Question 1

Find the determinant of the matrix.

Accepted Answer

A) - 392,544 
B) - 1,570,176 
C) - 98,136 
D) - 392,545 
E) 392,544 
A) - 392,544 
B) - 1,570,176 
C) - 98,136 
D) - 392,545 
E) 392,544

Question 2

Use the method of substitution to solve the system.

Accepted Answer

A) ( 0, 2 ) 
B) ( 4, 0 ) 
C) ( 4, 0 ), ( 0, 2 ) 
D) ( 4, 1 ), ( 0, 2 ) 
E) no solution 
A) ( 0, 2 ) 
B) ( 4, 0 ) 
C) ( 4, 0 ), ( 0, 2 ) 
D) ( 4, 1 ), ( 0, 2 ) 
E) no solution

Question 3

Find the determinant of the matrix.

Accepted Answer

A) -1083.6 
B) -173 
C) -433.44 
D) -443.44 
A) -1083.6 
B) -173 
C) -433.44 
D) -443.44

Question 4

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 5

Find the determinant of the matrix after introducing zeros.

Accepted Answer

A) 15 
B) - 17 
C) - 18 
D) - 16 
E) 0 
A) 15 
B) - 17 
C) - 18 
D) - 16 
E) 0

Question 6

Find the values of b such that the system   has no solution.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 7

Use the method of substitution to solve the system.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 8

Use the method of substitution to solve the system.

Accepted Answer

A) ( 7, 0 ), ( 3, 2 ) 
B) ( 7, 0 ) 
C) ( 3, 2 ) 
D) ( 7, 1 ), ( 3, 2 ) 
E) no solution 
A) ( 7, 0 ), ( 3, 2 ) 
B) ( 7, 0 ) 
C) ( 3, 2 ) 
D) ( 7, 1 ), ( 3, 2 ) 
E) no solution

Question 9

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.25, and a regular notebook, which sells for $0.9. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 8,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?

Accepted Answer

A) 2,500 deluxe and 5,000 regular 
B) 2,000 deluxe and 6,000 regular 
C) 2,300 deluxe and 5,000 regular 
D) 3,000 deluxe and 5,000 regular 
E) 3,000 deluxe and 6,000 regular 
A) 2,500 deluxe and 5,000 regular 
B) 2,000 deluxe and 6,000 regular 
C) 2,300 deluxe and 5,000 regular 
D) 3,000 deluxe and 5,000 regular 
E) 3,000 deluxe and 6,000 regular

Question 10

Let   be the identity matrix of order 2, and let   . Find the polynomial   for the given matrix A in order to find the zeros of   .
(In the study of matrices,   is the characteristic polynomial of A, and the zeros of   are the characteristic values (eigenvalues) of A.)

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

A manufacturer of cell phones makes a profit of $26 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 240 phones. How many of each type should be produced daily in order to maximize the profit?

Accepted Answer

A) 160 standard and 60 deluxe 
B) 30 standard and 80 deluxe 
C) 80 standard and 160 deluxe 
D) 200 standard and 40 deluxe 
E) 160 standard and 80 deluxe 
A) 160 standard and 60 deluxe 
B) 30 standard and 80 deluxe 
C) 80 standard and 160 deluxe 
D) 200 standard and 40 deluxe 
E) 160 standard and 80 deluxe

Question 12

The data in the table are generated by the function   . Approximate the unknown constants a and b to four decimal places. x
1 2 3 4
F ( x )
0)67654 0.44668 0.29492 0.19472

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

A manufacturer of cell phones makes a profit of $24 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 200 phones. How many of each type should be produced daily in order to maximize the profit?

Accepted Answer

A) 120 standard and 80 deluxe 
B) 60 standard and 140 deluxe 
C) 30 standard and 80 deluxe 
D) 120 standard and 60 deluxe 
E) 160 standard and 40 deluxe 
A) 120 standard and 80 deluxe 
B) 60 standard and 140 deluxe 
C) 30 standard and 80 deluxe 
D) 120 standard and 60 deluxe 
E) 160 standard and 40 deluxe

Question 14

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 15

Use Cramer's rule, whenever possible, to solve the system.

Accepted Answer

A)    
B)    
C)    
D) The equations are dependent. 
E) The system is inconsistent. 
A)    
B)    
C)    
D) The equations are dependent. 
E) The system is inconsistent.

Question 16

Find the partial fraction decomposition.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Accepted Answer

A) maximum of 20 at   
B) maximum of 24 at   
C) maximum of 0 at   
D) maximum of 22 at   
E) maximum of 18 at   
A) maximum of 20 at   
B) maximum of 24 at   
C) maximum of 0 at   
D) maximum of 22 at   
E) maximum of 18 at

Question 18

Solve the system using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent. 
E) The equations are dependent. 
A)    
B)    
C)    
D) The system is inconsistent. 
E) The equations are dependent.

Question 19

Find the values of b such that the system   has no solution.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 20

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Find the determinant of the matrix.

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Solve the system using the inverse method.

Find the determinant of the matrix after introducing zeros.

Find the values of b such that the system has no solution.

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of . (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x 1 2 3 4 F ( x ) 0)67654 0.44668 0.29492 0.19472

Solve the system using the inverse method.

Use Cramer's rule, whenever possible, to solve the system.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Solve the system using the inverse method.

Find the values of b such that the system has no solution.

Solve the system using the inverse method.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Exam 9: Systems of Equations and Inequalities

Find the determinant of the matrix.

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Solve the system using the inverse method.

Find the determinant of the matrix after introducing zeros.

Find the values of b such that the system has no solution.

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of . (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

The data in the table are generated by the function . Approximate the unknown constants a and b to four decimal places. x 1 2 3 4 F ( x ) 0)67654 0.44668 0.29492 0.19472

Solve the system using the inverse method.

Use Cramer's rule, whenever possible, to solve the system.

Find the partial fraction decomposition.

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Solve the system using the inverse method.

Find the values of b such that the system has no solution.

Solve the system using the inverse method.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Find the partial fraction decomposition. $Find the partial fraction decomposition.$