Exam 5: Systems of Equations and Inequalities

Use Linear Programming to Solve Problems 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. -Objective Function: z = -5x - y Find maximum.

Solve the problem. -Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to make a hat and 4 hours to make an afghan, and she has no more than 51 hours available. She has material for no More than 12 items and no more than 10 afghans. The bazaar will sell the hats for $20 each and the afghans For $8 each. How many of each should she make to maximize the income for the bazaar? What is the Maximum income?

Solve the system by the substitution method. - xy=6 +=37

Determine if the given ordered triple is a solution of the system. - (5,4,-3) x-y+z=12 x+y+z=6 x+y-z=-4

Solve the problem. -Ms. Adams received a bonus check for $15,000. She decided to divide the money among three different investments. With some of the money, she purchased a municipal bond paying 5.6% simple interest. She Invested twice the amount she paid for the municipal bond in a certificate of deposit paying 4.7% simple Interest. Ms. Adams placed the balance of the money in a money market account paying 3.2% simple Interest. If Ms. Adams' total interest for one year was $561, how much was placed in each account?

Solve the system of equations by the substitution method. - x+y =-9 y =-4x

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. - $x - 4 y = 3$ $- 5 x + 20 y = - 15$

Solve the problem. -A doctor has told a sick patient to take vitamin pills. The patient needs at least 29 units of vitamin A, at least 7 units of vitamin B, and at least 26 units of vitamin C. The red vitamin pills cost 10¢ each and contain 7 units of A, 1 unit of B, and 2 units of C. The blue vitamin pills cost 20¢ each and contain 4 units of A, 1 Unit of B, and 6 units of C. How many pills should the patient take each day to minimize costs?

Solve the system by the addition method. - -2x-5y=-17 5x-3y=-4

Decompose P/Q, Where Q Has Repeated Linear Factors Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. - $\frac { 8 x ^ { 2 } + 15 x + 2 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$

Decompose P/Q, Where Q Has Only Distinct Linear Factors Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants. 1) $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$ A) $\frac { A } { x + 6 } + \frac { B } { x + 2 }$ B) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }$ C) $\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }$ D) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$ - $\frac { x - 17 } { ( x - 2 ) ( x - 5 ) }$

Graph the inequality. - $x^{2}+y^{2} \leq 1$

Graph the inequality. - $- 2 x - 5 y \leq 10$

Graph the inequality. - $y>3^{x}$

Solve Nonlinear Systems By Addition Solve the system by the addition method. - $x ^ { 2 } - y ^ { 2 } = 25$ $16 x ^ { 2 } + 25 y ^ { 2 } = 400$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 11 inches longer than the width. Find the width.

Solve the problem. -An-Mei owns a business making and selling jackets. She has a fixed cost of $2100. It costs $97 to produce each jacket. The selling price is $118 per jacket. Determine the number of jackets that must be made and Sold in order to break even.

Solve the problem. -Julie and Eric row their boat (at a constant speed)21 miles downstream for 3 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 7 hours. Find the rate of the current.

Solve the problem. -The Little Town Arts Center charges $24 for adults, $12 for senior citizens, and $6 for children under 12 for their live performances on Sunday afternoon. This past Sunday, the paid revenue was $9162 for 683 tickets Sold. There were 43 more children than adults. How many children attended?

Graph the solution set of the system of inequalities or indicate that the system has no solution. -