 A.1.1: Fill in the blanks. A real number is ________ if it can be written ...
 A.1.2: Fill in the blanks. ________ numbers have infinite nonrepeating dec...
 A.1.3: Fill in the blanks. The distance between a point on the real number...
 A.1.4: Fill in the blanks. A number that can be written as the product of ...
 A.1.5: Fill in the blanks. An integer that has exactly two positive factor...
 A.1.6: Fill in the blanks. An algebraic expression is a collection of lett...
 A.1.7: Fill in the blanks. The ________ of an algebraic expression are tho...
 A.1.8: Fill in the blanks. The numerical factor of a variable term is the ...
 A.1.9: Fill in the blanks. The ________ ________ states that if ab _ 0, th...
 A.1.10: In Exercises 710, use a calculator to find the decimal form of the ...
 A.1.11: In Exercises 11 and 12,approximate the numbers and place the correc...
 A.1.12: In Exercises 11 and 12,approximate the numbers and place the correc...
 A.1.13: In Exercises 1318, plot the two real numbers on the real number lin...
 A.1.14: In Exercises 1318, plot the two real numbers on the real number lin...
 A.1.15: In Exercises 1318, plot the two real numbers on the real number lin...
 A.1.16: In Exercises 1318, plot the two real numbers on the real number lin...
 A.1.17: In Exercises 1318, plot the two real numbers on the real number lin...
 A.1.18: In Exercises 1318, plot the two real numbers on the real number lin...
 A.1.19: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.20: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.21: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.22: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.23: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.24: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.25: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.26: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.27: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.28: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.29: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.30: In Exercises 1930, (a) give a verbal description of the subset of r...
 A.1.31: In Exercises 3138, use inequality notation to describe the set. All...
 A.1.32: In Exercises 3138, use inequality notation to describe the set. All...
 A.1.33: In Exercises 3138, use inequality notation to describe the set. is ...
 A.1.34: In Exercises 3138, use inequality notation to describe the set. is ...
 A.1.35: In Exercises 3138, use inequality notation to describe the set. is ...
 A.1.36: In Exercises 3138, use inequality notation to describe the set. is ...
 A.1.37: In Exercises 3138, use inequality notation to describe the set. The...
 A.1.38: In Exercises 3138, use inequality notation to describe the set. The...
 A.1.39: In Exercises 3948, evaluate the expression.
 A.1.40: In Exercises 3948, evaluate the expression.
 A.1.41: In Exercises 3948, evaluate the expression.
 A.1.42: In Exercises 3948, evaluate the expression.
 A.1.43: In Exercises 3948, evaluate the expression.
 A.1.44: In Exercises 3948, evaluate the expression.
 A.1.45: In Exercises 3948, evaluate the expression.
 A.1.46: In Exercises 3948, evaluate the expression.
 A.1.47: In Exercises 3948, evaluate the expression.
 A.1.48: In Exercises 3948, evaluate the expression.
 A.1.49: In Exercises 4954, place the correct symbol (<, >, or =) between th...
 A.1.50: In Exercises 4954, place the correct symbol (<, >, or =) between th...
 A.1.51: In Exercises 4954, place the correct symbol (<, >, or =) between th...
 A.1.52: In Exercises 4954, place the correct symbol (<, >, or =) between th...
 A.1.53: In Exercises 4954, place the correct symbol (<, >, or =) between th...
 A.1.54: In Exercises 4954, place the correct symbol (<, >, or =) between th...
 A.1.55: In Exercises 5560, find the distance between a and b.
 A.1.56: In Exercises 5560, find the distance between a and b.
 A.1.57: In Exercises 5560, find the distance between a and b.
 A.1.58: In Exercises 5560, find the distance between a and b.
 A.1.59: In Exercises 5560, find the distance between a and b.
 A.1.60: In Exercises 5560, find the distance between a and b.
 A.1.61: In Exercises 6164, the accounting department of a sports drink bott...
 A.1.62: In Exercises 6164, the accounting department of a sports drink bott...
 A.1.63: In Exercises 6164, the accounting department of a sports drink bott...
 A.1.64: In Exercises 6164, the accounting department of a sports drink bott...
 A.1.65: Federal Deficit The bar graph shows the federal government receipts...
 A.1.66: Veterans The table shows the number of living veterans (in thousand...
 A.1.67: In Exercises 6772, use absolute value notation to describe the situ...
 A.1.68: In Exercises 6772, use absolute value notation to describe the situ...
 A.1.69: In Exercises 6772, use absolute value notation to describe the situ...
 A.1.70: In Exercises 6772, use absolute value notation to describe the situ...
 A.1.71: In Exercises 6772, use absolute value notation to describe the situ...
 A.1.72: In Exercises 6772, use absolute value notation to describe the situ...
 A.1.73: In Exercises 7378, identify the terms. Then identify the coefficien...
 A.1.74: In Exercises 7378, identify the terms. Then identify the coefficien...
 A.1.75: In Exercises 7378, identify the terms. Then identify the coefficien...
 A.1.76: In Exercises 7378, identify the terms. Then identify the coefficien...
 A.1.77: In Exercises 7378, identify the terms. Then identify the coefficien...
 A.1.78: In Exercises 7378, identify the terms. Then identify the coefficien...
 A.1.79: In Exercises 7984, evaluate the expression for each value of x. (If...
 A.1.80: In Exercises 7984, evaluate the expression for each value of x. (If...
 A.1.81: In Exercises 7984, evaluate the expression for each value of x. (If...
 A.1.82: In Exercises 7984, evaluate the expression for each value of x. (If...
 A.1.83: In Exercises 7984, evaluate the expression for each value of x. (If...
 A.1.84: In Exercises 7984, evaluate the expression for each value of x. (If...
 A.1.85: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.86: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.87: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.88: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.89: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.90: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.91: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.92: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.93: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.94: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.95: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.96: In Exercises 8596, identify the rule(s) of algebra illustrated by t...
 A.1.97: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.98: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.99: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.100: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.101: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.102: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.103: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.104: In Exercises 97104, perform the operation(s). (Write fractional ans...
 A.1.105: (a) Use a calculator to complete the table. (b) Use the result from...
 A.1.106: (a) Use a calculator to complete the table. (b) Use the result from...
 A.1.107: True or False? In Exercises 107 and 108, determine whether the stat...
 A.1.108: True or False? In Exercises 107 and 108, determine whether the stat...
 A.1.109: Exploration Consider and where (a) Are the values of the expression...
 A.1.110: Think About It Is there a difference between saying that a real num...
 A.1.111: Think About It Because every even number is divisible by 2, is it p...
 A.1.112: Writing Describe the differences among the sets of natural numbers,...
 A.1.113: In Exercises 113 and 114, use the real numbers A, B, and C shown on...
 A.1.114: In Exercises 113 and 114, use the real numbers A, B, and C shown on...
 A.1.115: Writing Can it ever be true that for a real number a? Explain.
Solutions for Chapter A.1: Real Numbers and Their Properties
Full solutions for Precalculus  7th Edition
ISBN: 9780618643448
Solutions for Chapter A.1: Real Numbers and Their Properties
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 115 problems in chapter A.1: Real Numbers and Their Properties have been answered, more than 14922 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Precalculus, edition: 7. Chapter A.1: Real Numbers and Their Properties includes 115 full stepbystep solutions. Precalculus was written by and is associated to the ISBN: 9780618643448.

Anchor
See Mathematical induction.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Common difference
See Arithmetic sequence.

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Factor
In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Identity function
The function ƒ(x) = x.

Law of sines
sin A a = sin B b = sin C c

Leastsquares line
See Linear regression line.

Linear regression
A procedure for finding the straight line that is the best fit for the data

Linear system
A system of linear equations

Multiplicative identity for matrices
See Identity matrix

Periodic function
A function ƒ for which there is a positive number c such that for every value t in the domain of ƒ. The smallest such number c is the period of the function.

Principle of mathematical induction
A principle related to mathematical induction.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Row operations
See Elementary row operations.

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.
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