Algebra and Trigonometry Enhanced with Graphing Utilities (7th Edition)

Chapter 11

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; Add x to both sides. ; Combine like terms. ; ... more

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inconsistent ; When a system of equations has at ... more

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consistent ; When a system of equations has at ... more

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; The solution gives the values that will work in... more

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consistent ; When a system of equations has at ... more

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Points of intersection determine solutions of a ... more

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The ordered triple satisfies the constraints in ... more

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; Substitute the values for , and into the ... more

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; Substitute the values for , and into the ... more

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; Substitute the values for x, y, and z into the ... more

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; Substitute the values for x, y ,and z into the ... more

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; Notice that the coefficients of are opposites... more

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; Note that the coefficients of are opposites.  ... more

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

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; Solve equation (2) for .   ; Substitute in ... more

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; Multiply equation (1) by 2 and Equation (2) by ... more

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; Multiply equation (1) by 3 and equation (2) by... more

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Inconsistent ; Multiply equation (1) by to make ... more

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Inconsistent ; Multiply equation (1) by 3 to make ... more

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; Solve equation (2) for y.  Notice that the ... more

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; Multiply Equation (1) by 6 and Equation (2) by ... more

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; Multiply Equation (1) by 6 and Equation (2) by ... more

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; Since the coefficients of y are opposites, add ... more

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; Multiply Equation (2) by 2 to clear fractions... more

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; Rewrite the equations in the system, using  and... more

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; Rewrite the equations in the system, using  and... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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Inconsistent ; For a system of three linear ... more

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Inconsistent ; For a system of three linear ... more

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, where is any real number. ; For a system of ... more

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, where z is any real number.  ; For a system of ... more

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Inconsistent ; For a system of three linear ... more

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Inconsistent ; For a system of three linear ... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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The length is 30 ft.  The width is 15 ft. ; ... more

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The length is 775 ft.  The width is 725 ft. ; ... more

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There were 23 CLs and 58 NCLs. ; Identify the ... more

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There were 110 paying As and 215 SCs. ; Identify ... more

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Person M should mix 22.5 pounds of Cs with the Ps... more

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Person C should mix 10 liters of the 30% solution ... more

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The average speed of the plane is 175 mph and the ... more

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The average wind speed is 30 mph. ; Identify the ... more

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Person M should purchase 80 sets of D1 and 120 ... more

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Each food item costs .  Each drink costs . ; ... more

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The total refund is . ; Identify the unknowns with... more

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Person P swims 4 mph.  The average speed of the ... more

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Person D should mix 50 mg of C1 with 75 mg of C2... more

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Person D should mix 30 units of P1 with 15 units ... more

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; There are three unknowns.  To find the value of... more

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; There are three unknowns.  To find the value of... more

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The ELOI is and the IR is . ; To solve the system... more

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The ELOI is and the IR is ; To solve the system ... more

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; For a system of three linear equations with ... more

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; For a system of three linear equations with ... more

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There are 100 OSs, 210 MSs, and 190 Bs. ; Identify... more

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There are 110 As, 220 Cs, and 75 SCs sold. ; ... more

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Person K should invest in TBIs, in TBOs, and in... more

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There is not sufficient information to determine ... more

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There is sufficient information.  Each sandwich ... more

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Person Be takes 30 hours, Person Bi takes 24 hours... more

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First, label the equations (1) and (2).  Then, ... more

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The substitution method is beneficial to use when ... more

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Substitute values of into the function and solve ... more

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; Replace with .  Then, exchange the variables ... more

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matrix ; A matrix is a rectangular array of ... more

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augmented ; An augmented matrix is a matrix used ... more

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third ; The first index i gives the row number of ... more

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With row echelon form, 1s appear on the diagonal ... more

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With reduced row echelon form, 1s appear on the ... more

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The matrix is in row echelon form since 1s appear ... more

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; Check the system of equations to confirm that ... more

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; Check the system of equations to confirm that ... more

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; Rewrite the system so that the equations are in... more

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; Rewrite the system so that the equations are in... more

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; Check the system of equations to confirm that ... more

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; Check the system of equations to confirm that ... more

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; Check the system to confirm that all variable ... more

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; Check the system of equations to confirm that ... more

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; Check the system to confirm that all variable ... more

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; Rewrite the system so that the equations are in... more

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; First, note that the equations are in standard ... more

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; First, note that the equations are in standard ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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; First, write the system associated with the ... more

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Consistent ; First, write the system of equations ... more

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Consistent ; First, write the system of equations ... more

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Inconsistent ; First, write the system of ... more

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Inconsistent ; First, write the system of ... more

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Consistent, where is a real number ; First, write... more

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Consistent, where is a real number ; First, write... more

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Consistent, where is a real number ; First, write... more

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Consistent, where is a real number ; First, write... more

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Consistent, where and represent any real number... more

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Consistent, where is any real number ; First, ... more

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Consistent, where is any real number ; First, ... more

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Consistent  ; First, write the system of equations... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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,  where is any real number ; Check the system ... more

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, where is any real number ; Check the system to... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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(8, 2, 0) ; Check the system to confirm that all ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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Inconsistent ; Check the system to confirm that ... more

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Inconsistent ; Check the system to confirm that ... more

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, where is any real number ; Check the system to... more

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, where is any real number ; Check the system to ... more

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Inconsistent  ; Check the system to confirm that ... more

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Inconsistent ; Check the system to confirm that ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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; Check the system to confirm that the equations ... more

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, where is any real number ; Check the system to... more

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Inconsistent ; Check the system to confirm that ... more

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, where is any real number ; Check the system to... more

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, where is any real number ; Check the system to... more

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; Check the system to confirm that the equations ... more

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Inconsistent ; Check the system to confirm that ... more

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, where and are real numbers ; Check the system... more

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,  where is any real number ; Check the system ... more

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; There are three unknowns.  Note that each point... more

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; There are three unknowns.  Note that each point... more

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; Each function evaluation represents an ordered ... more

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; Each function evaluation represents an ordered ... more

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Person D should provide servings of fish, ... more

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Person D should provide serving of the meat, ... more

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Person C should invest in TBIs, in TBOs, and in... more

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The DC is , the LC is , and TC is . ; Identify the... more

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There are Type D, Type B, and Type S produced... more

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There are cases of O juice, cases of G juice, ... more

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; Write the equations in standard form.  All ... more

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; Write the equations in standard form.  All ... more

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 S1S2S3 ; Identify the unknowns with variables.  ... more

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 P1P2P3 ; Identify the unknowns with variables.  ... more

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First, write the equations in standard form.  All ... more

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An augmented matrix can be written in row echelon ... more

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; Place all terms on the left side of the ... more

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First, factor the numerator and the denominator.  ... more

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; The given function can be graphed using ... more

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and . ; Since the degree of is 4, the function ... more

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; To use Cramer's Rule to solve for , the ... more

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If , then when . ; If , then when . ; more

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If , then the system of linear equations is either... more

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Multiplying a row or column by a nonzero number ... more

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If  , then .  If , then  .  So the determinants ... more

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; Move from left to right.  Multiply the number ... more

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; Move from left to right.  Multiply the number ... more

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; Move from left to right.  Multiply the number ... more

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; Move from left to right.  Multiply the number ... more

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; To find the first cofactor, Start with the ... more

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; Since there are no in the determinant, ... more

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; The determinant has three cofactors.  Each ... more

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; The determinant has three cofactors.  Each ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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, use different method ; According to Cramer's ... more

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, use different method ; According to Cramer's ... more

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; According to Cramer’s Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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, use different method ; According to Cramer's ... more

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, use different method ; According to Cramer's ... more

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; According to Cramer's Rule, the solution to a ... more

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; According to Cramer's Rule, the solution to a ... more

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, use different method ; According to Cramer's ... more

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, use different method ; According to Cramer's ... more

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; Notice that is exchanged with .  If two rows ... more

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; Notice that is multiplied by .  If a row or ... more

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; First, note that the entries, , and are ... more

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; First, note that is moved to .   If two rows ... more

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; First, note that is moved to .   If two rows ... more

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; Observe that multiplying Column 1 by and ... more

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; First, note that is moved to .   If two rows ... more

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; First, note that is obtained by multiplying ... more

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; Find the determinant.  Then, solve the ... more

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; Find the determinant.  Then, solve the ... more

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; Find the determinant.  Then, solve the ... more

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; Find the determinant.  Then, solve the ... more

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; Find the determinant.  Then, solve the ... more

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; Find the determinant.  Then, solve the ... more

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; First, compute the value of the determinant.  ... more

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Suppose , , and lie on the same line with .  The ... more

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; Label the vertices , , and .  Then, substitute ... more

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; First, find the area of each triangle.  Label ... more

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; The technique using the determinants is faster ... more

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; Label the vertices as , , and .  Then, ... more

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The circle has center and radius . ; Label the ... more

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  ; Expand down Column 3 to find the value of the ... more

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If , then and .  So and .If , then and .  So ... more

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   ; Expand across to find the value of the ... more

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   ; Multiply by .  Then, expand across to find ... more

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  ; Expand across to find the value of the ... more

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   ; Expand across to find the value of the ... more

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The possible rational zeros are   ; Use the ... more

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First, graph the basic function .   ; Compare to... more

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; Use the definition of logarithm to convert the ... more

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square ; A matrix is called a square matrix if it ... more

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The sum of two or more matrices is found by adding... more

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For square matrices and , the products and are ... more

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inverse ; For any square matrix (given that is ... more

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The identity matrix is the multiplicative ... more

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; Since is a nonsingular matrix, its inverse ... more

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The size of a matrix is given as "number of rows ... more

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The size of a matrix is given as "number of rows ... more

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; Write the addition as the sum of the ... more

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; Write the subtraction as the difference of the ... more

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; Multiply times each entry of . ; more

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; Multiply times each entry of . ; more

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; Find by multiplying each entry of by , and ... more

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; Find by multiplying each entry of by , and ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Write  the entries of the product by ... more

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; Write the addition as the sum of the ... more

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; Find by adding the corresponding entries of ... more

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; Find by multiplying each row of by each ... more

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; Find by multiplying each row of by each ... more

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; Find by multiplying each row of by each ... more

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; Find by multiplying each row of by each ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Write the entries of the product by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Form the augmented matrix . ; Find by ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Form the augmented matrix where is the given ... more

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; Form the augmented matrix where is the given ... more

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; Form the augmented matrix where is the given ... more

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; Form the augmented matrix where is the given ... more

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; Form the augmented matrix where is the given ... more

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; Form the augmented matrix where is the given ... more

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; Set the graphing utility into matrix mode.Some ... more

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; Set the graphing utility into matrix mode.Some ... more

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; Set the graphing utility into matrix mode.Some ... more

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; Set the graphing utility into matrix mode.Some ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Write the coefficient matrix , the variable ... more

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; Use elimination method to solve the system of ... more

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; Use elimination method to solve the system of ... more

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; Solve the system of equations using the ... more

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; Solve the system of equations using the ... more

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or  no solution ; Solve the system of equations ... more

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or  no solution ; Solve the system of equations ... more

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; Solve the system of equations using the ... more

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; Solve the system of equations using the ... more

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 Each entry of the square of the matrix represents... more

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\ ; Form the augmented matrix where is the given... more

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A scheduling matrix for students can be ... more

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When multiplying matrices and , the row and the... more

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No ; The matrix equation is equal to will not ... more

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If exists, the system of equations represented by... more

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; Use the property that if is a real zero of a ... more

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; Multiply both sides of the equation by and then... more

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Simplify both sides of the equation.  The left ... more

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The degree of the numerator is 2 and the degree of... more

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; Factor the GCF, , from each term in the ... more

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This is a proven theorem for polynomials with real... more

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Proper ; The degree of the numerator is 1 and the ... more

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Proper ; The degree of the numerator is 1 and the ... more

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Improper; ; Compare the degrees of the numerator ... more

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Improper; ; Compare the degrees of the numerator ... more

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Improper;   ; Compare the degrees of the numerator... more

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Improper; ; Compare the degrees of the numerator ... more

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Improper; ; Multiply the factors in the numerator ... more

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Improper; ; Multiply the factors in the numerator ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Since the denominator is a difference of two ... more

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; Since the denominator is a difference of two ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; Determine the case number/s by looking at the ... more

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; ; ; Follow these general steps: Divide the ... more

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;; ; Follow these general steps: Divide the ... more

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;; ; Divide the numerator by the denominator using... more

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3.85 years ; For an amount to double, the final ... more

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; The expression denotes a composite function ... more

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Substitute to find y-intercept. ; Substitute to ... more

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Compare the equation with the equation of parabola... more

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Rearrange the terms and write the equation in the ... more

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; Rearrange the terms and write the equation in ... more

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Substitute for in the second equation and solve ... more

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Substitute for in the second equation and solve ... more

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; Substitute for in the second equation and ... more

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Substitute for in the second equation and solve ... more

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; Substitute for in the second equation and ... more

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; Substitute for in the second equation and ... more

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; Substitute for in second equation and solve ... more

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; Substitute for in the second equation and ... more

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

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

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; Substitute for in the second equation and ... more

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; Substitute for in the first equation and ... more

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

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

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

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; Substitute for in the second equation and ... more

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No solution. ; Rearrange the terms of second ... more

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; Substitute for in the first equation and ... more

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; Substitute the expression for from the first ... more

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Add and subtract and in the first equation ... more

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, , , ; Solve the second equation for . ; ... more

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

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, ; Substitute for in the second equation and ... more

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

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

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, , , ; Solve the second equation for . ; ... more

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

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

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, ; Multiply the second equation by 4 and add it ... more

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, ; Multiply the second equation by 2 and ... more

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, ; Multiply the first equation by 5 and the ... more

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, ; Multiply the first equation by 2 and subtract... more

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, ; Multiply the second equation by 2 and add it ... more

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, ; Multiply the second equation by 5 and subtract... more

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No real solution ; Multiply the first equation by ... more

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No real solution ; Multiply the first equation by ... more

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