Get answer: Use the diagrams to find the unknown measures of angles or lengths of sides

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. The perimeter of a square with side length y

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. The perimeter of a rectangle with length x and width x - 5.

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. The sum of three consecutive integers if the first is z.

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. The sum of three consecutive odd integers if the first integer is x.

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. The total amount of money (in cents) in x nickels, 1x + 32 dimes, and 2x quarters. (Hint: The value of a nickel is 5 cents, the value of a dime is 10 cents, and the value of a quarter is 25 cents.)

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. The total amount of money (in cents) in y quarters, 7y dimes, and 12y - 12 nickels. (Use the hint for Exercise 5.)

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. A piece of land along Bayou Liberty is to be fenced and subdivided as shown so that each rectangle has the same dimensions. Express the total amount of fencing needed as an algebraic expression in x.

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. A flooded piece of land near the Mississippi River in New Orleans is to be surveyed and divided into 4 rectangles of equal dimension. Express the total amount of fencing needed as an algebraic expression in x.

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. Write the perimeter of the floor plan shown as an algebraic expression in x.

Write the following as algebraic expressions. Then simplify. See Examples 1 and 2. Write the perimeter of the floor plan shown as an algebraic expression in x.

Solve. For Exercises 11 and 12, the solutions have been started for you. See Example 3. Four times the difference of a number and 2 is the same as 2, increased by four times the number, plus twice the number. Find the number. Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Four times the difference of a number and 2 is the same as 2, increased by four times the number, plus twice the number. Find the number. Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.)

Solve. For Exercises 11 and 12, the solutions have been started for you. See Example 3. Twice the sum of a number and 3 is the same as five times the number, minus 1, minus four times the number. Find the number.

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET A second number is five times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 415, find the numbers.

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET A second number is 6 less than a first number. A third number is twice the first number. If the sum of the three numbers is 306, find the numbers.

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET The United States consists of 2271 million acres of land. Approximately 29% of this land is federally owned. Find the number of acres that are not federally owned. (Source: U.S. General Services Administration)

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET The state of Nevada contains the most federally owned acres of land in the United States. If 90% of the states 70 million acres of land is federally owned, find the number of acres that are not federally owned. (Source: U.S. General Services Administration)

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET In 2010, 8476 earthquakes occurred in the United States. Of these, 91.4% were minor tremors with magnitudes of 3.9 or less on the Richter scale. How many minor earthquakes occurred in the United States in 2010? Round to the nearest whole. (Source: U.S. Geological Survey National Earthquake Information Center)

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET Of the 1543 tornadoes that occurred in the United States during 2010, 27.7% occurred during the month of June. How many tornadoes occurred in the United States during June 2010? Round to the nearest whole. (Source: Storm Prediction Center)

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET In a recent survey, 15% of online shoppers in the United States say that they prefer to do business only with large, well-known retailers. In a group of 1500 online shoppers, how many are willing to do business with any size retailers? (Source: Inc.com)

Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET In 2010, the restaurant industry employed 9% of the U.S. workforce. If there are estimated to be 141 million Americans in the workforce, how many people are employed by the restaurant industry? Round to the nearest tenth of a million. (Source: National Restaurant Association, U.S. Bureau of Labor Statistics)

The following graph is called a circle graph or a pie chart. The circle represents a whole, or in this case, 100%. This particular graph shows the number of minutes per day that people use email at work. Use this graph to answer Exercises 21 through 24. What percent of email users at work spend less than 15 minutes on email per day?

The following graph is called a circle graph or a pie chart. The circle represents a whole, or in this case, 100%. This particular graph shows the number of minutes per day that people use email at work. Use this graph to answer Exercises 21 through 24. Among email users at work, what is the most common time spent on email per day?

The following graph is called a circle graph or a pie chart. The circle represents a whole, or in this case, 100%. This particular graph shows the number of minutes per day that people use email at work. Use this graph to answer Exercises 21 through 24. If it were estimated that a large company has 4633 employees, how many of these would you expect to be using email more than 3 hours per day?

The following graph is called a circle graph or a pie chart. The circle represents a whole, or in this case, 100%. This particular graph shows the number of minutes per day that people use email at work. Use this graph to answer Exercises 21 through 24. If it were estimated that a medium-size company has 250 employees, how many of these would you expect to be using email between 2 and 3 hours per day?

Use the diagrams to find the unknown measures of angles or lengths of sides. Recall that the sum of the angle measures of a triangle is 180. See Example 5. 91

Use the diagrams to find the unknown measures of angles or lengths of sides. Recall that the sum of the angle measures of a triangle is 180. See Example 5. 3x x(x  10)

Use the diagrams to find the unknown measures of angles or lengths of sides. Recall that the sum of the angle measures of a triangle is 180. See Example 5. (4x) m (5x  1) m (5x  3) m Perimeter is 102 meters

Use the diagrams to find the unknown measures of angles or lengths of sides. Recall that the sum of the angle measures of a triangle is 180. See Example 5. (2x) cm (3.5x) cm (3x  7) cm Perimeter is 75 centimeters

Use the diagrams to find the unknown measures of angles or lengths of sides. Recall that the sum of the angle measures of a triangle is 180. See Example 5. (2.5x 9) in. 1.5x in. Perimeter is 99 inches.

Use the diagrams to find the unknown measures of angles or lengths of sides. Recall that the sum of the angle measures of a triangle is 180. See Example 5. (9.2x 3) ft (9.2x 3) ft Perimeter is 324 feet.

Solve. See Example 6. The sum of three consecutive integers is 228. Find the integers.

Solve. See Example 6. The sum of three consecutive odd integers is 327. Find the integers.

Solve. See Example 6. The ZIP codes of three Nevada locationsFallon, Fernley, and Gardnerville Ranchosare three consecutive even integers. If twice the first integer added to the third is 268,222, find each ZIP code.

Solve. See Example 6. During a recent year, the average SAT scores in math for the states of Alabama, Louisiana, and Michigan were 3 consecutive integers. If the sum of the first integer, second integer, and three times the third integer is 2637, find each score.

Solve. See Examples 1 through 6. Many companies predict the growth or decline of various technologies. The following data is based on information from Techcrunchies, a technological information site. Notice that the first table is the predicted increase in the number of Wi-Fi-enabled cell phones (in millions), and the second is the predicted percent increase in the number of Wi-Fi-enabled cell phones in the United States Use the middle column in the table to find the predicted number of Wi-Fi-enabled cell phones for each year.

Solve. See Examples 1 through 6. Many companies predict the growth or decline of various technologies. The following data is based on information from Techcrunchies, a technological information site. Notice that the first table is the predicted increase in the number of Wi-Fi-enabled cell phones (in millions), and the second is the predicted percent increase in the number of Wi-Fi-enabled cell phones in the United States Use the middle column in the table to find the predicted percent increase in the number of Wi-Fi-enabled cell phones for each year.

Solve. The occupations of biomedical engineers, skin care specialists, and physician assistants are among the 10 with the largest growth from 2008 to 2018. The number of physician assistant jobs will grow 7 thousand less than three times the number of biomedical engineer jobs. The number of skin care specialist jobs will grow 9 thousand more than half the number of biomedical engineer jobs. If the total growth of these three jobs is predicted to be 56 thousand, find the predicted growth of each job. (Source: U.S. Department of Labor, Bureau of Labor Statistics)

Solve. The occupations of farmer or rancher, file clerk, and telemarketer are among the 10 jobs with the largest decline from 2008 to 2018. The number of file clerk jobs is predicted to decline 11 thousand more than the number of telemarketer jobs. The number of farmer or rancher jobs is predicted to decline 3 thousand more than twice the number of telemarketer jobs. If the total decline of these three jobs is predicted to be 166 thousand, find the predicted decline of each job. (Source: U.S. Department of Labor, Bureau of Labor Statistics)

Solve. The B767-300ER aircraft has 88 more seats than the B737- 200 aircraft. The F-100 has 32 fewer seats than the B737-200 aircraft. If their total number of seats is 413, find the number of seats for each aircraft. (Source: Air Transport Association of America)

Solve. Cowboy Stadium, home of the Dallas Cowboys of the NFL, seats approximately 9800 more fans than does Candlestick Park, home of the San Francisco 49ers. Soldier Field, home of the Chicago Bears, seats 8700 fewer fans than Candlestick Park. If the total seats in these three stadiums is 211,700, how many seats are in each of the three stadiums?

Solve. A new fax machine was recently purchased for an office in Hopedale for $464.40 including tax. If the tax rate in Hopedale is 8%, find the price of the fax machine before tax.

Solve. A premedical student at a local university was complaining that she had just paid $158.60 for her human anatomy book, including tax. Find the price of the book before taxes if the tax rate at this university is 9%.

Solve. The median compensation for a U.S. university president was $436,000 for the 20082009 academic year. Calculate the salary of a university president who received a 2.3% raise.

Solve. In 2009, the population of Brazil was 191.5 million. This represented a decrease in population of 3.7% from 2000. What was the population of Brazil in 2000? Round to the nearest tenth of a million. (Source: Population Reference Bureau)

Solve. In 2010, the population of Swaziland was 1,200,000 people. From 2010 to 2050, Swazilands population is expected to increase by 50%. Find the expected population of Swaziland in 2050. (Source: Population Reference Bureau)

Solve. Dana, an auto parts supplier headquartered in Toledo, Ohio, recently announced it would be cutting 11,000 jobs worldwide. This is equivalent to 15% of Danas workforce. Find the size of Danas workforce prior to this round of job layoffs. Round to the nearest whole. (Source: Dana Corporation)

Recall that two angles are complements of each other if their sum is 90. Two angles are supplements of each other if their sum is 180. Find the measure of each angle. One angle is three times its supplement increased by 20. Find the measures of the two supplementary angles.

Recall that two angles are complements of each other if their sum is 90. Two angles are supplements of each other if their sum is 180. Find the measure of each angle. One angle is twice its complement increased by 30. Find the measure of the two complementary angles.

Recall that the sum of the angle measures of a triangle is 180. Find the measures of the angles of a triangle if the measure of one angle is twice the measure of a second angle and the third angle measures 3 times the second angle decreased by 12.

Recall that the sum of the angle measures of a triangle is 180. Find the angles of an isoceles triangle whose two base angles are equal and whose third angle is 10 less than three times a base angle

Recall that the sum of the angle measures of a triangle is 180. Two frames are needed with the same perimeter: one frame in the shape of a square and one in the shape of an equilateral triangle. Each side of the triangle is 6 centimeters longer than each side of the square. Find the side lengths of each frame. (An equilateral triangle has sides that are the same length.)

Recall that the sum of the angle measures of a triangle is 180. Two frames are needed with the same perimeter: one frame in the shape of a square and one in the shape of a regular pentagon. Each side of the square is 7 inches longer than each side of the pentagon. Find the side lengths of each frame. (A regular polygon has sides that are the same length.)

The sum of the first and third of three consecutive even integers is 156. Find the three even integers.

The sum of the second and fourth of four consecutive integers is 110. Find the four integers.

Daytona International Speedway in Florida has 37,000 more grandstand seats than twice the number of grandstand seats at Darlington Motor Raceway in South Carolina. Together, these two race tracks seat 220,000 NASCAR fans. How many seats does each race track have? (Source: NASCAR)

For the 20102011 National Hockey League season, the payroll for the San Jose Sharks was $5,986,667 more than that of the Montreal Canadiens. The total payroll for these two teams was $113,103,333. What was the payroll for these two teams for the 20102011 NHL season?

The sum of the populations of the metropolitan regions of New York, Tokyo, and Mexico City is 75.56 million. Use this information and Example 2 in this section to find the population of each metropolitan region. (Source: United Nations Department of Economic and Social Affairs)

The airports in London, Paris, and Frankfurt have a total of 177.1 million annual arrivals and departures. Use this information and Practice 2 in this section to find the number at each airport.

Suppose the perimeter of the triangle in Example 1b in this section is 483 feet. Find the length of each side.

Suppose the perimeter of the trapezoid in Practice 1b in this section is 110 meters. Find the lengths of its sides and bases.

Incandescent, fluorescent, and halogen bulbs are lasting longer today than ever before. On average, the number of bulb hours for a fluorescent bulb is 25 times the number of bulb hours for a halogen bulb. The number of bulb hours for an incandescent bulb is 2500 less than the halogen bulb. If the total number of bulb hours for the three types of bulbs is 105,500, find the number of bulb hours for each type. (Source: Popular Science magazine)

Falkland Islands, Iceland, and Norway are the top three countries that have the greatest Internet penetration rate (percent of population) in the world. Falkland Islands has a 6.8 percent greater penetration rate than Iceland. Norway has a 2.3 percent less penetration rate than Iceland. If the sum of the penetration rates is 284.1, find the Internet penetration rate in each of these countries. (Source: Internet World Stats)

During the 2010 Major League Baseball season, the number of wins for the Milwaukee Brewers, Houston Astros, and Chicago Cubs was three consecutive integers. Of these three teams, the Milwaukee Brewers had the most wins. The Chicago Cubs had the least wins. The total number of wins by these three teams was 228. How many wins did each team have in the 2010 season?

In the 2010 Winter Olympics, Austria won more medals than the Russian Federation, which won more medals than South Korea. If the numbers of medals won by these three countries are three consecutive integers whose sum is 45, find the number of medals won by each. (Source: Vancouver 2010)

The three tallest hospitals in the world are Guys Tower in London, Queen Mary Hospital in Hong Kong, and Galter Pavilion in Chicago. These buildings have a total height of 1320 feet. Guys Tower is 67 feet taller than Galter Pavilion, and the Queen Mary Hospital is 47 feet taller than Galter Pavilion. Find the heights of the three hospitals.

The official manual for traffic signs is the Manual on Uniform Traffic Control Devices published by the Government Printing Office. The rectangular sign below has a length 12 inches more than twice its height. If the perimeter of the sign is 312 inches, find its dimensions.

Find the value of each expression for the given values. See Section 1.3. 4ab - 3bc; a = -5, b = -8, and c = 2

Find the value of each expression for the given values. See Section 1.3. ab + 6bc; a = 0, b = -1, and c = 9

Find the value of each expression for the given values. See Section 1.3. n2 - m2 ; n = -3 and m = -8

Find the value of each expression for the given values. See Section 1.3. 2n2 + 3m2 ; n = -2 and m = 7

Find the value of each expression for the given values. See Section 1.3. P + PRT; P = 3000, R = 0.0325, and T = 2

Find the value of each expression for the given values. See Section 1.3. 1 3 lwh; l = 37.8, w = 5.6, and h = 7.9

For Exercise 36, the percents have a sum of 300%. Is this possible? Why or why not?

In your own words, explain the differences in the tables for Exercises 35 and 36.

Find an angle such that its supplement is equal to 10 times its complement.

Find an angle such that its supplement is equal to twice its complement increased by 50.

The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) "The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) "

The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) Predict the average annual number of cigarettes smoked by an American adult in 2015. To do so, let x = 15 (since 2015 - 2000 = 15) and find y.

The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) Predict the average annual number of cigarettes smoked by an American adult in 2020. To do so, let x = 20 (since 2020 - 2000 = 20) and find y.

The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) Use the result of Exercise 78 to predict the average daily number of cigarettes smoked by an American adult in 2015. Round to the nearest whole. Do you think this number represents the average daily number of cigarettes smoked by an adult? Why or why not?

The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) Determine whether there are three consecutive integers such that their sum is three times the second integer.

The average annual number of cigarettes smoked by an American adult continues to decline. For the years 20002009, the equation y = -94.8x + 2049 approximates this data. Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. (Source: Centers for Disease Control) Determine whether there are two consecutive odd integers such that 7 times the first exceeds 5 times the second by 54.

To break even in a manufacturing business, income or revenue R must equal the cost of production C. Use this information to answer Exercises 83 through 86. The cost C to produce x skateboards is C = 100 + 20x. The skateboards are sold wholesale for $24 each, so revenue R is given by R = 24x. Find how many skateboards the manufacturer needs to produce and sell to break even. (Hint: Set the cost expression equal to the revenue expression and solve for x.)

To break even in a manufacturing business, income or revenue R must equal the cost of production C. Use this information to answer Exercises 83 through 86. The revenue R from selling x computer boards is given by R = 60x, and the cost C of producing them is given by C = 50x + 5000. Find how many boards must be sold to break even. Find how much money is needed to produce the break-even number of boards.

To break even in a manufacturing business, income or revenue R must equal the cost of production C. Use this information to answer Exercises 83 through 86. In your own words, explain what happens if a company makes and sells fewer products than the break-even number.

To break even in a manufacturing business, income or revenue R must equal the cost of production C. Use this information to answer Exercises 83 through 86. In your own words, explain what happens if more products than the break-even number are made and sold.