Suppose that an open box is to be made from a square sheet

Solve. See Example 1. 2x = 210 + 3x

Solve. See Example 1. 3x = 28x + 1

Solve. See Example 1. x - 22x = 8

Solve. See Example 1. x - 22x = 4

Solve. See Example 1. 29x = x + 2

Solve. See Example 1. 216x = x + 3

Solve. See Example 2. 2 x + 3 x - 1 = 1

Solve. See Example 2. 6 x2 = 3 x + 1

Solve. See Example 2. 3 x + 4 x + 2 = 2

Solve. See Example 2. 5 x - 2 + 4 x + 2 = 1

Solve. See Example 2. 7 x2 - 5x + 6 = 2x x - 3 - x x - 2

Solve. See Example 2. 11 2x2 + x - 15 = 5 2x - 5 - x x + 3

Solve. See Example 3. p4 - 16 = 0

Solve. See Example 3. x4 + 2x2 - 3 = 0

Solve. See Example 3. 4x4 + 11x2 = 3

Solve. See Example 3. z4 = 81

Solve. See Example 3. z4 - 13z2 + 36 = 0

Solve. See Example 3. 9x4 + 5x2 - 4 = 0

Solve. See Examples 4 and 5 x2/3 - 3x1/3 - 10 = 0

Solve. See Examples 4 and 5 x2/3 + 2x1/3 + 1 = 0

Solve. See Examples 4 and 5 15n + 122 + 215n + 12 - 3 = 0

Solve. See Examples 4 and 5 1m - 622 + 51m - 62 + 4 = 0

Solve. See Examples 4 and 5 2x2/3 - 5x1/3 = 3

Solve. See Examples 4 and 5 3x2/3 + 11x1/3 = 4

Solve. See Examples 4 and 5 1 + 2 3t - 2 = 8 13t - 222

Solve. See Examples 4 and 5 2 - 7 x + 6 = 15 1x + 622

Solve. See Examples 4 and 5 20x2/3 - 6x1/3 - 2 = 0

Solve. See Examples 4 and 5 4x2/3 + 16x1/3 = -15

Solve. See Examples 1 through 5. a4 - 5a2 + 6 = 0

Solve. See Examples 1 through 5. x4 - 12x2 + 11 = 0

Solve. See Examples 1 through 5. 2x x - 2 + x x + 3 = - 5 x + 3

Solve. See Examples 1 through 5. 5 x - 3 + x x + 3 = 19 x2 - 9

Solve. See Examples 1 through 5. 1p + 222 = 91p + 22 - 20

Solve. See Examples 1 through 5. 214m - 322 - 914m - 32 = 5

Solve. See Examples 1 through 5. 2x = 211x + 3

Solve. See Examples 1 through 5. 4x = 22x + 3

Solve. See Examples 1 through 5. x2/3 - 8x1/3 + 15 = 0

Solve. See Examples 1 through 5. x2/3 - 2x1/3 - 8 = 0

Solve. See Examples 1 through 5. y3 + 9y - y2 - 9 = 0

Solve. See Examples 1 through 5. x3 + x - 3x2 - 3 = 0

Solve. See Examples 1 through 5. 2x2/3 + 3x1/3 - 2 = 0

Solve. See Examples 1 through 5. 6x2/3 - 25x1/3 - 25 = 0

Solve. See Examples 1 through 5. x-2 - x-1 - 6 = 0

Solve. See Examples 1 through 5. y-2 - 8y-1 + 7 = 0

Solve. See Examples 1 through 5. x - 2x = 2

Solve. See Examples 1 through 5. x - 23x = 6

Solve. See Examples 1 through 5. x x - 1 + 1 x + 1 = 2 x2 - 1

Solve. See Examples 1 through 5. x x - 5 + 5 x + 5 = - 1 x2 - 25

Solve. See Examples 1 through 5. p4 - p2 - 20 = 0

Solve. See Examples 1 through 5. x4 - 10x2 + 9 = 0

Solve. See Examples 1 through 5. 1x + 321x2 - 3x + 92 = 0

Solve. See Examples 1 through 5. 1x - 621x2 + 6x + 362 = 0

Solve. See Examples 1 through 5. 1 = 4 x - 7 + 5 1x - 722

Solve. See Examples 1 through 5. 3 + 1 2p + 4 = 10 12p + 422

Solve. See Examples 1 through 5. 27y4 + 15y2 = 2

Solve. See Examples 1 through 5. 8z4 + 14z2 = -5

Solve. See Examples 1 through 5. x - 219 - 2x - 2 = 0

Solve. See Examples 1 through 5. x - 217 - 4x - 3 = 0

Solve. For Exercises 59 and 60, the solutions have been started for you. See Examples 6 and 7. Roma Sherry drove 330 miles from her hometown to Tucson. During her return trip, she was able to increase her speed by 11 miles per hour. If her return trip took 1 hour less time, find her original speed and her speed returning home. Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. Let x = original speed x + 11 = return@trip speed Organize the information in a table. 2. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: 3. SOLVE and 4. INTERPRET

Solve. For Exercises 59 and 60, the solutions have been started for you. See Examples 6 and 7. A salesperson drove to Portland, a distance of 300 miles. During the last 80 miles of his trip, heavy rainfall forced him to decrease his speed by 15 miles per hour. If his total driving time was 6 hours, find his original speed and his speed during the rainfall. Start the solution: 1. UNDERSTAND the problem. Reread it as many times as needed. Let x = original speed x - 15 = rainfall speed Organize the information in a table. 2. TRANSLATE into an equation. (Fill in the blanks below.) 3. SOLVE and 4. INTERPRET

A jogger ran 3 miles, decreased her speed by 1 mile per hour, and then ran another 4 miles. If her total time jogging was 1 3 5 hours, find her speed for each part of her run.

Mark Keatons workout consists of jogging for 3 miles and then riding his bike for 5 miles at a speed 4 miles per hour faster than he jogs. If his total workout time is 1 hour, find his jogging speed and his biking speed.

A Chinese restaurant in Mandeville, Louisiana, has a large goldfish pond around the restaurant. Suppose that an inlet pipe and a hose together can fill the pond in 8 hours. The inlet pipe alone can complete the job in one hour less time than the hose alone. Find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone. Round each to the nearest tenth of an hour.

A water tank on a farm in Flatonia, Texas, can be filled with a large inlet pipe and a small inlet pipe in 3 hours. The large inlet pipe alone can fill the tank in 2 hours less time than the small inlet pipe alone. Find the time to the nearest tenth of an hour each pipe can fill the tank alone.

Bill Shaughnessy and his son Billy can clean the house together in 4 hours. When the son works alone, it takes him an hour longer to clean than it takes his dad alone. Find how long to the nearest tenth of an hour it takes the son to clean alone.

Together, Noodles and Freckles eat a 50-pound bag of dog food in 30 days. Noodles by himself eats a 50-pound bag in 2 weeks less time than Freckles does by himself. How many days to the nearest whole day would a 50-pound bag of dog food last Freckles?

The product of a number and 4 less than the number is 96. Find the number.

A whole number increased by its square is two more than twice itself. Find the number.

Suppose that an open box is to be made from a square sheet of cardboard by cutting out squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 300 cubic inches, find the original dimensions of the sheet of cardboard. a. The ? in the drawing above will be the length (and the width) of the box as shown. Represent this length in terms of x. b. Use the formula for volume of a box, V = l # w # h, to write an equation in x. c. Solve the equation for x and give the dimensions of the sheet of cardboard. Check your solution.

Suppose that an open box is to be made from a square sheet of cardboard by cutting out squares from each corner as shown and then folding along the dotted lines. If the box is to have a volume of 128 cubic inches, find the original dimensions of the sheet of cardboard. a. The ? in the drawing above will be the length (and the width) of the box as shown. Represent this length in terms of x. b. Use the formula for volume of a box, V = l # w # h, to write an equation in x. c. Solve the equation for x and give the dimensions of the sheet of cardboard. Check your solution.

A sprinkler that sprays water in a circular pattern is to be used to water a square garden. If the area of the garden is 920 square feet, find the smallest whole number radius that the sprinkler can be adjusted to so that the entire garden is watered.

Suppose that a square field has an area of 6270 square feet. See Exercise 71 and find a new sprinkler radius.

Solve each inequality. See Section 2.4. 5x 3 + 2 7

Solve each inequality. See Section 2.4. 2x 3 + 1 6 2

Solve each inequality. See Section 2.4. y - 1 15 7 - 2 5

Solve each inequality. See Section 2.4. z - 2 12 6 1 4

Find the domain and range of each graphed relation. Decide which relations are also functions. See Section 3.2. 2 4 2 5 1 4 1 3 3 5 5 3 4 1 321 2 4 5 x y 78. 2 4

Find the domain and range of each graphed relation. Decide which relations are also functions. See Section 3.2. 1 3 3 5

Find the domain and range of each graphed relation. Decide which relations are also functions. See Section 3.2. 5 5 3 4 1 3

Find the domain and range of each graphed relation. Decide which relations are also functions. See Section 3.2. 1 4 1 3 3 5 5

Solve. 5y3 + 45y - 5y2 - 45 = 0

Solve. 10x3 + 10x - 30x2 - 30 = 0

Solve. 3x-2 - 3x-1 - 18 = 0

Solve. 2y-2 - 16y-1 + 14 = 0

Solve. 2x3 = -54

Solve. y3 - 216 = 0

Write a polynomial equation that has three solutions: 2, 5, and -7

Write a polynomial equation that has three solutions: 0, 2i, and -2i.

During the seventh stage of the 2010 ParisNice bicycle race, Thomas Voeckler posted the fastest average speed, but Alberto Contador won the race. The seventh stage was 119 kilometers long. Voecklers average speed was 0.0034 meters per second faster than Contadors. Traveling at these average speeds, Contador took 3 seconds longer than Voeckler to complete the race stage. (Source: Based on data from cyclingnews.com) a. Find Thomas Voecklers average speed during the seventh stage of the 2010 ParisNice cycle race. Round to three decimal places. b. Find Alberto Contadors average speed during the seventh stage of the 2010 ParisNice cycle race. Round to three decimal places. c. Convert Voecklers average speed to miles per hour. Round to three decimal places.

Use a graphing calculator to solve Exercise 29. Compare the solution with the solution from Exercise 29. Explain any differences.