Earthquake intensity, 490–493
Economics
functions in, 227–228
Leontief input-output model and, 589, 599–600, 628–629
multiplier effect and, 738, 747
supply-side, 384
Einstein, Albert, 130
Electricity
alternating current and, 119, 125
direct variation and, 404–405
Ohm’s law and, 539
parallel circuits and, 539
Element(s)
in matrices, 590
of sets,
Elementary row operations, 592–594
Elimination method
Gaussian, 528–529
for solving systems of linear equations, 519–520
for systems of nonlinear equations, 553–554
Ellipses, 660, 676–689
applications involving, 684–685
defined, 676–677
equation of, 677–679, 680–682
graphing, 679
horizontal, 678
reflecting property of, 684
translations of, 680–684
vertical, 678
Empty set,
End behavior, of a polynomial function, 335–337
Entries, in matrices, 590
Equality
of complex numbers, 121
of matrices, 606–607
of numbers,
Equal ordered pairs, 175
Equal sign (=),
Equations
of an ellipse, 677–679, 680–682
of a circle, standard, 191–192
conditional, 82, 86
defined, 81
depressed, 358–359
equivalent, 82, 85, 86
exponential. See Exponential equations
functions defined by, 218–219
graphs of. See Graphs and graphing
of a hyperbola, 691, 693–694, 696
inconsistent, 82, 85, 86
involving absolute value, 158–161
involving radicals, 133–136
linear. See Linear equations; Linear equations in one variable
logarithmic, 479–482
in logarithmic and exponential form, 445–446
matrix, 609
nonquadratic, factoring for solving, 131–132
of a parabola, 662–666
quadratic. See Quadratic equations
quadratic in form, 137–138
rational, 132–133
with rational exponents, 136–137
solving, 82
systems of. See Systems of linear equations in three variables; Systems of linear equations in two variables; Systems of nonlinear equations
Equilibrium point, 521
Equivalent equations, 82, 85, 86
Equivalent inequalities, 145
ESWL (extracorporeal shock-wave lithotripsy), 676
Euler, Leonhard, 120, 216, 435
Euler number, 435
Even degree, power functions of, 334
Even functions, 239–240, 241
Events
complements of, probability of, 783–784
mutually exclusive, probability of, 782–783
probability of, 778–781
Expanding by cofactors, 639
Experimental probabilities, 784–785
Exponent(s)
defined,
evaluating expressions using,
integer, –, 20–21
negative, 20–21
rational, 68–71
rational, equations with, 136–137
rules of, 21–24, 27, 425
zero, 20–21
Exponential equations
applications of, 478–479
with different bases, solving, 477
of quadratic form, 477–478
solving, 476–478
Exponential expressions, simplifying, 25
Exponential functions, 423–443
defined, 424
evaluating, 424–425
finding, 430
graphing, 425–427
growth and decay and, 436–438
interest calculations using, 430–436
natural, 436
properties of, 426–427
transformations on, 427–430
Exponential growth/decay, 436–438, 741
formula for, in logarithmic form, 469
Exponential inequalities, 482–483
Extracorporeal shock-wave lithotripsy (ESWL), 676
Extraneous solutions (roots), of rational equations, 132
Extreme values, 237, 238–239