Solutions for Precalculus
Problem 1SP:
a. Write the set representation by the graph interval notation and set builder notation. b. Given...Problem 4SP:
Use the definition of absolute value to rewrite each expression without absolute value bars....Problem 5SP:
Write an absolute value expression that represents the distance between 9 and 2 on the number line....Problem 6SP:
Simplify.502[121+3(13)2]Problem 7SP:
Simplify.123(5x2y)+5(3x)yProblem 8SP:
a. The sale price S on a lawn mower is the difference of the original price P and the amount of...Problem 2PE:
Z=,3,2,1,0,1,2,3, is called the set of .Problem 3PE:
R is the notation used to denote the set of .Problem 5PE:
Write an absolute value expression to represent the distance between a and b on the real number...Problem 6PE:
The properties of addition and multiplication indicate that the order in which two real number are...Problem 7PE:
The associative property of addition indicates that a+b+c= and the associative property of...Problem 9PE:
For Exercises 9-10, write an English sentence to represent the algebraic statement. a.3Nb.3.1WProblem 10PE:
For Exercises 9-10, write an English sentence to represent the algebraic statement. a.25Qb.QProblem 11PE:
For exercise 11-12, determine whether the statement is true or false. a.5Nb.5Wc.5Zd.5QProblem 12PE:
For exercise 11-12, determine whether the statement is true or false. a.13Nb.13Wc.13Zd.13QProblem 17PE:
For Exercise 13-18, write each statement as an inequality. The quantity (m+4) exceed 70Problem 18PE:
For Exercise 13-18, write each statement as an inequality. The quantity n7 is approximately equal to...Problem 28PE:
For Exercise 25-30, graph the given set and write down the corresponding interval notation. (See...Problem 31PE:
For Exercises 31-36 interval notation is given for several sets of real numbers. Graph the set and...Problem 32PE:
For Exercises 31-36 interval notation is given for several sets of real numbers. Graph the set and...Problem 34PE:
For Exercises 31-36 interval notation is given for several sets of real numbers. Graph the set and...Problem 35PE:
For Exercises 31-36 interval notation is given for several sets of real numbers. Graph the set and...Problem 36PE:
For Exercises 31-36 interval notation is given for several sets of real numbers. Graph the set and...Problem 41PE:
Refer to sets, C D, and F and find the union or intersection of sets as indicated. Write the answers...Problem 43PE:
For Exercises 4 3-46, find the union or intersection of the given intervals. Write the answer, in...Problem 44PE:
For Exercises 4 3-46, find the union or intersection of the given intervals. Write the answer, in...Problem 45PE:
For Exercises 4 3-46, find the union or intersection of the given intervals. Write the answer, in...Problem 46PE:
For Exercises 4 3-46, find the union or intersection of the given intervals. Write the answer, in...Problem 47PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 48PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 49PE:
For Exercises 47-58 simplify each expression by writing the expression without absolute value bars....Problem 51PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 52PE:
For Exercises 47-58 simplify each expression by writing the expression without absolute value bars....Problem 53PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 54PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 55PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 56PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 57PE:
For Exercises 47- 58 simplify each expression by writing the expression without absolute value bars....Problem 59PE:
For Exercises 59- 64, write an absolute value expression to represent the distance between the two...Problem 60PE:
For Exercises 59- 64, write an absolute value expression to represent the distance between the two...Problem 61PE:
For Exercises 59- 64, write an absolute value expression to represent the distance between the two...Problem 62PE:
For Exercises 59- 64, write an absolute value expression to represent the distance between the two...Problem 63PE:
For Exercises 59- 64, write an absolute value expression to represent the distance between the two...Problem 64PE:
For Exercises 59- 64, write an absolute value expression to represent the distance between the two...Problem 65PE:
For Exercises 65-78, simplify the expressions. (See Example 6) a.42b.(4)2c.42d.4e.4f.4Problem 66PE:
For Exercises 65-78, simplify the expressions. (See Example 6) a.92b.(9)2c.92d.9e.9f.9Problem 67PE:
For Exercises 65-78, simplify the expressions. (See Example 6) a.83b.83c.83d.100e.100f.100Problem 79PE:
For Exercise 79-84, combine like terms. 14w33w3+w3Problem 85PE:
For Exercise 85-90, apply the distributive property (4x)Problem 99PE:
Jake is 1yr younger than Charlotte. a. Write a model for Jake's age J in terms of Charlotte's age C....Problem 100PE:
For a recent NFL season, Aaron Rodgers had 9 more touchdown passes than Joe Flacco. a. Write a model...Problem 102PE:
When Ms. Celano has excellent service at a restaurant, the amount she leaves for a tip tis at least...Problem 103PE:
Suppose that an object is dropped from a height h. Its velocity v at impact with the ground is give...Problem 104PE:
The height of a sunflower plant can be determined by the time t in weeks after the seed has...Problem 105PE:
A power company charges one household S.0. 12 per kilo watt-hour (kWh) and $14.89 in monthly taxes....Problem 106PE:
A utility company charges a base rate for water usage of 19.50 per month, plus $4.58 for every...Problem 107PE:
The cost C(in)$ to rent an apartment is $640 per month, plus a $500 nonrefundable security deposit,...Problem 108PE:
For a certain the cost Cin$ for taking class in first semester is $105 per credit-hour, $35 each...Problem 110PE:
For Exercise 109-114, evaluate each expression for the given values of the variables....Problem 113PE:
For Exercise 109-114, evaluate each expression for the given values of the variables....Problem 116PE:
Under selected conditions, a sedan gets 22 mpg in city driving and 32 mpg for highway driving. The...Problem 117PE:
When is a parenthesis used when writing interval notation?Problem 119PE:
Explain the difference between the commutative property of addition and the associative property of...Problem 120PE:
Explain why 0 has no multiplicative inverse.Problem 121PE:
Ifn0,thennn=.Problem 122PE:
Ifn0,thennn=.Problem 123PE:
Ifn0,thenn+n=.Problem 124PE:
Ifn0,thenn+n=.Problem 125PE:
Ifn0,thenn=.Problem 126PE:
Ifn0,thenn=.Problem 127PE:
For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real...Problem 128PE:
For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real...Problem 129PE:
For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real...Problem 130PE:
For Exercises 127- 130, determine the sign of the expression. Assume that, a, b and c are real...Browse All Chapters of This Textbook
Chapter R - Review Of PrerequisitesChapter R.1 - Sets And The Real Number LineChapter R.2 - Exponents And RadicalsChapter R.3 - Polynomials And FactoringChapter R.4 - Rational Expressions And More Operations On RadicalsChapter R.5 - Equations With Real SolutionsChapter R.6 - Complex Numbers And More Quadratic EquationsChapter R.7 - Applications Of EquationsChapter R.8 - Linear, Compound, And Absolute Value InequalitiesChapter 1 - Functions And Relations
Chapter 1.1 - The Rectangular Coordinate System And Graphing UtilitiesChapter 1.2 - CirclesChapter 1.3 - Functions And RelationsChapter 1.4 - Linear Equations In Two Variables And Linear FunctionsChapter 1.5 - Applications Of Linear Equations And ModelingChapter 1.6 - Transformations Of GraphsChapter 1.7 - Analyzing Graphs Of Functions And Piecewise-defined FunctionsChapter 1.8 - Algebra Of Functions And Function CompositionChapter 2 - Polynomial And Rational FunctionsChapter 2.1 - Quadratic Functions And ApplicationsChapter 2.2 - Introduction To Polynomial FunctionsChapter 2.3 - Division Of Polynomials And The Remainder And Factor TheoremsChapter 2.4 - Zeros Of PolynomialsChapter 2.5 - Rational FunctionsChapter 2.6 - Polynomial And Rational InequalitiesChapter 2.7 - VariationChapter 3 - Exponential And Logarithmic FunctionsChapter 3.1 - Inverse FunctionsChapter 3.2 - Exponential FunctionsChapter 3.3 - Logarithmic FunctionsChapter 3.4 - Properties Of LogarithmsChapter 3.5 - Exponential And Logarithmic Equations And ApplicationsChapter 3.6 - Modeling With Exponential And Logarithmic FunctionsChapter 4 - Trigonometric FunctionsChapter 4.1 - Angles And Their MeasureChapter 4.2 - Trigonometric Functions Defined On The Unit CircleChapter 4.3 - Right Triangle TrigonometryChapter 4.4 - Trigonometric Functions Of Any AngleChapter 4.5 - Graphs Of Sine And Cosine FunctionsChapter 4.6 - Graphs Of Other Trigonometric FunctionsChapter 4.7 - Inverse Trigonometric FunctionsChapter 5 - Analytic TrigonometryChapter 5.1 - Fundamental Trigonometric IdentitiesChapter 5.2 - Sum And Difference FormulasChapter 5.3 - Double-angle, Power-reducing, And Half-angle FormulasChapter 5.4 - Product-to-sum And Sum-to-product FormulasChapter 5.5 - Trigonometric EquationsChapter 6 - Applications Of Trigonometric FunctionsChapter 6.1 - Applications Of Right TrianglesChapter 6.2 - The Law Of SinesChapter 6.3 - The Law Of CosinesChapter 6.4 - Harmonic MotionChapter 7 - Trigonometry Applied To Polar Coordinate Systems And VectorsChapter 7.1 - Polar CoordinatesChapter 7.2 - Graphs Of Polar EquationsChapter 7.3 - Complex Numbers In Polar FormChapter 7.4 - VectorsChapter 7.5 - Dot ProductChapter 8 - Systems Of Equations And InequalitiesChapter 8.1 - Systems Of Linear Equations In Two Variables And ApplicationsChapter 8.2 - Systems Of Linear Equations In Three Variables And ApplicationsChapter 8.3 - Partial Fraction DecompositionChapter 8.4 - Systems Of Nonlinear Equations In Two VariablesChapter 8.5 - Inequalities And Systems Of Inequalities In Two VariablesChapter 8.6 - Linear ProgrammingChapter 9 - Matrices And Determinants And ApplicationsChapter 9.1 - Solving Systems Of Linear Equations Using MatricesChapter 9.2 - Inconsistent Systems And Dependent EquationsChapter 9.3 - Operations On MatricesChapter 9.4 - Inverse Matrices And Matrix EquationsChapter 9.5 - Determinants And Cramer’s RuleChapter 10 - Analytic GeometryChapter 10.1 - The EllipseChapter 10.2 - The HyperbolaChapter 10.3 - The ParabolaChapter 10.4 - Rotation Of AxesChapter 10.5 - Polar Equations Of ConicsChapter 10.6 - Plane Curves And Parametric EquationsChapter 11 - Sequences, Series, Induction, And ProbabilityChapter 11.1 - Sequences And SeriesChapter 11.2 - Arithmetic Sequences And SeriesChapter 11.3 - Geometric Sequences And SeriesChapter 11.4 - Mathematical InductionChapter 11.5 - The Binomial TheoremChapter 11.6 - Principles Of CountingChapter 11.7 - Introduction To Probability
Book Details
Julie Miller wrote her developmental math series because students were coming into her Precalculus course underprepared. They weren’t mathematically mature enough to understand the concepts of math nor were they fully engaged with the material. She began her developmental mathematics offerings with intermediate algebra to help bridge that gap. The Precalculus series is a carefully constructed end to that bridge that uses the highly effective pedagogical features from her fastest growing developmental math series. What sets Julie Miller’s series apart is that it addresses course issues through an author-created digital package that maintains a consistent voice and notation throughout the program. This consistency--in videos, PowerPoints, Lecture Notes, and Group Activities--coupled with the power of ALEKS and Connect Hosted by ALEKS, ensures that students master the skills necessary to be successful in Precalculus and can carry them through to the calculus sequence.
Sample Solutions for this Textbook
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