Solve the system by the substitution method. -\[\begin{array} { l } x - 6 y = - 52 \\ x ^ { 2 } + 12 y = 112 \end{array}\]

A) $\{ ( - 4,8 ) , ( 2,9 ) \}$ B) $\{ ( - 58 , - 1 ) , ( 2,9 ) \}$ C) $\{ ( - 52,0 ) , ( - 58 , - 1 ) \}$ D) $\{ ( - 4,8 ) , ( - 52,0 ) \}$ A) $\{ ( - 4,8 ) , ( 2,9 ) \}$ B) $\{ ( - 58 , - 1 ) , ( 2,9 ) \}$ C) $\{ ( - 52,0 ) , ( - 58 , - 1 ) \}$ D) $\{ ( - 4,8 ) , ( - 52,0 ) \}$

Solve the system. If there is more than one solution, write the general solution. -\[\begin{array} { l } x + y - 2 z = 9 \\ 3 x + y + 2 z = 15 \\ x - 5 y + 22 z = - 27 \end{array}\] Solution $\{ - 2 z + 3,4 z + 6 , z \mid z$ is any real number $\}$

A) $( 1,10,1 ) , ( 1 , - 2 , - 2 ) , ( 5 , - 4 , - 1 )$ B) $( 3,6,0 ) , ( - 1,14,2 ) , ( 1 , - 2 , - 2 )$ C) $( 3,6,0 ) , ( 1,10,1 ) , ( - 1,14,2 )$ D) $( 1,10,1 ) , ( - 1,14,2 ) , ( 5 , - 4 , - 1 )$ A) $( 1,10,1 ) , ( 1 , - 2 , - 2 ) , ( 5 , - 4 , - 1 )$ B) $( 3,6,0 ) , ( - 1,14,2 ) , ( 1 , - 2 , - 2 )$ C) $( 3,6,0 ) , ( 1,10,1 ) , ( - 1,14,2 )$ D) $( 1,10,1 ) , ( - 1,14,2 ) , ( 5 , - 4 , - 1 )$

Exam 5: Systems of Equations and Inequalities

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+4y+3z=45 x-y+5z=30 -x+4y+3z=

(Multiple Choice)

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Question 41

Graph the solution set. - x+3y\geq6 x-y\leq-6

(Multiple Choice)

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Question 42

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - +>16 +\leq64

(Multiple Choice)

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Question 43

Solve the problem. -Camille and Sasha each make an ice cream sundae. Camille gets 2 scoops of Cherry ice cream and 1 scoop of Mint Chocolate Chunk ice cream for a total of 46 g of fat. Sasha has 3 scoops of Cherry ice Cream and 2 scoop of Mint Chocolate Chunk ice cream for a total of 77 g of fat. How many grams Of fat does 1 scoop of each type of ice cream have?

(Multiple Choice)

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Question 44

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - b+5c =7 12a-c =18 -6a+3b =-19

(Multiple Choice)

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Question 45

Determine if the ordered triple is a solution to the system of equations. - -4x+8y+2z=-40 -9x+8y+8z=-27;(-4,-6,-1) -8x+6y-8z=14

(Multiple Choice)

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Question 46

Find the partial fraction decomposition. - $\frac { - 7 x ^ { 3 } - 10 x ^ { 2 } - 48 x - 60 } { x ^ { 4 } + 13 x ^ { 2 } + 36 }$

(Multiple Choice)

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Question 47

Solve the problem. -A basketball player scored 33 points in one game. In basketball, some baskets are worth 3 points, some are worth 2 points, and free-throws are worth 1 point. He scored four more 2-point baskets Than he did 3-point baskets. The number of free throws equaled the sum of the number of 2-point And 3-point shots made. How many free-throws did he make?

(Multiple Choice)

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Question 48

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The points of intersection of a feasible region are called the ________of the region.

(Short Answer)

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Question 49

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - $6 x = \frac { y } { 4 } - 5$ $0.24 x - 0.01 y = - 0.2$

(Multiple Choice)

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Question 50

Use the substitution $u = \frac { 1 } { x } \text { and } v = \frac { 1 } { y }$ to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. - +=-4 -=20

(Multiple Choice)

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Question 51

Solve the system by the substitution method. - x-6y=-52 +12y=112

(Multiple Choice)

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Question 52

Solve the problem. -Given $f ( x ) = m x + b$ , find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$ .

(Multiple Choice)

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Question 53

Find the partial fraction decomposition. (Hint: Use the rational zero theorem to factor the denominator.) - $\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }$

(Multiple Choice)

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Question 54

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { x ^ { 3 } - 10 x ^ { 2 } - 7 x - 3 } { x ^ { 4 } + 4 x ^ { 2 } + 4 }$

(Multiple Choice)

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Question 55

Determine the values of x and y that produce the maximum value of the objective function on the feasible region. Determine the maximum value of the objective function on the feasible region. - x\geq0,y\geq0 110x+70y\leq8,600 x+y\leq100 Maximize: z=35x+30y

(Multiple Choice)

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Question 56

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. - $\text { Maximize: } z = 2 x + 3 y$ $Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. - \text { Maximize: } z = 2 x + 3 y$

(Multiple Choice)

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Question 57

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - +=3 +=2

(Multiple Choice)

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Question 58

Solve the system. If there is more than one solution, write the general solution. - x+y-2z=9 3x+y+2z=15 x-5y+22z=-27 Solution $\{ - 2 z + 3,4 z + 6 , z \mid z$ is any real number $\}$

(Multiple Choice)

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Question 59

Find all solutions of the form (a, b, c, d). - $5 a + b - c + d = - 19$ $3 b + 4 c - 4 d = 24$ $+ 5 c + 4 d = 11$ $2 a + 3 b - 3 c = - 5$

(Multiple Choice)

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Question 60

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+4y+3z=45 x-y+5z=30 -x+4y+3z=

Graph the solution set. - x+3y\geq6 x-y\leq-6

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - +>16 +\leq64

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - b+5c =7 12a-c =18 -6a+3b =-19

Determine if the ordered triple is a solution to the system of equations. - -4x+8y+2z=-40 -9x+8y+8z=-27;(-4,-6,-1) -8x+6y-8z=14

Find the partial fraction decomposition. - $\frac { - 7 x ^ { 3 } - 10 x ^ { 2 } - 48 x - 60 } { x ^ { 4 } + 13 x ^ { 2 } + 36 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The points of intersection of a feasible region are called the ________of the region.

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - $6 x = \frac { y } { 4 } - 5$ $0.24 x - 0.01 y = - 0.2$

Use the substitution $u = \frac { 1 } { x } \text { and } v = \frac { 1 } { y }$ to rewrite the equations in the system in terms of the variables u and v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original system in terms of x and y. - +=-4 -=20

Solve the system by the substitution method. - x-6y=-52 +12y=112

Solve the problem. -Given $f ( x ) = m x + b$ , find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$ .

Find the partial fraction decomposition. (Hint: Use the rational zero theorem to factor the denominator.) - $\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }$

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { x ^ { 3 } - 10 x ^ { 2 } - 7 x - 3 } { x ^ { 4 } + 4 x ^ { 2 } + 4 }$

Determine the values of x and y that produce the maximum value of the objective function on the feasible region. Determine the maximum value of the objective function on the feasible region. - x\geq0,y\geq0 110x+70y\leq8,600 x+y\leq100 Maximize: z=35x+30y

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - +=3 +=2

Solve the system. If there is more than one solution, write the general solution. - x+y-2z=9 3x+y+2z=15 x-5y+22z=-27 Solution $\{ - 2 z + 3,4 z + 6 , z \mid z$ is any real number $\}$

Find all solutions of the form (a, b, c, d). - $5 a + b - c + d = - 19$ $3 b + 4 c - 4 d = 24$ $+ 5 c + 4 d = 11$ $2 a + 3 b - 3 c = - 5$

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 5: Systems of Equations and Inequalities

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+4y+3z=45 x-y+5z=30 -x+4y+3z=

Graph the solution set. - x+3y\geq6 x-y\leq-6

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - +>16 +\leq64

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - b+5c =7 12a-c =18 -6a+3b =-19

Determine if the ordered triple is a solution to the system of equations. - -4x+8y+2z=-40 -9x+8y+8z=-27;(-4,-6,-1) -8x+6y-8z=14

Find the partial fraction decomposition. - −7x3−10x2−48x−60x4+13x2+36\frac { - 7 x ^ { 3 } - 10 x ^ { 2 } - 48 x - 60 } { x ^ { 4 } + 13 x ^ { 2 } + 36 }x4+13x2+36−7x3−10x2−48x−60​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The points of intersection of a feasible region are called the ________of the region.

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 6x=y4−56 x = \frac { y } { 4 } - 56x=4y​−5 0.24x−0.01y=−0.20.24 x - 0.01 y = - 0.20.24x−0.01y=−0.2

Solve the system by the substitution method. - x-6y=-52 +12y=112

Solve the problem. -Given f(x)=mx+bf ( x ) = m x + bf(x)=mx+b , find mmm and bbb if f(−6)=−7f ( - 6 ) = - 7f(−6)=−7 and f(−12)=−11f ( - 12 ) = - 11f(−12)=−11 .

Find the partial fraction decomposition. (Hint: Use the rational zero theorem to factor the denominator.) - 11x2+19x−7x3+2x2−15x−36\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }x3+2x2−15x−3611x2+19x−7​

Determine the values of x and y that produce the maximum value of the objective function on the feasible region. Determine the maximum value of the objective function on the feasible region. - x\geq0,y\geq0 110x+70y\leq8,600 x+y\leq100 Maximize: z=35x+30y

Determine the values of x and y that produce the maximum value of the objective function on the given feasible region. - Maximize: z=2x+3y\text { Maximize: } z = 2 x + 3 y Maximize: z=2x+3y

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - +=3 +=2

Solve the system. If there is more than one solution, write the general solution. - x+y-2z=9 3x+y+2z=15 x-5y+22z=-27 Solution {−2z+3,4z+6,z∣z\{ - 2 z + 3,4 z + 6 , z \mid z{−2z+3,4z+6,z∣z is any real number }\}}

Find all solutions of the form (a, b, c, d). - 5a+b−c+d=−195 a + b - c + d = - 195a+b−c+d=−19 3b+4c−4d=243 b + 4 c - 4 d = 243b+4c−4d=24 +5c+4d=11+ 5 c + 4 d = 11+5c+4d=11 2a+3b−3c=−52 a + 3 b - 3 c = - 52a+3b−3c=−5

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Find the partial fraction decomposition. - $\frac { - 7 x ^ { 3 } - 10 x ^ { 2 } - 48 x - 60 } { x ^ { 4 } + 13 x ^ { 2 } + 36 }$

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - $6 x = \frac { y } { 4 } - 5$ $0.24 x - 0.01 y = - 0.2$

Solve the problem. -Given $f ( x ) = m x + b$ , find $m$ and $b$ if $f ( - 6 ) = - 7$ and $f ( - 12 ) = - 11$ .

Find the partial fraction decomposition. (Hint: Use the rational zero theorem to factor the denominator.) - $\frac { 11 x ^ { 2 } + 19 x - 7 } { x ^ { 3 } + 2 x ^ { 2 } - 15 x - 36 }$

Solve the system. If there is more than one solution, write the general solution. - x+y-2z=9 3x+y+2z=15 x-5y+22z=-27 Solution $\{ - 2 z + 3,4 z + 6 , z \mid z$ is any real number $\}$

Find all solutions of the form (a, b, c, d). - $5 a + b - c + d = - 19$ $3 b + 4 c - 4 d = 24$ $+ 5 c + 4 d = 11$ $2 a + 3 b - 3 c = - 5$