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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

(a) Do all systems of linear inequalities have solutions? Explain. No(b) Write a system of linear inequalities that has no solution.
A company makes car seats and strollers. Each car seat and stroller passes through three processes: assembly, safety testing, and packaging. A car seat requires 1 hr in assembly, 2 hr in safety
To make one package of all-beef hot dogs, a manufacturer uses 1 lb of beef; to make one package of regular hot dogs, the manufacturer uses 1/2 lb each of beef and pork. The profit on the all-beef hot
A dietitian prepares a special diet using two food groups, A and B. Each ounce of food group A contains 3 units of vitamin C and 1 unit of vitamin D. Each ounce of food group B contains 1 unit of
A paint supplier has two machines that produce both indoor paint and outdoor paint. To meet one of its contractual obligations, the company must produce at least 60 gal of indoor paint and 100 gal of
A company manufactures two types of washers, top load and front load. The company can manufacture a maximum of 18 washers per day. It makes a profit of $20 on top load machines and $25 on front load
The Boards and Blades Company manufactures skateboards and in-line skates. The company can produce a maximum of 20 skateboards and pairs of in-line skates per day. It makes a profit of $25 on a
The bookstore at St. Peters-burg College sells Apple tablets and Samsung tablets. Based on demand, it is necessary to stock at least twice as many Apple tablets as Samsung tablets. The costs to the
Ruben is on a special diet. He must consume fewer than 500 calories at a meal that consists of one serving of chicken and one serving of rice. The meal must contain at least 150 calories from each
A set of constraints and a profit function are given.(a) Graph the constraints and determine the vertices of the feasible region.(b) Use the vertices obtained in part (a) to determine the
A set of constraints and a profit function are given.(a) Graph the constraints and determine the vertices of the feasible region.(b) Use the vertices obtained in part (a) to determine the
A set of constraints and a profit function are given.(a) Graph the constraints and determine the vertices of the feasible region.(b) Use the vertices obtained in part (a) to determine the
A set of constraints and a profit function are given.(a) Graph the constraints and determine the vertices of the feasible region.(b) Use the vertices obtained in part (a) to determine the
A set of constraints and a profit function are given.(a) Graph the constraints and determine the vertices of the feasible region.(b) Use the vertices obtained in part (a) to determine the
A set of constraints and a profit function are given.(a) Graph the constraints and determine the vertices of the feasible region.(b) Use the vertices obtained in part (a) to determine the
A feasible region and its vertices are shown. Determine the maximum and minimum values of the given objective function.K = 40x + 50y (2, 5) (4, 3) 3 (5, 2) (4, 1) (1, 1) 1 2 3 4 5 6 X: 4-
A feasible region and its vertices are shown. Determine the maximum and minimum values of the given objective function.K = 2x + 3y y↑ :60 50 |(10, 40) 40 (50, 30) 30 (10, 20) 20 10 (20, 10) (50,
A feasible region and its vertices are shown. Determine the maximum and minimum values of the given objective function.K =10x + 8y УТ 25 200 (0, 20). (8, 16). (15, 11) 15 10 (20, 0) -> (0, 0)| 5 10
A feasible region and its vertices are shown. Determine the maximum and minimum values of the given objective function.K = 6x + 4y y↑ (0, 4) 40 (2, 3) 3. 1. (5, 0) (0, 0) 1 2 3 4 5 6
Graph the system of linear inequalities and indicate the solution set.x ≤ 0 y ≤ 0
Graph the system of linear inequalities and indicate the solution set.x ≥ 1y ≥ 1
Graph the system of linear inequalities and indicate the solution set.3x - 2y ≥ 6x - y ≤ 3
Graph the system of linear inequalities and indicate the solution set.x + 2y ≤ 43x - y ≥ -6
Graph the system of linear inequalities and indicate the solution set.x + y < 43x + 2y ≥ 6
Graph the system of linear inequalities and indicate the solution set.x - 3y ≤ 3 x + 2y ≥ 4
Graph the system of linear inequalities and indicate the solution set.4x + 3y > 8y ≤ x + 1
Graph the system of linear inequalities and indicate the solution set.y ≤ - x + 5x - y < 3
Graph the system of linear inequalities and indicate the solution set.3x - y ≤ 6y < x - 4
Graph the system of linear inequalities and indicate the solution set.y > x - 4x + y < 5
Draw the graph of the inequality.y ≤ 3x - 4
Draw the graph of the inequality.3x - 2y < 12
Draw the graph of the inequality.y ≥ -2x + 1
Draw the graph of the inequality.5x + 2y ≥ 10
Draw the graph of the inequality.x + 2y ≤ 0
Draw the graph of the inequality.x + y > 0
Draw the graph of the inequality.-x + 2y < 2
Draw the graph of the inequality.3x + 2y < 6
Draw the graph of the inequality.4y - 3x ≥ 8
Draw the graph of the inequality.3x - 4 y ≤ 8
Draw the graph of the inequality.x + 2y > 4
Draw the graph of the inequality.2x - 3y > 6
Draw the graph of the inequality.y < -2x + 2
Draw the graph of the inequality.y ≥ 2x - 6
Draw the graph of the inequality.y < - x - 2
Draw the graph of the inequality.y > x + 1
For each inequality, determine whether (-2, 4) is a solution to the inequality.(a) 4x - 2y < -10(b) 4x - 2y ≤ -10(c) 4x - 2y > -10(d) 4x - 2y ≥ -10
For each inequality, determine whether (2, 1) is a solution to the inequality.(a) 4x + 2y < 0(b) 4x + 2y ≤ 10(c) 4x + 2y ≥ 10(d) 4x + 2y >10
Fill in the blank with an appropriate word, phrase, or symbol(s).The maximum and minimum values of the objective function occur at the _________ of the feasible region.
Fill in the blank with an appropriate word, phrase, or symbol(s).In a linear programming problem, the function used for the quantity that we want to maximize or minimize is called the ________
Fill in the blank with an appropriate word, phrase, or symbol(s).The points of intersection of the boundaries of the feasible region are called _______.
Fill in the blank with an appropriate word, phrase, or symbol(s).In a linear programming problem, the shaded region formed by graphing the system of inequalities is called the __________ region.
Fill in the blank with an appropriate word, phrase, or symbol(s).In a linear programming problem the restrictions that are represented by linear inequalities are called the __________ .
Fill in the blank with an appropriate word, phrase, or symbol(s).The solution set to a system of linear inequalities is the set of all _______ pairs that are common to all the inequalities in the
Fill in the blank with an appropriate word, phrase, or symbol(s).The set of points that satisfy all inequalities in a system of linear inequalities is called the _______ set.
Fill in the blank with an appropriate word, phrase, or symbol(s).When graphing an inequality in two variables, if the inequality contains either ≤ or ≥ use a(n) ______ line.
Fill in the blank with an appropriate word, phrase, or symbol(s).When graphing an inequality in two variables, if the inequality contains either < or > use a(n) ______ line.
Fill in the blank with an appropriate word, phrase, or symbol(s).The set of all points in a plane on one side of a line is called a(n) _______.
In parts (a)–(d), make up a system of linear equations whose solution will be the ordered pair given. (a) (0, 0) (b) (1, 0) (c) (0, 1)
When solving a system of linear equations by the substitution method, a student obtained the equation 0 = 0 and gave the solution as (0, 0). What is the student’s error?
Construct a system of two linear equations that has an infinite number of solutions. Explain how you know the system has an infinite number of solutions.
Construct a system of two linear equations that has no solution. Explain how you know the system has no solution.
The substitution or addition methods can also be used to solve a system of three linear equations in three variables. Consider the following system. x + y + z = 7 x - y + 2z = 9-x + 2y + z
Develop a system of linear equations that has (6, 5) as its solution. Explain how you developed your system of equations.
Solve the following system of equations for u and v by first substituting x for 1/u and y for 1/v.1/u + 2/v = 83/u - 1/v = 3
Indicate whether the graph shown represents a consistent, inconsistent, or dependent system.(a)(b)(c) y. Line 1 х Line 2 y1 -> Line 2 Line 1
(a) If the two lines in a system of equations have different slopes, how many solutions will the system have? (b) If the two lines in a system of equations have the same slope but different
Jose€™s salary can be modeled by the equation y = 39,000 + 1200t, and Charlie€™s salary can be modeled by the equation y = 45,000 + 700t, where t represents the number of years
Car repair costs at Steve€™s Garage can be modeled by the equation C = 200 + 50x, and the repair costs at Greg€™s Garage can be modeled by the equation C = 375 + 25x, where x
Membership in Oakwood Country Club costs $3000 per year and entitles a member to play a round of golf for a greens fee of $18. At Pinecrest Country Club, membership costs $2500 per year and the
The cost to purchase a particular type of hardwood flooring at Home Depot is $2.65 per square foot. In addition, the installation cost is $468.75. The cost to purchase the same flooring at Hardwood
Jayne recently purchased a high-speed copier for her home office and wants to purchase a service contract on the copier. She is considering two sources for the service contract. Ace Office charges
Nathan, a salesperson, is considering two job offers. At Harbor Sales, Nathan’s salary would be $249 per week plus a 15% commission of sales. At Industrial Sales, his salary would be $300 per week
Dave wants to purchase 20 pounds of party mix for a total of $30. To obtain the mixture, he will mix nuts that cost $3 per pound with pretzels that cost $1 per pound. How many pounds of each should
Antonio is a chemist and needs 15 liters (l) of a 25% hydrochloric acid solution. He discovers he is out of the 25% hydrochloric acid solution. He checks his supply shelf and finds he has a large
The Garden Factory purchased 4 tons of topsoil and 3 tons of mulch for $1529. The next week the company purchased 2 tons of topsoil and 5 tons of mulch for $1405. Determine the price per ton for
Jaafar owns a total of 50 shares of stock, some in Under Armour and some in Hershey Company. On a particular day, Under Armour stock closed at $73 per share and Hershey Company stock closed at $85
A manufacturer sells television stands for $125 per stand. The manufacturing costs consist of a fixed cost of $6750 and a production cost of $50 per stand. (a) Write the cost and revenue
SoundsGreat manufactures and sells earbuds. They sell their earbuds for $40 per unit. The manufacturing costs consist of a fixed cost of $4050 and a production cost of $15 per unit. (a) Write
A manufacturer sells Blu-ray Disc players for $150 per unit. Manufacturing costs consist of a fixed cost of $3850 and a production cost of $115 per unit.(a) Write the cost and revenue equations.(b)
Benjamin€™s Backpacks can sell backpacks for $25 per backpack. The costs for making the backpacks are a fixed cost of $400 and a production cost of $15 per backpack.(a) Write the cost and
Tom’s Tree and Landscape Service charges $200 for a consultation fee plus $60 per hour for labor, and Lawn Perfect Landscape Service charges $305 for a consultation fee plus $25 per hour for
The cost of renting a medium-sized truck at U-Haul Rental is $30 per day plus $0.79 a mile. The cost of renting a similar truck at Discount Rentals is $24 per day plus $0.85 a mile. (a) Write a
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 6x + 6y = 14x + 9y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.2x - 4y = 43x - 2y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 4x + y = 6-8x - 2y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 4x - 2y = 64y = 8x -
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 2x + 3y = 65x - 4y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 3x - 5y = -62x + 4y
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 3x - 4y = 11x + 2y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 2x + y = 11x + 3y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. x + 2y = 153x + y = 5
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. 4x + 3y = -12x - y =
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent. x + y = 6-2x +
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.2x - y = -4-3x - y = 6
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.4x + 2y = 23x - 2y = 12
Solve the system of equations by the addition method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.x + y = 43x - y = 8
Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.2x + y = 12x = (-1/2)y
Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.3x + y = 15x = -1/3
Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.x - y = -1y = 2x + 4
Solve the system of equations by the substitution method. If the system does not have a single ordered pair as a solution, state whether the system is inconsistent or dependent.x + 2y = 6y = 2x + 3

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