Exam 8: Systems of Equations and Inequalities

Solve Problems Using Systems in Three Variables -A ceramics workshop makes serving bowls, platters, and bread baskets to sell at its Winter Festival. A serving bowl takes 3 hours to prepare, 2 hours to paint, and 8 hours to fire. A platter takes 15 hours to prepare, 3 hours to paint, and 4 hours to fire. A bread basket takes 4 hours to prepare, 16 hours to paint, and 7 hours to fire. If the workshop has 92 hours for prep time, 60 hours for painting, and 94 hours for firing, how many of each can be made?

Write the partial fraction decomposition of the rational expression. - $\frac { x - 3 } { ( x - 5 ) ( x - 4 ) }$

Solve Nonlinear Systems By Substitution - $x + y = 7$ $x ^ { 2 } + y ^ { 2 } = - 16 y + 109$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - x+y\leq5 y\geq2x-3 x\geq0 y\geq0

Use Linear Programming to Solve Problems -Objective Function Constraints $z = 7 x + 6 y$ x\geq0 y\geq0 3x+y\leq21 x+y\leq10 x+2y\geq12

Graph the solution set of the system of inequalities or indicate that the system has no solution. - y>-1 x\geq-4

Use Linear Programming to Solve Problems -Objective Function z=3x+5y x\geq0 y\geq0 2x+y\leq15 x-3y\geq-3 Constraints

Decompose P/Q, Where Q Has a Nonrepeated Prime Quadratic Factor - $\frac { 6 x + 4 } { ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) }$

Solve Systems of Linear Equations in Three Variables - x-y+3z=13 5x+z=5 x+2y+z=9

Write the word or phrase that best completes each statement or answers the question. -The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin $\mathrm { A }$ , and 90 units of vitamin C daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin $A$ , and 10 units of vitamin $C$ . $A$ cup of dietary drink $Y$ provides 60 calories, 6 units of vitamin $A$ , and 30 units of vitamin $C$ . Set up a system of linear inequalities that describes the minimum daily requirements for calories and vitamins. Let $x =$ number of cups of dietary drink $X$ , and $y =$ number of cups of dietary drink $Y$ . Write all the constraints as a system of linear inequalities.

Solve Problems Using Systems of Linear Equations -As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers are willing to produce greater quantities of the product. The weekly supply and demand models for a certain type of television are as follows: Demand: $\mathrm { N } = - 4 p + 690$ Supply: $N = 2.6 \mathrm { p }$ where $p$ is the price in dollars per television. How many of these televisions can be sold and supplied at $\$ 120$ per television?

Write the word or phrase that best completes each statement or answers the question. -Eric's Carpentry manufactures two types of bookshelves that are 4 feet tall and 3 feet wide, a basic model and a deluxe model. Each basic bookshelf requires 1.5 hours for assembly and 1 hour for finishing; each deluxe model requires 2.5 hours for assembly and 1 hour for finishing. Two assemblers and one finisher are employed by the company, and each works 40 hours per week. Eric can sell more basic models than deluxe models, so he wants the number of basic models produced to be 50% more than the number of deluxe 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?

Systems of Linear Equations in Three Variables 1 Verify the Solution of a System of Linear Equations in Three Variables - (-2,1,-3) x+4y+5z=-13 2y+2z=-4 z=-3

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - x+6y=3 5x+30y=15

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - $y = \frac { 1 } { 2 } x + 3$ $x - 2 y = - 6$

Write the partial fraction decomposition of the rational expression. - $\frac { 6 x ^ { 2 } - x - 11 } { x ^ { 3 } - x }$

Solve Nonlinear Systems By Substitution - 12+8=72 y=x+3

Solve Nonlinear Systems By Substitution - $x ^ { 2 } + y ^ { 2 } = 25$ $x - y = 1$

Graph the solution set of the system of inequalities or indicate that the system has no solution. - -3x+y>3 -3x+y<-1

Graph a Nonlinear Inequality in Two Variables - $( x - 3 ) ^ { 2 } + ( y - 5 ) ^ { 2 } > 4$