Exam 8: Systems of Equations and Inequalities

Verify that the values of the variables listed are solutions of the system of equations. - x = -4, y = 5

Encode or decode the given message, as requested, numbering the letters of the alphabet 1 through 26 in their usual order. -Use the coding matrix and its inverse A to decode the cryptogram

Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. -

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -

Write the word or phrase that best completes each statement or answers the question. -A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How muchof each type of tea should be used?

Write the partial fraction decomposition of the rational expression. -

Write the partial fraction decomposition of the rational expression. -

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -

Write the word or phrase that best completes each statement or answers the question. -A company manufactures three types of wooden chairs at two different locations. In one week, the mainlocation produces 18 Kitui chairs, 12 Goa chairs, and 6 Santa Fe chairs while the secondary locationproduces 10 Kitui chairs, 3 Goa chairs, and 5 Santa Fe chairs.(a)Find a 2 by 3 matrix representing the above data.(b)If each Kitui chair requires 25 board-feet of wood, a Goa chair requires 29 board-feet of wood, and aSanta Fe requires 30 board-feet of wood, find a 3 by 1 matrix representing the amount of material.(c)Multiply the 2 by 3 matrix found in part a and the 3 by 1 matrix found in part b to get a 2 by 1 matrixshowing the weekʹs usage of material at both locations.

Each matrix is nonsingular. Find the inverse of the matrix. Be sure to check your answer. -

Write the word or phrase that best completes each statement or answers the question. -An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feetwide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written onthem and the artist wants the words to all be horizontal in the final mosaic. The word tiles come in twosizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each shouldbe used to minimize the cost? What is the minimum cost?

Find the maximum or minimum value of the given objective function of a linear programming problem. The figure illustrates the graph of the feasible points. -z = 2x + 3y. Find maximum and minimum.

Write the word or phrase that best completes each statement or answers the question. -Ericʹs Carpentry manufactures two types of bookshelves that are 4 feet tall and 3 feet wide, a basic modeland a deluxe model. Each basic bookshelf requires 1.5 hours for assembly and 1 hour for finishing; eachdeluxe model requires 2.5 hours for assembly and 1 hour for finishing. Two assemblers and one finisherare employed by the company, and each works 40 hours per week. Eric can sell more basic models thandeluxe models, so he wants the number of basic models produced to be 50% more than the number ofdeluxe models produced. If he makes $50 profit on the basic models and $65 profit on the deluxe models,how many should he make to maximize the profit? What is the maximum profit?

Write the word or phrase that best completes each statement or answers the question. -The difference of two numbers is 5 and the difference of their squares is 55. Find the numbers.

Solve the system of equations using substitution. -

Solve the system of equations by substitution. -

Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. -

Write the word or phrase that best completes each statement or answers the question. -There were approximately 100 vehicles sold at a particular dealership last month. The dealer tracks salesby age group for marketing purposes. The number of 36- to 59-year-old buyers and the number of buyers60 and older combined exceeds the number of buyers 35 and younger by 34. If the number of buyers in theoldest group is doubled, it is 37 less than the number of users in the middle group. Find the number ofbuyers in each of the three age groups.

Write the augmented matrix for the system. -

Graph the system of inequalities. -