Solutions for Precalculus
Problem 1SP:
Solve. 5v42=2v73Problem 2SP:
Identify each equation as a conditional equation, a contradiction, or an identity. Then give the...Problem 3SP:
Solve the equation. 103x213x=40Problem 5SP:
Solve the equation by completing the square and applying the square root property. 3x224x6=0Problem 8SP:
Solve. 3xx5=2x+1+2x2+40x24x5Problem 9SP:
Solve the equations. a.524t=50b.5=6c7+9Problem 10SP:
Solve the equations. a.3x4=2x+1b.4+x=4xProblem 11SP:
Solve the equation. t+7=t5Problem 12SP:
Solve. 1+n+4=3n+1Problem 13SP:
Solve the equation. 2x43/4=54Problem 14SP:
Solve for v. E=12mv2v0Problem 15SP:
Solve for p.cp2dp=kProblem 4PE:
An is an equation that is true for some values of the variable for which the expression in the...Problem 7PE:
Given ax2+bx+c=0(a0), write the quadratic formula.Problem 21PE:
In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The...Problem 22PE:
For a recent year, the cost C(in$) for tuition and fees for x credit-hours at a public college was...Problem 23PE:
For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an...Problem 24PE:
For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an...Problem 25PE:
For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an...Problem 26PE:
For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an...Problem 27PE:
For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an...Problem 28PE:
For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an...Problem 29PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) n2+5n=24Problem 30PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) y2=187yProblem 31PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) 8tt+3=2t5Problem 32PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) 6mm+4=m15Problem 33PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) 3x2=12xProblem 34PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) z2=25zProblem 35PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) m+4m5=8Problem 36PE:
For Exercises 29-36, solve by applying the zero-product property. (See Example 3) n+2n4=27Problem 42PE:
For Exercises 37-42, solve by using the square root property. (See Example 4) 3z+11210=110Problem 43PE:
For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial....Problem 44PE:
For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial....Problem 45PE:
For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial....Problem 46PE:
For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial....Problem 47PE:
For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial....Problem 48PE:
For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial....Problem 49PE:
For Exercises 49-54, solve by completing the square and applying the square root property. (See...Problem 50PE:
For Exercises 49-54, solve by completing the square and applying the square root property. (See...Problem 51PE:
For Exercises 49-54, solve by completing the square and applying the square root property. (See...Problem 52PE:
For Exercises 49-54, solve by completing the square and applying the square root property. (See...Problem 53PE:
For Exercises 49-54, solve by completing the square and applying the square root property. (See...Problem 54PE:
For Exercises 49-54, solve by completing the square and applying the square root property. (See...Problem 57PE:
For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 6x+5x3=2x7x+5+x12Problem 58PE:
For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 5c+72c3=2cc+1535Problem 59PE:
For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 12x227=514xProblem 61PE:
For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 0.4y2=2y2.5Problem 62PE:
For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 0.09n2=0.42n0.49Problem 88PE:
For Exercises 85-102, solve the equations. (See Examples 9 and 10) a.m+1=5b.m+1=0c.m+1=1Problem 123PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) A=lwforlProblem 124PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) E=IRforRProblem 125PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) P=a+b+cforcProblem 126PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) W=KTforKProblem 127PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 7x+2y=8foryProblem 128PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 3x+5y=15foryProblem 129PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 5x4y=2foryProblem 130PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 7x2y=5foryProblem 131PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) S=n2(a+d)fordProblem 132PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) S=n2[2a+(n1)d]foraProblem 133PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 6=4x+txforxProblem 134PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 8=3x+kxforxProblem 135PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 6x+ay=bx+5forxProblem 136PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 3x+2y=cx+dforxProblem 137PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) A=r2forr0Problem 138PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) V=r2hforr0Problem 139PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) a2+b2=c2fora0Problem 140PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) a2+b2+c2=d2forc0Problem 141PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) kw2cw=rforwProblem 142PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) dy2+my=pforyProblem 143PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) s=v0t+12at2fortProblem 144PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) S=2rh+r2hforrProblem 145PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 1f=1p+1qforpProblem 146PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 1R=1R1+1R2+1R3forR3Problem 147PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 16+x2y2=zforxProblem 148PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) 4+x2+y2=zforyProblem 149PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) P1V1T1=P2V2T2forT1Problem 150PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) t1s1v1=t2s2v2forv2Problem 151PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) T=2LgforgProblem 152PE:
For Exercises 123-152, solve for the specified variable. (See Examples 14-15) t=2sgforsProblem 153PE:
For Exercises 153-156, solve the equation. 3x2x1x+62=0Problem 154PE:
For Exercises 153-156, solve the equation. 5y3y4y+12=0Problem 155PE:
For Exercises 153-156, solve the equation. 98t349t28t+4=0Problem 156PE:
For Exercises 153-156, solve the equation. 2m3+3m2=92m+3Problem 157PE:
Explain why the value 5 is not a solution xx5+15=5x5 .Problem 161PE:
For Exercises 161-166, write an equation with integer coefficients and the variable x that has the...Problem 162PE:
For Exercises 161-166, write an equation with integer coefficients and the variable x that has the...Problem 163PE:
For Exercises 161-166, write an equation with integer coefficients and the variable x that has the...Problem 164PE:
For Exercises 161-166, write an equation with integer coefficients and the variable x that has the...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
We offer sample solutions for Precalculus homework problems. See examples below:
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