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Problem 1E:

Give an example of each of the following: (a) A natural number (b) An integer that is not a natural...

Problem 2E:

Complete each statement and name the property of real numbers you have used. (a) ab = __________;...

Problem 3E:

Express the set of real numbers between but not including 2 and 7 as follows. (a) In set-builder...

Problem 4E:

The symbol | x | stands for the __________of the number x. If x is not 0, then the sign of | x | is...

Problem 5E:

The distance between a and b on the real line is d(a, b) = __________. So the distance between 5 and...

Problem 6E:

Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 6. (a) Is the sum of...

Problem 7E:

Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 7. (a) Is a b equal...

Problem 8E:

Yes or No? If No, give a reason. Assume that a and b are nonzero real numbers. 8. (a) Is the...

Problem 9E:

Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c)...

Problem 10E:

Real Numbers List the elements of the given set that are (a) natural numbers (b) integers (c)...

Problem 11E:

Properties of Real Numbers State the property of real numbers being used. 11. 3 + 7 = 7 + 3

Problem 12E:

Properties of Real Numbers State the property of real numbers being used. 12. 4(2 + 3) = (2 + 3)4

Problem 13E:

Properties of Real Numbers State the property of real numbers being used. 13. (x + 2y) + 3z = x +...

Problem 14E:

Properties of Real Numbers State the property of real numbers being used. 14. 2(A + B) = 2A + 2B

Problem 15E:

Properties of Real Numbers State the property of real numbers being used. 15. (5x + 1)3 = 15x + 3

Problem 16E:

Properties of Real Numbers State the property of real numbers being used. 16. (x + a)(x + b) = (x +...

Problem 17E:

Properties of Real Numbers State the property of real numbers being used. 17. 2x(3 + y) = (3 + y)2x

Problem 18E:

Properties of Real Numbers State the property of real numbers being used. 18. 7(a + b + c) = 7(a +...

Problem 19E:

Properties of Real Numbers Rewrite the expression using the given property of real numbers. 19....

Problem 20E:

Properties of Real Numbers Rewrite the expression using the given property of real numbers. 20....

Problem 21E:

Properties of Real Numbers Rewrite the expression using the given property of real numbers. 21....

Problem 22E:

Properties of Real Numbers Rewrite the expression using the given property of real numbers. 22....

Problem 23E:

Properties of Real Numbers Use properties of real numbers to write the expression without...

Problem 24E:

Properties of Real Numbers Use properties of real numbers to write the expression without...

Problem 25E:

Properties of Real Numbers Use properties of real numbers to write the expression without...

Problem 26E:

Properties of Real Numbers Use properties of real numbers to write the expression without...

Problem 27E:

Properties of Real Numbers Use properties of real numbers to write the expression without...

Problem 28E:

Properties of Real Numbers Use properties of real numbers to write the expression without...

Problem 31E:

Arithmetic Operations Perform the indicated operations. 31. (a) 23(632) (b) (3+14)(145)

Problem 32E:

Arithmetic Operations Perform the indicated operations. 32. (a) 223322 (b) 25+12110+315

Problem 33E:

Inequalities Place the correct symbol (, , or =) in the space. 33. (a) 372 (b) 372 (c) 3.572

Problem 34E:

Inequalities Place the correct symbol (, , or =) in the space. 34. (a) 230.67 (b) 230.67 (c)...

Problem 36E:

Inequalities State whether each inequality is true or false. 36. (a) 31.7325 (b) 1.73253

Problem 39E:

(a) x is positive. (b) t is less than 4. (c) a is greater than or equal to . (d) x is less than 13...

Problem 40E:

(a) y is negative. (b) z is greater than 1. (c) b is at most 8. (d) w is positive and is less than...

Problem 44E:

Sets Find the indicated set if A=1,2,3,4,5,6,7B=2,4,6,8C=7,8,9,10 44. (a) A B C (b) A B C

Problem 47E:

Intervals Express the interval in terms of inequalities, and then graph the interval. 47. (3, 0)

Problem 48E:

Intervals Express the interval in terms of inequalities, and then graph the interval. 48. (2, 8]

Problem 49E:

Intervals Express the interval in terms of inequalities, and then graph the interval. 49. [2, 8)

Problem 50E:

Intervals Express the interval in terms of inequalities, and then graph the interval. 50. [6,12]

Problem 51E:

Intervals Express the interval in terms of inequalities, and then graph the interval. 51. [2, )

Problem 52E:

Intervals Express the interval in terms of inequalities, and then graph the interval. 52. (, 1)

Problem 53E:

Intervals Express the inequality in interval notation, and then graph the corresponding interval....

Problem 54E:

Intervals Express the inequality in interval notation, and then graph the corresponding interval....

Problem 55E:

Intervals Express the inequality in interval notation, and then graph the corresponding interval....

Problem 56E:

Intervals Express the inequality in interval notation, and then graph the corresponding interval....

Problem 57E:

Intervals Express the inequality in interval notation, and then graph the corresponding interval....

Problem 58E:

Intervals Express the inequality in interval notation, and then graph the corresponding interval....

Problem 61E:

Intervals Graph the set. 61. (2, 0) (1, 1)

Problem 62E:

Intervals Graph the set. 62. (2, 0) (1, 1)

Problem 63E:

Intervals Graph the set. 63. [4, 6] [0, 8)

Problem 64E:

Intervals Graph the set. 64. [4, 6) [0, 8)

Problem 65E:

Intervals Graph the set. 65. (, 4) (4, )

Problem 66E:

Intervals Graph the set. 66. (, 6] (2, 10)

Problem 75E:

Distance Find the distance between the given numbers. 75. (a) 2 and 17 (b) 3 and 21 (c) 118and310

Problem 76E:

(a) 715and121 (b) 38 and 57 (c) 2.6 and 1.8

Problem 77E:

Repeating Decimal Express each repeating decimal as a fraction. (See the margin note on page 3.) 77....

Problem 78E:

Repeating Decimal Express each repeating decimal as a fraction. (See the margin note on page 3.) 78....

Problem 81E:

Simplifying Absolute Value Express the quantity without using absolute value. 81. |a b|, where a b

Problem 82E:

Simplifying Absolute Value Express the quantity without using absolute value. 82. a + b + |a b |,...

Problem 83E:

Signs of Numbers Let a, b, and c be real numbers such that a 0, b 0, and c 0. Find the sign of...

Problem 84E:

Signs of Numbers Let a, b, and c be real numbers such that a 0, b 0, and c 0. Find the sign of...

Problem 85E:

Area of a Garden Marys backyard vegetable garden measures 20 ft by 30 ft, so its area is 20 30 =...

Problem 86E:

Temperature Variation The bar graph shows the daily high temperatures for Omak, Washington, and...

Problem 87E:

Mailing a Package The post office will accept only packages for which the length plus the girth...

Problem 88E:

DISCUSS: Sums and Products of Rational and Irrational Numbers Explain why the sum, the difference,...

Problem 89E:

DISCOVER PROVE: Combining Rational and Irrational Numbers Is 12+2 rational or irrational? Is...

Problem 90E:

DISCOVER: Limiting Behavior of Reciprocals Complete the tables. What happens to the size of the...

Problem 91E:

DISCOVER: Locating Irrational Numbers on the Real Line Using the figures below, explain how to...

Problem 92E:

PROVE: Maximum and Minimum Formulas Let max(a, b) denote the maximum and min(a, b) denote the...

Problem 93E:

WRITE: Real Numbers in the Real World Write a paragraph describing different real-world situations...

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(a) What does the set of natural numbers consist of? What does the set of integers consist of? Give...Composition of Functions Find the functions f g, g f, f f, and g g and their domains. 58....Define each concept. (a) Function (b) Domain and range of a function (c) Graph of a function (d)...(a) What is the degree of a quadratic function f? What is the standard form of a quadratic function?...Let f be the exponential function with base a. (a) Write an equation that defines f. (b) Write an...(a) What is the unit circle, and what is the equation of the unit circle? (b) Use a diagram to...(a) How is the degree measure of an angle defined? (b) How is the radian measure of an angle...What is an identity? What is a trigonometric identity?(a) Explain the polar coordinate system. (b) Graph the points with polar coordinates (2, /3) and (1,...

(a) What is a vector in the plane? How do we represent a vector in the coordinate plane? (b) Find...(a) What are the three methods we use to solve a system of equations? (b) Solve the system by the...(a) Give the geometric definition of a parabola. (b) Give the equation of a parabola with vertex at...(a) What is a sequence? What notation do we use to denote the terms of a sequence? (b) Find a...(a) Explain what is meant by limxa f(x) = L. (b) If limx2 f(x) = 5, is it possible that f(2) = 3?...

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