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# 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

Solutions for Chapter A.1
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##### ISBN: 9780618643448

This 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 step-by-step 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 step-by-step solutions. Precalculus was written by and is associated to the ISBN: 9780618643448.

Key Calculus Terms and definitions covered in this textbook
• 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 three-dimensional 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

• Least-squares 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 x-coordinates (horizontal stretch) by the constant 1/c, or all of the y-coordinates (vertical stretch) of the points by a constant c, c, > 1.

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