Truck Scheduling A small company thatmanufactures two models of exercise machines hasan

An ordered pair is a ________ of an inequality in and when the inequality is true after and are substituted for and respectively.

The ________ of an inequality is the collection of all solutions of the inequality.

A ________ of a system of inequalities in and is a point that satisfies each inequality in the system.

A ________ ________ of a system of inequalities in two variables is the region common to the graphs of every inequality in the system.

In Exercises 518, sketch the graph of the inequality. y < 5  x2

In Exercises 518, sketch the graph of the inequality. y2  x < 0

In Exercises 518, sketch the graph of the inequality. x  6

In Exercises 518, sketch the graph of the inequality. x < 4

In Exercises 518, sketch the graph of the inequality. y > 7

In Exercises 518, sketch the graph of the inequality. 10  y

In Exercises 518, sketch the graph of the inequality. y < 2  x

In Exercises 518, sketch the graph of the inequality. y > 4x  3

In Exercises 518, sketch the graph of the inequality. 2y  x  4

In Exercises 518, sketch the graph of the inequality. 5x  3y  15

In Exercises 518, sketch the graph of the inequality. x  12  y  22 < 9

In Exercises 518, sketch the graph of the inequality. x  12   y  42 > 9

In Exercises 518, sketch the graph of the inequality. y  1 1  x2

In Exercises 518, sketch the graph of the inequality. y > 15 x2  x  4

In Exercises 1928, use a graphing utility to graph the inequality. y < ln x

In Exercises 1928, use a graphing utility to graph the inequality. y  2  lnx  3

In Exercises 1928, use a graphing utility to graph the inequality. y < 4x5

In Exercises 1928, use a graphing utility to graph the inequality. y  22x0.5  7

In Exercises 1928, use a graphing utility to graph the inequality. y  6  y < 3.8x  1.1 32 x

In Exercises 1928, use a graphing utility to graph the inequality. y < 3.8x  1.1

In Exercises 1928, use a graphing utility to graph the inequality. x2  5y  10  0

In Exercises 1928, use a graphing utility to graph the inequality. 2x2  y  3 > 0

In Exercises 1928, use a graphing utility to graph the inequality. 145 2 y  3x2  6  0

In Exercises 1928, use a graphing utility to graph the inequality. 1 10 x2  38 y < 145

In Exercises 2932, write an inequality for the shaded region shown in the figure.

In Exercises 2932, write an inequality for the shaded region shown in the figure.

In Exercises 2932, write an inequality for the shaded region shown in the figure.

In Exercises 2932, write an inequality for the shaded region shown in the figure.

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities.  x  y  1 x  y  1 y  0

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. 3x x  4y y < > > 12 0 0

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x2  y x y    7 2 0

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. 4x2  y x y  2  1  1

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. 2x  y > 2 6x  3y < 2

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x  7y > 5x  2y > 6x  5y > 36 5 6

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. 5x  3y > 9 3x x 2x  2y <  4y >  y < 6 2 3

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities.  x  2y < 6  5x  3y > 9

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x > y2 x < y  2

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x  y2 > 0 x  y > 2

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x2  y2  36 x2  y2  9

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x2 4x   y2 3y  25  0

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. 3x  4  x  y < y2 0

In Exercises 3346, sketch the graph (and label the vertices) of the solution set of the system of inequalities. x < 2y  y2 0 < x  y

In Exercises 4752, use a graphing utility to graph the solution set of the system of inequalities. y  3x  1 y  x2  1

In Exercises 4752, use a graphing utility to graph the solution set of the system of inequalities. y < y > x2  2x  3 x2  4x  3

In Exercises 4752, use a graphing utility to graph the solution set of the system of inequalities.  y  1  x2 y < x3  2x  1 y > 2x x  1

In Exercises 4752, use a graphing utility to graph the solution set of the system of inequalities. y  x4  2x2  1  y  1  x2

In Exercises 4752, use a graphing utility to graph the solution set of the system of inequalities. x2y  1 0 < x  4 y  4

In Exercises 4752, use a graphing utility to graph the solution set of the system of inequalities.  y  y  2  ex 22 0 x  2

In Exercises 5360, write a system of inequalities to describe the region.

In Exercises 5360, write a system of inequalities to describe the region.

In Exercises 5360, write a system of inequalities to describe the region.

In Exercises 5360, write a system of inequalities to describe the region.

In Exercises 5360, write a system of inequalities to describe the region. Rectangle: vertices at 4, 3, 9, 3, 9, 9, 4, 9

In Exercises 5360, write a system of inequalities to describe the region. Parallelogram: vertices at 0, 0, 4, 0, 1, 4, 5, 4

In Exercises 5360, write a system of inequalities to describe the region. Triangle: vertices at 0, 0, 6, 0, 1, 5

In Exercises 5360, write a system of inequalities to describe the region. Triangle: vertices at 1, 0, 1, 0, 0, 1

In Exercises 6164, (a) graph the systems representing the consumer surplus and producer surplus for the supply and demand equations and (b) find the consumer surplus and producer surplus. p  50  0.5x p  0.125x

In Exercises 6164, (a) graph the systems representing the consumer surplus and producer surplus for the supply and demand equations and (b) find the consumer surplus and producer surplus. p  100  0.05x p  25  0.1x

In Exercises 6164, (a) graph the systems representing the consumer surplus and producer surplus for the supply and demand equations and (b) find the consumer surplus and producer surplus. p  140  0.00002x p  80  0.00001x

In Exercises 6164, (a) graph the systems representing the consumer surplus and producer surplus for the supply and demand equations and (b) find the consumer surplus and producer surplus. p  400  0.0002x p  225  0.0005x

Production A furniture company produces tables and chairs. Each table requires 1 hour in the assembly center and hours in the finishing center. Each chair requires hours in the assembly center and hours in the finishing center. The assembly center is available 12 hours per day, and the finishing center is available 15 hours per day. Find and graph a system of inequalities describing all possible production levels.

Inventory A store sells two models of laptop computers. Because of the demand, the store stocks at least twice as many units of model A as of model B. The costs to the store for the two models are $800 and $1200, respectively. The management does not want more than $20,000 in computer inventory at any one time, and it wants at least four model A laptop computers and two model B laptop computers in inventory at all times. Find and graph a system of inequalities describing all possible inventory levels.

Investment Analysis A person plans to invest up to $20,000 in two different interest-bearing accounts. Each account is to contain at least $5000. Moreover, the amount in one account should be at least twice the amount in the other account. Find and graph a system of inequalities to describe the various amounts that can be deposited in each account.

Ticket Sales For a concert event, there are $30 reserved seat tickets and $20 general admission tickets. There are 2000 reserved seats available, and fire regulations limit the number of paid ticket holders to 3000. The promoter must take in at least $75,000 in ticket sales. Find and graph a system of inequalities describing the different numbers of tickets that can be sold.

Truck Scheduling A small company that manufactures two models of exercise machines has an order for 15 units of the standard model and 16 units of the deluxe model. The company has trucks of two different sizes that can haul the products, as shown in the table. Find and graph a system of inequalities describing the numbers of trucks of each size that are needed to deliver the order.

A dietitian designs a special dietary supplement using two different foods. Each ounce of food X contains 20 units of calcium, 15 units of iron, and 10 units of vitamin B. Each ounce of food Y contains 10 units of calcium, 10 units of iron, and 20 units of vitamin B. The minimum daily requirements of the diet are 300 units of calcium, 150 units of iron, and 200 units of vitamin B. (a) Write a system of inequalities describing the different amounts of food X and food Y that can be used. (b) Sketch a graph of the region corresponding to the system in part (a). (c) Find two solutions of the system and interpret their meanings in the context of the problem.

Health A persons maximum heart rate is where is the persons age in years for The American Heart Association recommends that when a person exercises, the person should strive for a heart rate that is at least 50% of the maximum and at most 85% of the maximum. (Source: American Heart Association) (a) Write a system of inequalities that describes the exercise target heart rate region. (b) Sketch a graph of the region in part (a). (c) Find two solutions to the system and interpret their meanings in the context of the problem.

Physical Fitness Facility An indoor running track is to be constructed with a space for exercise equipment inside the track (see figure). The track must be at least 125 meters long, and the exercise space must have an area of at least 500 square meters. (a) Find a system of inequalities describing the requirements of the facility. (b) Graph the system from part (a).

In Exercises 73 and 74, determine whether the statement is true or false. Justify your answer. The area of the figure defined by the system is 99 square units.

In Exercises 73 and 74, determine whether the statement is true or false. Justify your answer. The following graph shows the solution of the system

Think About It After graphing the boundary of the inequality explain how you decide on which side of the boundary the solution set of the inequality lies.

HOW DO YOU SEE IT? Match the system of inequalities with the graph of its solution. [The graphs are labeled (i), (ii), (iii), and (iv).]

Graphical Reasoning Two concentric circles have radii and where The area between the circles is at least 10 square units. (a) Find a system of inequalities describing the constraints on the circles. (b) Use a graphing utility to graph the system of inequalities in part (a). Graph the line in the same viewing window. (c) Identify the graph of the line in relation to the boundary of the inequality. Explain its meaning in the context of the problem.

Changing the Inequality Symbol The graph of the solution of the inequality is shown in the figure. Describe how the solution set would change for each of the following. (a) (b) 2 4 2 4 6 2 6 x y x  2y  6 x  2y > 6