Graph the equation and state the slope of the line if the slope exists (see Example 9). x = -2
> Appreciation of a House A house initially cost $150,000. The value, V, of the house after n years if it appreciates at a constant rate of 4% per year can be determined by the function V = f(n) = +150,000(1.04)n. (a) Determine f(8) and explain its meaning
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. 3x + 4y - 8 = 0
> Evaluate the function for the given value of x. f (x) = 4x - 1, x = 2
> Are indicated on the graph in Fig. 6.22.Write the coordinates of the indicated point.
> The radicand in the quadratic formula, b2 - 4ac, is called the discriminates. How many real number solutions will the quadratic equation have if the discriminant is (a) greater than 0, (b) equal to 0, or (c) less than zero? Explain your answer.
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. 3x + 2y = 6
> Determine whether the set of ordered pairs is a function. {(4, 2), (4, -3), (4, 5)}
> Determine the area of the triangle.
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. The sum of the areas of the surfaces of a three-dimensional figure is called the figure’s _____________ area. 4. A polyhedron whose bases are congruent polygons and whose sides are pa
> Plot all the points on the same axes. (4.5, 3.5)
> Height of a Rocket A model rocket is launched from a hill 80 feet above sea level. The launch site is next to the ocean, and the rocket wil fall into the ocean. The rocket’s height, h, above sea level can be determined by the equation h = -16t 2 + 64t +
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7.
> Determine whether the set of ordered pairs is a function. {(-1, 2), (-1, 4), (-1, 6),(-1, 9)}
> Graph the equation, using the x- and y-intercepts, as in Example 4. x - y = 3
> Gardner and Walkway CJ’s garden is surrounded by a uniform-width walkway. The garden and walkway together cover an area of 320 square feet. If the dimensions of the garden are 12 feet by 16 feet, determine the width of the walkway.
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. y = 3x - 1
> Determine whether the set of ordered pairs is a function. {(-4, 2), (1, 5), (3, -7), (5, 6)}
> Graph the equation, using the x- and y-intercepts, as in Example 4. x - y = 4
> Solve the equation, using the quadratic formula. If the equation has no real solution, so state. 5x2 - 4x = -2
> (2). The ordered pair or ordered pairs that satisfy all equations in a system of equations is called the _________ to the system of equations. (4). A system of equations that has at least one solution is called a(n) _______ system of equations. (6). If t
> Graph the equation using the slope and y-intercept, as in Examples 6 and 7. y = -x – 2
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Graph the equation by plotting points, as in Example 3.
> Solve the equation, using the quadratic formula. If the equation has no real solution, so state. 4x2 + 7x - 1 = 0
> Determine the slope of the line through the given points. If the slope is undefined, so state. (2, 1) and (-5, -9)
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Graph the equation by plotting points, as in Example 3. 3y = 2x – 3
> Hourly Temperature The following graph indicates the hourly temperature, in degrees Fahrenheit, in Rochester, New York, from 10 a.m. through 8 p.m. on Monday, September 8, 2014. The function t1x2 = -0.48x2 + 5.0x + 64.38 can be used to estimate the hourl
> Determine the slope of the line through the given points. If the slope is undefined, so state. (2, 6) and (2, -3)
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. Since clock 12 arithmetic, under the operation of addition, contains only the elements 51, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 126, the mathematical system is ______ . 4. In clock 12 arith
> Graph the equation by plotting points, as in Example 3. y - 4x = 8
> When solving a system of linear equations by the substitution method, a student obtained the equation 0 = 0 and gave the solution as 10, 02. What is the student’s error?
> Determine the slope of the line through the given points. If the slope is undefined, so state. (-3, -5) and (-1, -2)
> Determine whether the graph represents a function. If it does represent a function, give its domain and range.
> Graph the equation by plotting points, as in Example 3. y = -2x + 3
> Construct a system of two linear equations that has no solution. Explain how you know the system has no solution.
> Determine the slope of the line through the given points. If the slope is undefined, so state. (-2, 6) and (-4, 9)
> 2x2 - 4x + 5 = 0 Solve the equation, using the quadratic formula. If the equation has no real solution, so state.
> Graph the equation by plotting points, as in Example 3. y = x – 2
> Develop a system of linear equations that has 16, 52 as its solution. Explain how you developed your system of equations.
> (2). A binary operation is an operation or rule that can be performed on exactly two elements of a set, with the result being a(n) ______ element. (4). A specific example illustrating that a property is not true is called a(n) _______ . (6). Since the pr
> Determine the slope of the line through the given points. If the slope is undefined, so state. (4, 3) and (3, 4)
> Solve the equation, using the quadratic formula. If the equation has no real solution, so state. x2 = -8x + 15
> Graph the equation and state the slope of the line if the slope exists (see Example 9). y = -4
> Fill in the blank to make a true statement. (66). 1 nanogram = _________ micrograms (68). 1 megagram = _________ nanograms
> Indicate whether the graph shown represents a consistent, inconsistent, or dependent system.
> Graph the equation, using the x- and y-intercepts, as in Example 4. 6x = 3y – 9
> Which of the following inequalities have the same graph? Explain how you determined your answer. (a) 2x - y < 8 (b) -2x + y > -8 (c) 2x - 4y < 16 (d) y > 2x - 8
> Salaries 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 since 2014. The graph at the top o
> Graph the equation, using the x- and y-intercepts, as in Example 4. 2x - y = 4
> Fill in the blanks with an appropriate word, phrase, or symbol(s). 2. Two lines that do not lie in the same plane and do not intersect are called _________ lines. 4. Two angles, the sum of whose measures is 90°, are called _________ angles. 6. An angle w
> 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 testing, and 1 hr in packaging. A stroller requires 3 hr in
> Determine which ordered pairs satisfy the given equation.
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Golf Club Membership Membership in Oakwood Country Club costs $3000 per year and entitles a member to play a round of golf for a g
> Graph the equation, using the x- and y-intercepts, as in Example 4. 3x - y = -6
> 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 vitamin C and 2 units of vitamin D. The minimum daily requ
> Determine which ordered pairs satisfy the given equation. 2x - 3y = 9 (0, -3) (2, 1) (-3, -5)
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Copy Service Jayne recently purchased a high-speed copier for her home office and wants to purchase a service contract on the copi
> Teresa’s five test grades for the semester are 86%, 78%, 68%, 92%, and 72%. Her final exam counts one-third of her final grade. What range of grades on her final exam would result in Teresa receiving a final grade of B in the course? (See Example 9.)
> 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 machines. No more than 5 front load machines can be man
> Determine which ordered pairs satisfy the given equation.
> (2). The name of the system of measurement primarily used in the United States today is the U.S. _________ system. (4). Three advantages of the metric system are that a) It is the worldwide accepted system of _________. b) There is only one base unit of
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Nut and Pretzel Mix Dave wants to purchase 20 pounds of party mix for a total of $30. To obtain the mixture, he will mix nuts that
> The Palm Beach State College Planning Committee wants to rent tents for the spring job fair. Rent-a-Tent charges $325 for setup and delivery of its tents. This fee is charged regardless of the number of tents delivered and set up. In addition, Rent-a-Ten
> The bookstore at St. Petersburg 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 store are $300 for an Apple tablet and $200 for a Samsung
> Determine which ordered pairs satisfy the given equation. 3x - y = -5 (0, 5) (-1, 2) (2, 1)
> Write a system of equations that can be used to solve the problem. Then solve the system and determine the answer. MODELING—Landscaping The Garden Factory purchased 4 tons of topsoil and 3 tons of mulch for $1529. The next week the company purchased 2 to
> The minimum speed for vehicles on a highway is 40 mph, and the maximum speed is 55 mph. If Philip has been driving nonstop along the highway for 4 hr, what range in miles could he have legally traveled?
> Expansion of (a 1 b) 2 In the figure, one side of the largest square has length a + b. Therefore, the area of the largest square is (a + b)2 . Answer the following questions to find a formula for the expansion of (a + b)2. (a) What is the area of the squ
> In Exercises 49–54, part of the question involves determining a system of equations that models the situation. MODELING—Manufacturing Television Stands A manufacturer sells television stands for $125 per stand. The manufacturing costs consist of a fixed
> Are indicated on the graph in Fig. 6.22.Write the coordinates of the indicated point.
> Water Cost In a specific region of the country, the amount of a customer’s water bill, W, is directly proportional to the average daily temperature for the month, T, the lawn area, A, and the square root of F, where F is the family size, and inversely pr
> Fill in the blank with an appropriate word, phrase, or symbol(s). 2. When graphing an inequality in two variables, if the inequality contains either < or > use a(n) ___________line. 4. The set of points that satisfy all inequalities in a system of li
> For a business to realize a profit, its revenue, R, must be greater than its costs, C; that is, a profit will result only if R ( C (the company breaks even when R = C). A dry cleaning store has a weekly cost equation of C = 0.25x + 1500 and a weekly reve
> Plasma Television The screen of a plasma television is in the shape of a rectangle with a diagonal of length 43 in. If the height of the screen is 21 in., determine the width of the screen. Round your answer to the nearest hundredth.
> In Exercises 49–54, part of the question involves determining a system of equations that models the situation. MODELING—Manufacturing Blu-ray Disc Players A manufacturer sells Blu-ray Disc players for $150 per unit. Ma
> Are indicated on the graph in Fig. 6.22.Write the coordinates of the indicated point.
> (a) Assume a varies directly as b2. If b is doubled, how will it affect a? (b) Assume a varies inversely as b2. If b is doubled, how will it affect a?
> The Kubys are celebrating their 75th wedding anniversary by having a party at the Diplomat Party House. They have budgeted $4000 for the party. If the party house charges a flat rate of $100 for set-up and clean-up, plus $30 per person, determine the max
> Docking a Boat Brian is bringing his boat into a dock that is 9 ft above the water level (see figure). If a 41-ft rope is attached to the dock on one side and to the boat on the other side, determine the horizontal distance from the dock to the boat.
> In Exercises 49–54, part of the question involves determining a system of equations that models the situation. MODELING—Landscaping Costs Tom’s Tree and Landscape Service charges $200 for a consultation fee plus $60 per hour for labor, and Lawn Perfect L
> Are indicated on the graph in Fig. 6.22.Write the coordinates of the indicated point.
> (a) If y varies inversely as x and the constant of proportionality is 0.3, does x vary directly or inversely as y? (b) Give the new constant of proportionality as x varies Inversely as y.
> Fill in the blank with an appropriate word, phrase, or symbols(s). 2. To find the x-intercept of the graph of a linear equation, set_________ equal to zero and solve the equation for x. 4. The ratio of the vertical change to the horizontal change for any
> Salary Plans Bobby recently accepted a sales position in Portland, Oregon. He can select between the two salary plans shown in the table. Determine the dollar amount of weekly sales that would result in Bobby earning more with Plan B than with Plan A.
> Quartz Countertops Larry wishes to have three quartz countertops installed in his new kitchen. The countertops are rectangular and have the following dimensions: 3½t ( 6 ft, 2½ft ( 8 ft, and 3 ft ( 11½ ft. The cost of the countertops is $84 per square fo
> 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 maximum and minimum profit. x + 2y ≤ 14 7x + 4y ( 28 x ( 2 x ≤
> Unemployment Rate The following graph shows the unemployment rate in the United States for the years 2005–2013 In which years, from 2005–2013, was the unemployment rate in the United States a) 7 5% b) 6 5.5% c) > 7.
> 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 = 1 4x + 9y = 4
> The number of phone calls between two cities during a given time period, N, varies directly as the populations p1 and p2 of the two cities and inversely to the distance, d, between them. If 100,000 calls are made between two cities 300 mi apart and the p
> Cost of a Lawn Service Jim and Wendy’s home lot is illustrated here. They wish to hire a lawn service to cut their lawn. M&M Lawn Service charges $0.03 per square yard of lawn. How much will it cost them to have their lawn cut?
> 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 maximum and minimum profit. x + y ≤50 x + 3y ≤ 90 x ( 0 y ( 0 P
> Graph the solution set of the inequality, where x is an integer, on the number line.
> 4x + y = 6 -8x - 2y = 13 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.
> Fill in the blanks with an appropriate word, phrase, or symbol(s) 2. Anything of value pledged by the borrower that the lender may sell or keep if the borrower does not repay the loan is called the _____or collateral. 4. When using the simple interest fo
> Guitar Strings The number of vibrations per second, v, of a guitar string varies directly as the square root of the tension, t, and inversely as the length of the string, l. If the number of vibrations per second is 5 when the tension is 225 kg and the l
> Nancy has just purchased a new house that is in need of new flooring. Use the measurements given on the floor plans of Nancy’s house to obtain the answer. Cost of Saxony Carpeting The cost of Saxony carpeting is $7.49 per square foot. T
> 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 maximum and minimum profit. x + 2y ≤ 6 3x + 2y ≤ 12 x ( 0 y ( 0
> -2 ( 2x + 3 ( 6 Graph the solution set of the inequality, where x is an integer, on the number line.
