graph is as follows... more

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; Label the given equations. ; Make the ... more

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; Label the two equations. ; Make the ... more

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\(\left\{ {\left( { - 1,1} \right)} \right\} ; ... more

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; Label the two given equations. ; Add equations... more

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Consistent: ; Rewrite the system of the linear ... more

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Inconsistent; No solution ; Rewrite the system of ... more

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Consistent: All points on the line . ; Rewrite the... more

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Consistent; ; Rewrite the system of the linear ... more

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Inconsistent ; Rewrite the system of the linear ... more

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Consistent: All points on the line ; Rewrite the ... more

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; Rewrite the system of linear equations into ... more

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;  Rewrite the system of linear equation into ... more

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Rewrite the equations in the slope-intercept form... more

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Rewrite the equations in the slope intercept form... more

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; Rewrite the equations in the slope intercept ... more

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; Rewrite the equations in the slope intercept ... more

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; Rewrite the equations in the slope intercept ... more

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; Rewrite the equations in the slope intercept ... more

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; Multiply by and by 3 to obtain the like ... more

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; Multiply by to obtain like coefficients of ... more

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; Multiply by to obtain like coefficients of ... more

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; Substitute the value of in . ; Use the ... more

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; Multiply by to obtain like coefficients of ... more

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; Multiply by to obtain like coefficients of ... more

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; Substitute the value of in . ; Use the ... more

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; Multiply by 5 and by 4 to obtain like ... more

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; Substitute the values and in . ; Solve for... more

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; Substitute the values and in . ; Solve for... more

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; Substitute the values and in . ; Solve for... more

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; Substitute the values and in . ; Solve for... more

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; Equate the equations of demand and supply to ... more

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; Equate the equations of demand and supply to ... more

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; Equate the equations of demand and supply to ... more

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; Equate the equations of demand and supply to ... more

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; Consider,is the speed of the plane.is the speed... more

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; ; Consider,is the speed of the boat.is the speed... more

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9 oranges7 grapefruits ; Consider that is the ... more

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300 calories cheese burgers230 calories french ... more

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Yes170 pairs of shoes and 80 pairs of shoes sold... more

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; Obtain the coefficients with different signs by... more

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; Obtain the coefficients with different signs by... more

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; Obtain the coefficients with different signs by... more

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; Obtain the coefficients with different signs by... more

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True ; A consistent system of linear equations can... more

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True ; If in a system of linear equations two ... more

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False, the graphing utility also estimates an ... more

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 Not possible because if the system of linear ... more

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; Obtain the coefficients with different signs by... more

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; Obtain the coefficients with different signs by... more

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; Add to each side of the given inequality and ... more

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; Add 10 to each part of the given inequality and... more

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; Rewrite the given inequality in double ... more

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; The inequality is true for all values of as ... more

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; Factor the inequality. ;   ; Find the critical ... more

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; Divide both sides by 3. ; Factor the expression... more

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; Simplify the expression using the identity, .... more

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; Use the power property for natural logarithm... more

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; Simplify the expression using the product ... more

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; Use the power property of logarithms with the ... more

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; Use the power property for natural logarithm... more

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; Use the power property for natural logarithm... more

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; Label the given equation. ; Substitute 3 for ... more

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; Label the given equation ; Since the leading ... more

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Inconsistent ; Since the leading coefficient in ... more

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; Label the given equation. ; Since the leading ... more

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; Since the leading coefficient in the first ... more

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; The expression is a proper fraction, so ... more

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; The expression is proper, so factorize the ... more

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: ; : 20; : 100 ; Substitute 1, 2, and 3 for nto ... more

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; Substitute 0, 3, and 6 for into the given ... more

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The problem is that the constant numerators and ... more

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Row-echelon  ; A “stair-step” pattern with leading... more

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Ordered triple ; An ordered triple is the ... more

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Gaussian  ; The system of equations can be solved ... more

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Non-square ; If the number of equations differs ... more

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Three-dimensional ; A  3-dimensional coordinate ... more

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Partial fraction decomposition ; Partial fraction ... more

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A consistent system can be an independent or ... more

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A system of equations either consistent or ... more

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; Label the equations as 1, 2, and 3. ; ... more

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; Label the given equation. ; Substitute for ... more

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; Label the given equation. ; Substitute 2 for ... more

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; Label the given equation  ; Substitute for ... more

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; Label the given equation. ; Substitute 11 for ... more

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; Label the given equation. ; Substitute for ... more

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  ; On adding equation 1 and equation 2, the ... more

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; On adding times equation 1 to equation 3, the ... more

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123 ; Since the coefficient of in equation 1 is a... more

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51 ; Since the coefficient of in the first ... more

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85 ; Divide the first equation by 2. ; Subtract 5 ... more

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; Divide the first equation by 2 to make 1 as the... more

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; Divide the first equation by 4.Subtract the ... more

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Inconsistent  ; Divide the first equation by five.... more

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Inconsistent  ; Divide the first equation by three... more

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; Label the three given equations. ; Subtract ... more

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; Divide the first equation by 3. ; Subtract ... more

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; Divide the first equation by 2. ; Subtract the ... more

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; Divide the first equation by 3. ; Subtract the ... more

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Inconsistent  ; Divide the first equation by .... more

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Inconsistent  ; Subtract thrice the first equation... more

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; Subtract 4 times of the first equation from the... more

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; Subtract the second equation from the first ... more

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Inconsistent  ; Divide the first equation by three... more

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Inconsistent  ; Subtract the first equation from ... more

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; Label the three given equations. ; Subtract ... more

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; Subtract four times the first equation from the... more

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; Divide the first equation by 2. ; Add the ... more

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; Divide the equation 1 by 12 to generate new ... more

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; Divide the equation (1) by 10. ; Subtract 19 ... more

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; Observe that with the given numbers, the ... more

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; Observe that with the given numbers, the ... more

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; Observe that with the given numbers, the ... more

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; Observe that with the given numbers, the ... more

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; Add the given points to form the first equation... more

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; Add the given points to form the first equation... more

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; ; ; ; Substitute 0 for and into the given ... more

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, , , ; Substitute 0 for and into the given ... more

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, , , . ; Substitute 0 for and into the given ... more

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, , , ; Substitute 0 for and into the given ... more

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; The expression is a proper fraction. Factorize ... more

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; The expression is a proper fraction. Factorize ... more

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; The fraction  is proper. Factorize the ... more

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; The fraction is proper. Factorize the ... more

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; The factor given in the denominator is a cubic ... more

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; The fraction is proper. Since the denominator ... more

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; The fraction is proper. Since the denominator ... more

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; The fraction is proper. Since the denominator ... more

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   ; Factor the expression in the denominator. ; ... more

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Factor the expression in the denominator. ; Use a ... more

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; Factor the expression in the denominator. ; Use... more

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; Factor the expression in the denominator. ; Use... more

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; Factor the expression in the denominator. ; Use... more

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; Factor the expression in the denominator. ; Use... more

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; Write the given rational expression as the sum ... more

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; Write the given rational expression as the sum ... more

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; The given rational expression is an improper ... more

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; The given rational expression is an improper ... more

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; The given rational expression is an improper ... more

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Perform division. ; Use the partial fraction to ... more

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; Factor the denominator of the given proper ... more

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; The given rational expression is a proper ... more

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Vertical asymptotes of the rational function and ... more

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Vertical asymptotes of the rational function and ... more

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; Substitute 1 for and 128 for into the given ... more

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; Substitute 1 for and 32 for into the given ... more

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; Substitute 1 for and 352 for into the given ... more

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; Substitute 1, 2, 3 for into the given position... more

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   ; Form a system of equations by entering the ... more

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; Form the system of equations by entering the ... more

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  ; Form the system of equations by entering the ... more

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Form the system of equations by entering the pair ... more

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  ; Form the system of equations by entering the ... more

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  ; Form the system of equations by entering the ... more

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; The circle passes through the given points, ... more

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  ; Form the system of equations by entering the ... more

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4% :$20,000; 6% : $2500; 8% :$7500 ; Let be the ... more

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8% : $300,000; 9% : $400,000: 10%: $75,000 ; Let ... more

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Certificate of deposit: ; municipal bonds: ; blue-... more

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Certificate of deposit: ; municipal bonds: ; blue-... more

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Number of free throws: 10; Number of two-point ... more

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Par-3 holes: 4; Par-4 holes: 10; Par-5 holes: 4 ; ... more

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: 1 amperes; : 2 amperes; : 1 amperes ; Label the ... more

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, , ; Subtract two times of the first equation ... more

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; ; ; ; Label the given equations. ; Divide ... more

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; ; ;  ; Label the given equations. ; Divide ... more

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; ; ; ; Label the given equations. ; Divide both ... more

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; ; ; ; Label the equations. ; Divide equation (1... more

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; Factor the denominator. ; Write the partial ... more

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False; The leading coefficient of the second ... more

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TrueThe system of three linear equations has no ... more

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No, the problem is not worked correctly. Divide ... more

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Not equivalent as there are two arithmetic errors... more

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; Substitute the values of and into the ... more

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; Assume that a system of equations has three ... more

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A system of equations has no solution if, upon ... more

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; ; ; Label the given equations. ; Subtract ... more

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: 2; : 2; : ; Label the given equations. ; Find ... more

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; Add 3 on both sides of the equation. ; Divide ... more

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; ; Add 2 to both sides. ; Divide both sides of ... more

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   ; The dimension of the matrix is given as  ,... more

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  ; The given system of linear equations is ... more

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  ;  Add times the first row to the second row of ... more

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; ; ; The given system of linear equations is ... more

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 The matrix is in row-echelon form. The matrix is ... more

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 ; ; ; The given system of linear equations is ... more

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No solution. ; The given system of linear ... more

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  ; The given system of linear equations is ... more

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  is the solution set of equations. ; The given ... more

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 Matrix ;  To solve the system of linear equations... more

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 reduced row-echelon ; A matrix is in reduced row-... more

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 Gauss-Jordan elimination ; The Gauss-Jordan ... more

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 Yes ;  Write the coefficient matrix for the given... more

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 No ;  Write the augmented matrix of the given ... more

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 Yes ; The augmented matrix is converted to the ... more

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  ; The dimension of the matrix is given as  ,... more

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  ; The dimension of the matrix is given as  , ... more

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  ;  The dimension of the matrix is given as  , ... more

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  ;  The dimension of the matrix is given as  ,... more

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  ;  The dimension of the matrix is given as  ,... more

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  ;  The dimension of the matrix is given as  ,... more

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  ; The given system of linear equations is ... more

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  ; The given system of linear equations is ... more

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  ; The given system of linear equations is ... more

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  ; The given system of linear equations is ... more

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  ; The given system of linear equations is ... more

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  ; The given system of linear equations is ... more

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  ;  Write the system of  linear equations with ... more

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  ; Write the system of  linear equations with the... more

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; Write the system of  linear equations with the ... more

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; Write the system of  linear equations with the ... more

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 Multiply the first row by . ; The new row ... more

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 Perform the operation  . ; In the original matrix... more

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 Perform the expression . ; In the original matrix... more

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 Interchange the first row with the second row. ; ... more

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  ;  For the original matrix, perform operation ... more

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  ;  For the original matrix, perform the ... more

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; Add  times the first row to the second row and... more

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; Interchange the first row with the second row.... more

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; Press 2nd and to enter the matrix menu of the ... more

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; Press 2nd and to enter the matrix menu of the ... more

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The matrix is in row-echelon form. The matrix is ... more

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The matrix is in row-echelon form. The matrix is ... more

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The matrix is not in row-echelon form. The matrix ... more

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The matrix is in row-echelon form. The matrix is ... more

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The matrix is in row-echelon form. The matrix is ... more

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The matrix is not in row-echelon form.The matrix ... more

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; Add times of the first row to the second row ... more

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; Add times of the first row to the second row ... more

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; Add times of the first row to the second row ... more

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; Multiply the first row by 3 and add it to the ... more

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; Enter the augmented matrix into the CAS. ; Use ... more

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; Enter the augmented matrix into the CAS. ; Use ... more

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; Enter the augmented matrix into the CAS. ; Use ... more

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; Enter the augmented matrix into the CAS. ; Use ... more

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;  The given matrix is in row-echelon form. So, ... more

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; Since the given matrix is in row-echelon form... more

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; Since the given matrix is in row-echelon form, ... more

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; Since the given matrix is in row-echelon form, ... more

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(7,-5) ; Convert the row-reduced echelon form to a... more

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( - 2,4)  ; Convert the row-reduced echelon to a ... more

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( - 4, - 8,2)  ; Convert the row-reduced echelon ... more

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(3, - 1,0)  ; Convert the row-reduced echelon to a... more

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; Write the system of linear equation as an ... more

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; Write the system of linear equation as an ... more

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Inconsistent  ; Write the augmented matrix from ... more

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Inconsistent ;  Write the augmented matrix from ... more

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; Write the system of the linear equation as an ... more

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 No solution ; Write the system of linear ... more

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; Write the system of linear equation in the form... more

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; Since the given system of linear equation is ... more

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; Since the given system of linear equation is ... more

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; Since the given system of linear equation is ... more

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;  Enter the augmented matrix into the CAS. ; Use... more

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; Enter the augmented matrix into the CAS. ; Use ... more

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;  Enter the augmented matrix into the graphing ... more

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: 1; : 0; : 4; : ; Enter the augmented matrix into... more

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  amperesamperes amperes ; Write the augmented ... more

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  ; Let be the amount borrowed at .Let be the ... more

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$1 bills: 15; $5 bills: 8; $10 bills: 2; $20 bills... more

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Glossy: 50 pounds; Semi-glossy: 35 pounds; Matte: ... more

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TrueBefore writing the augmented matrix in row ... more

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False, is a reduced row echelon form of a ... more

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; Add the first row to the second row to obtain ... more

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No, because it may have more than one solution. ; ... more

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  ; Form a table for the values of for different ... more

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Slant asymptote: Vertical asymptote: ; Use the ... more

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  ; Multiply matrix by 3. ;   ; Multiply matrix ... more

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is the associative property of scalar ... more

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is the left distributive property. If a matrix is... more

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No ; Consider the matrices and .From the ... more

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; Since matrix is of dimension and matrix is ... more

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: 5; : ; Equate the entries of both the matrices.... more

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: 13; : 12 ; Equate the entries of both the ... more

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  ; Compare the corresponding values of the ... more

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  ; Compare the corresponding values of the ... more

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  ; Apply the distributive property. ; Perform ... more

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; Since the number of columns of matrix is equal... more

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Not possible ; Since the number of columns of ... more

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; Since the number of columns of matrix is equal... more

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; Since matrix is of dimension and matrix is ... more

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  ; For , should satisfy the condition . Thus, ... more

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100 100100 ; Let , , and represent the number of ... more

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50300 50 ; Let , , and represent the number of ... more

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ERR: INVALID DIMDeterminant is defined only for ... more

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  ; Enter the matrix into the CAS to obtain the ... more

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32 ; Write the determinant of the given matrix as... more

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0 ; Write the determinant of the given matrix as... more

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31 ; Write the determinant of the given matrix as... more

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0 ; If , the value of , there will be no need to ... more

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0 ; If , the value of , there will be no need to ... more

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; If , the value of , there will be no need to ... more

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; If , the value of , there will be no need to ... more

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  ; Enter the matrix into the CAS to obtain the ... more

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7441  ; Enter the matrix into the CAS to obtain ... more

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566  ; Enter the matrix into the CAS to obtain the... more

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; Expand the cofactors in the first column. ; ... more

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3 ; Expand the cofactors in the first row.Find the... more

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110       25       23         47       149... more

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square units ; Assume that , , and . Represent the... more

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square units ; Assume that , , and . Represent the... more

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; Assume that , , and . Represent the values in ... more

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; Assume that , , and . Represent the values in ... more

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  ; Evaluate the determinant of the coefficient ... more

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  ; Evaluate the determinant of the coefficient ... more

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miles per hour; miles per hour ; Let be the ... more

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4105 ; Let the number of par-3 holes, par-4 holes... more

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$16000$13000$11000 ; Let the amount invested at 7... more

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; The dimensions of a matrix are determined by ... more

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; The dimensions of a matrix are determined by ... more

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; The dimensions of a matrix are determined by ... more

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; The dimensions of the matrix are determined by ... more

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;  Since the given system of linear equations is ... more

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; Since the given system of linear equations is ... more

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; Since the given system of linear equations is ... more

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  ; Multiply the first row by . ; Add -3 times of ... more

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; Enter the augmented matrix into CAS. ; Use the ... more

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Inconsistent system; No solution  ; Write the ... more

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  ; Write the augmented matrix using the system of... more

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; Write the augmented matrix using the system of ... more

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; Write the augmented matrix using the system of ... more

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  ; Write the augmented matrix using the system of... more

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; Write the augmented matrix using the system of ... more

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Inconsistent ; Write the augmented matrix using ... more

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Inconsistent ; Write the augmented matrix from the... more

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Inconsistent; No solution  ; Enter the augmented ... more

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Determine the product .Determine the product .From... more

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; Enter the given matrix into CAS. ; Use the rref... more

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; Enter the given matrix into CAS. ; Use the rref... more

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Not possible ; Write the given system of equations... more

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Inconsistent system of equationsSolution not ... more

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0 ; Denote the matrix by .  ; Since the matrix has... more

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550 ; Write the determinant of the given matrix as... more

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78 ; Write the determinant of the given matrix as... more

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130 ; Let the given matrix be .Since the value of... more

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; Let the given matrix be .Since the value of if... more

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20 ; Let the given matrix be .Since the value of ... more

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279 ; Let the given matrix be .Since the value of... more

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; Let the given matrix be .Since the value of if... more

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16 square units ; Let , , and . Represent the ... more

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24 square units ; Let , , and . Represent the ... more

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square units ; Let , , and . Represent the values ... more

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square units ; Let , , and . Represent the values ... more

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48 square units ; Consider the coordinates , , and... more

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64 square units ; Consider the coordinates , , and... more

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FalseThe graphical method will not give an exact ... more

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TrueMatrix addition is performed by adding ... more

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