Saarinen, Eero, 318

Sales, composite functions applied to, 289–290

Scalar multiplication, of matrices, 608

Scientific notation, 25–26

• converting decimals to, 26

Scott, David R., 30

Search range for an aircraft, 158, 161–162

Secant line, 242

Second component, of ordered pairs, 175

Semitones, 495

Sense, of an inequality, 146

Sequences, 716–723

• arithmetic. See Arithmetic sequences

• factorial notation and, 721–722

• finite, 716

• general term of, 719

• geometric. See Geometric sequences

• graphing, 717–718

• infinite, 716

• recursive formulas and, 719–721

• summation notation and, 722–723

Series, 723–724

Set-builder notation, 7

Set notation, 9

Sets of numbers

• classifying, 3

• of real numbers, 3, 4–5, 7–9

Shareholders, 551

Sigma notation, 722–723

Sign(s)

• Descartes’s Rule of Signs and, 367–368

• variations of, 367–368

Sign-chart method, for solving inequalities, 151–153

Simple interest, 94–95, 430–431

Simplification

• of complex fractions, 56–57

• exponential expressions, 25

• of expressions having rational exponents, 70–71

• of rational expressions, 51–52

• of square roots, 63–64

Slope, 198–200

Slope-intercept form, 202

Social Security numbers, 767, 769

Solutions

• of an equation, 82, 185

• of an inequality, 145

• of an inequality in two variables, 558

• extraneous, 132

• optimal, 571

• of a system of equations, 515

• of a system of inequalities in two variables, 562

• of a system of linear equations in three variables, number of, 530–532

Solution sets

• of an inequality in two variables, 558

• feasible, 571

• of a system inequalities in two variables, 562–564

Sørensen, Søren, 489

Sound, loudness of, 493–495

Space junk, 729, 734–735

Special products, 34–35, 37

Square, completing, solving quadratic equations by, 109–111

Square matrices, 590

Square root(s), 61–64

• of negative numbers, multiplication involving, 123

• of perfect squares and their ratios, 62

• principal, 61

• simplifying, 63–64

Square root function, 251, 257

Square root method, for solving quadratic equations, 108

Square root property, 61, 108

Squaring, of binomial sums or differences, 35–36

Squaring function, 257

• graphing, 239–240

Standard form

• for a complex number, 120

• for equation of a circle, 191–192

• of equation of a hyperbola, 691

• for the equation of an ellipse, 677, 682–683

• for the equation of a parabola, 663

• linear equations in one variable in, 83

• polynomials in, 31

• for a quadratic function, 319–321

Star brightness, 497

Statins, 225–226

Steinmetz, Charles, 119

Step functions, 256

Stock market investments, 551, 554–555

Stretching graphs of functions, 269–272

Strings, 716

Substitution method

• for solving systems of linear equations, 517–518

• for systems of nonlinear equations, 552

Subtraction. See also Difference(s)

• of complex numbers, 121

• of fractions, 14

• of matrices, 608–609

• of polynomials, 32–33

• of radical expressions, 65–66

• of rational expressions, 53–56

• of real numbers, 13–14

Sum(s). See also Addition

• of an infinite geometric series, 746–747

• binomial, squaring, 35–36

• of cubes, factoring, 45–46

• of a finite arithmetic sequence, 732–735

• of a finite geometric sequence, 743–744

• of functions, 282

• of terms, product of difference of terms and, 36–38

Summation notation, 722–723, 724

Supply-side economics, 384

Sylvester, James Joseph, 607

Symmetry, 188–191

• of an ellipse, 678

• of even and odd functions, 239, 240

• tests for, 188

Synthetic division, 355–356

Systems of equations, 514–522. See also Systems of linear equations; Systems of linear equations in three variables; Systems of linear equations in two variables; Systems of nonlinear equations

Systems of inequalities, 562–569

• linear, in two variables, 562–564

• nonlinear, 565–566

Systems of linear equations. See also Systems of linear equations in three variables; Systems of linear equations in two variables

• matrices compared with, 593–594

• matrices for solving, 590–595

• solving using matrix inverses, 627–628

Systems of linear equations in three variables, 527–538

• application involving, 534–535

• consistent and inconsistent, 530

• with dependent or independent equations, 530, 531

• Gaussian elimination method and, 528–530

• geometric interpretation of, 533

• nonsquare, 532–533

• number of solutions of, 530–532

Systems of linear equations in two variables, 514–522

• applications involving, 521–522

• elimination (addition) method for solving, 519–520

• graphical method for solving, 515–516

• substitution method for solving, 517–519

Systems of nonlinear equations, 514, 551–557

• applications involving, 554–555

• elimination method for solving, 553–554

• substitution method for solving, 552