Intermediate Algebra (Hardcover)
Intermediate Algebra (Hardcover)
4th Edition
ISBN: 9780073384498
Author: Julie Miller, Molly O'Neill, Nancy Hyde
Publisher: MCGRAW-HILL HIGHER EDUCATION
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter R1, Problem 1GA
To determine

The goals of taking this course and discuss them with your group members.

Expert Solution & Answer
Check Mark

Explanation of Solution

The main goals of taking this course can be summarized as below:

(1) Linear equations and Inequalities in one variable:

After learning this topic, if we have given a linear equation with one variable,

  • We will be able to clear fraction
  • We will be able to use the distributive property
  • We will be able to use the addition and multiplication properties

If we have given a literal equation, then we'll be able to

  • Solve for any given variable

If we have given an inequality with one variable, then we'll be able to:

  • Solve the inequality algebraically
  • Describe the solution of inequality using inequality notation and interval notation
  • Solve and graph the solutions of absolute value inequality

(2) Linear equations in two variables and Functions:

After learning this topic, if we have given a linear equation with two variable, we will be able to:

  • Understand and Transform the equation of line in different form like: slope-intercept form, point-slope form or standard form
  • Identify the slope and y-intercept of any equation of line
  • Graph the equation of line using slope and y-intercept

If we have given an inequality with two variables, then we will be able to:

  • Solve the solution graphically
  • Write the solution in interval notation using the parentheses and square bracket as per the inequality sign

If we have given a function in any of the algebraic, table, graph or in context form, we will be able to:

  • Identify a function as a relationship of the dependent variable and independent variable
  • Demonstrate the proper use of the function notation
  • Identify domain and range of the function from algebraic equation or from the graph
  • Evaluate the function value at any point
  • Identify dependent and independent variables in context

(3) System of Linear equations and Inequalities:

After learning this topic, if we have given a system of linear equation with two variable, we will be able to:

  • Solve the system of equation by substitution method, addition method or graphing method
  • Compare the real life models expressed by linear functions
  • Identify the number of solutions, that is, one solution, infinitely many solutions or no solution
  • Interpret the solution of system given in context

If we have given linear inequalities with two variables, we will be able to:

  • Solve the equalities using the graphing method
  • Solve the compound inequalities

If we have given linear inequalities with three variables, we will be able to:

  • Solve the system of equations algebraically
  • Solve the system of equations using matrices

(4) Polynomials:

After learning this topic, if we have given polynomials, we will be able to:

  • Identify the degree of the polynomial and the like terms in the polynomial
  • Perform the basic operations on polynomials, like addition, subtraction, multiplication and division of polynomials
  • Factor by grouping
  • Factor trinomials using splitting the middle term
  • Factor binomials and trinomials
  • solve equations using zero product rule and square root property

(5) Rational Expressions and Rational equations:

After learning this topic, if we have given a rational expression or equation, we will be able to:

  • Simplify the rational expressions and equations
  • Perform the basic operations like addition, subtraction, multiplication and division of rational expressions
  • Simplify the complex fractions

(6) Radicals and Complex numbers:

After learning this topic, if we have given a radical number or expression, we will be able to:

  • Simplify the radical expression using the exponent rules
  • Perform the basic operations, like addition, subtraction, multiplication and division of radical expressions
  • Rationalize the radicals in rational expressions
  • Change simple rational exponents to radical form and vice versa

If we have given a complex number, then we will be able to

  • Write the complex number in standard form
  • Perform the basic operations, like addition, subtraction, multiplication and division of complex numbers
  • Find the complex conjugates to divide the complex numbers

(7) Quadratic Equation, Function and Inequalities:

After learning this topic, if we have given a quadratic equation or expression, we will be able to:

  • Factor the quadratic equations
  • Solve the quadratic equation to find the zeros of the equation
  • Solve the quadratic equations using different methods, like quadratic formula, splitting the middle term, completing the square method or graphically
  • Identify the shape of the parabola by identifying the dependent and independent variable
  • Identify the vertex of the parabola

(8) Exponential and Logarithmic functions:

After learning this topic, if we have given an exponential function, we will be able to:

  • Identify the growth or decay factor
  • Determine the growth or decay rates
  • Identify the exponential growth/decay and continuous growth/decay
  • Identify the increasing or decreasing graph of given exponential function

If we have given a logarithmic equation, we will be able to:

  • Expand the logarithmic expression using the logarithmic rules
  • Combine the logarithmic expression using the logarithmic rules
  • Differentiate between regular log and natural log
  • Graph the logarithmic functions

(9) Conic sections:

After learning this topic, we will be able to:

  • Find the distance between any two points, midpoint of line segment connecting two points
  • Identify and differentiate between different conics, like circle, parabola, ellipse and hyperbola
  • Solve the system of non linear equations with two variables
  • Graph the solutions of two non linear inequalities

(9)Binomial expansions, Sequences and Series:

After learning this topic, we will be able to:

  • Expand a binomial of higher order
  • Identify the series and sequences and their general terms
  • Use of Arithmetic and Geometric sequence and series in real life applications.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
How long is a guy wire reaching from the top of a 15​-foot pole to a point on the ground 9-feet from the​ pole?       Question content area bottom Part 1 The guy wire is exactly feet long. ​(Type an exact​ answer, using radicals as​ needed.) Part 2 The guy wire is approximatelyfeet long. ​(Round to the nearest​ thousandth.)
Question 6 Not yet answered Marked out of 5.00 Flag question = If (4,6,-11) and (-12,-16,4), = Compute the cross product vx w k
Consider the following vector field v^-> (x,y): v^->(x,y)=2yi−xj What is the magnitude of the vector v⃗  located in point (13,9)? [Provide your answer as an integer number (no fraction). For a decimal number, round your answer to 2 decimal places]
Knowledge Booster
Background pattern image
Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Propositional Logic, Propositional Variables & Compound Propositions; Author: Neso Academy;https://www.youtube.com/watch?v=Ib5njCwNMdk;License: Standard YouTube License, CC-BY
Propositional Logic - Discrete math; Author: Charles Edeki - Math Computer Science Programming;https://www.youtube.com/watch?v=rL_8y2v1Guw;License: Standard YouTube License, CC-BY
DM-12-Propositional Logic-Basics; Author: GATEBOOK VIDEO LECTURES;https://www.youtube.com/watch?v=pzUBrJLIESU;License: Standard Youtube License
Lecture 1 - Propositional Logic; Author: nptelhrd;https://www.youtube.com/watch?v=xlUFkMKSB3Y;License: Standard YouTube License, CC-BY
MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY