Intermediate Algebra
19th Edition
ISBN: 9780998625720
Author: Lynn Marecek
Publisher: OpenStax College
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Chapter 12.4, Problem 12.62TI
Use Pascal’s
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Chapter 12 Solutions
Intermediate Algebra
Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Find a general term for the sequence whose first...Ch. 12.1 - Find a general term for the sequence whose first...Ch. 12.1 - Find a general term for the sequence whose first...Ch. 12.1 - Find a general term for the sequence whose first...
Ch. 12.1 - Find a general term for the sequence whose first...Ch. 12.1 - Find a general term for the sequence whose first...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Write the first five terms of the sequence whose...Ch. 12.1 - Expand the partial sum and five its value: i=153i.Ch. 12.1 - Expand the partial sum and five its value: i=154i.Ch. 12.1 - Expand the partial sum and five its value:...Ch. 12.1 - Expand the partial sum and five its value:...Ch. 12.1 - Write each sum using summation notation:...Ch. 12.1 - Write each sum using summation notation:...Ch. 12.1 - Write each sum using summation notation:...Ch. 12.1 - Write each sum using summation notation: 2+46+810.Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - 3In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first terms...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, write the first five...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, find a general term...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - In the following exercises, using factorial...Ch. 12.1 - the following exercises, using factorial notation,...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, expand the partial sum...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In the following exercises, write each sum using...Ch. 12.1 - In your own words, explain how to write the terms...Ch. 12.1 - Which terms of the sequence are negative when the...Ch. 12.1 - In your own words, explain what is meant by n!...Ch. 12.1 - Explain what each part of the notation k=1122k...Ch. 12.2 - Determine if each sequence is arithmetic. If so,...Ch. 12.2 - Determine if each sequence is arithmetic. If so,...Ch. 12.2 - Write the first five terms of the sequence where...Ch. 12.2 - Write the first five terms of the sequence where...Ch. 12.2 - Find the twenty-seventh term of a sequence where...Ch. 12.2 - Find the eighteenth term of a sequence where the...Ch. 12.2 - Find the eleventh term of a sequence where the...Ch. 12.2 - Find the nineteenth term of a sequence where the...Ch. 12.2 - Find the first term and common difference of a...Ch. 12.2 - Find the first term and common difference of a...Ch. 12.2 - Find the sum of the first 30 terms of the...Ch. 12.2 - Find the sum of the first 30 terms of the...Ch. 12.2 - Find the sum of the first 50 terms of the...Ch. 12.2 - Find the sum of the first 50 terms of the...Ch. 12.2 - Find the sum: i=130(6i4).Ch. 12.2 - Find the sum: i=135(5i3).Ch. 12.2 - In the following exercises, determine if each...Ch. 12.2 - In the following exercises, determine if each...Ch. 12.2 - In the following exercises, determine if each...Ch. 12.2 - In the following exercises, determine if each...Ch. 12.2 - In the following exercises, determine if each...Ch. 12.2 - In the following exercises, determine if each...Ch. 12.2 - In the following exercises, write the first five...Ch. 12.2 - In the following exercises, write the first five...Ch. 12.2 - In the following exercises, write the first five...Ch. 12.2 - In the following exercises, write the first five...Ch. 12.2 - In the following exercises, write the first five...Ch. 12.2 - In the following exercises, write the first five...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the term...Ch. 12.2 - In the following exercises, find the first term...Ch. 12.2 - In the following exercises, find the first term...Ch. 12.2 - In the following exercises, find the first term...Ch. 12.2 - In the following exercises, find the first term...Ch. 12.2 - In the following exercises, find the first term...Ch. 12.2 - In the following exercises, find the first term...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find the sum of the...Ch. 12.2 - In the following exercises, find each sum. 117....Ch. 12.2 - In the following exercises, find each sum. 118....Ch. 12.2 - In the following exercises, find each sum. 119....Ch. 12.2 - In the following exercises, find each sum. 120....Ch. 12.2 - In the following exercises, find each sum. 121....Ch. 12.2 - In the following exercises, find each sum. 122....Ch. 12.2 - In your own words, explain how to determine...Ch. 12.2 - ?In your own words, explain how the first two...Ch. 12.2 - In your own words, explain how to find the general...Ch. 12.2 - In your own words, explain how to find the sum of...Ch. 12.3 - Determine if each sequence is geometric. If so...Ch. 12.3 - Determine if each sequence is geometric. If so...Ch. 12.3 - Write the first five terms of the sequence where...Ch. 12.3 - Write the first five terms of the sequence where...Ch. 12.3 - Find the thirteenth term of a sequence where the...Ch. 12.3 - Find the twelfth term of a sequence where the...Ch. 12.3 - Find the ninth term of the sequence...Ch. 12.3 - Find the eleventh term of the sequence...Ch. 12.3 - Find the sum of the first 20 terms of the...Ch. 12.3 - Find the sum of the first 20 terms of the...Ch. 12.3 - Find the sum: i=1156(2)i.Ch. 12.3 - Find the sum: i=1105(2)i.Ch. 12.3 - Find the sum of the infinite geometric series...Ch. 12.3 - Find the sum of the infinite geometric series...Ch. 12.3 - Write the repeating decimal 0.4 as a fraction.Ch. 12.3 - Write the repeating decimal 0.8 as a fraction.Ch. 12.3 - What is the total effect on the economy of a...Ch. 12.3 - What is the total effect on the economy of a...Ch. 12.3 - New grandparents decide to invest 3200 per month...Ch. 12.3 - Arturo just got his first full-time job after...Ch. 12.3 - In the following exercises, determine if the...Ch. 12.3 - In the following exercises, determine if the...Ch. 12.3 - In the following exercises, determine if the...Ch. 12.3 - In the following exercises, determine if the...Ch. 12.3 - In the following exercises, determine if the...Ch. 12.3 - In the following exercises, determine if the...Ch. 12.3 - In the following exercises, determine if each...Ch. 12.3 - In the following exercises, determine if each...Ch. 12.3 - In the following exercises, determine if each...Ch. 12.3 - In the following exercises, determine if each...Ch. 12.3 - In the following exercises, determine if each...Ch. 12.3 - In the following exercises, determine if each...Ch. 12.3 - In the following exercises, write the first five...Ch. 12.3 - In the following exercises, write the first five...Ch. 12.3 - In the following exercises, write the first five...Ch. 12.3 - In the following exercises, write the first five...Ch. 12.3 - In the following exercises, write the first five...Ch. 12.3 - In the following exercises, write the first five...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the indicated...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of the...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, find the sum of each...Ch. 12.3 - In the following exercises, write each repeating...Ch. 12.3 - In the following exercises, write each repeating...Ch. 12.3 - In the following exercises, write each repeating...Ch. 12.3 - In the following exercises, write each repeating...Ch. 12.3 - In the following exercises, write each repeating...Ch. 12.3 - In the following exercises, write each repeating...Ch. 12.3 - In the following exercises, solve the problem....Ch. 12.3 - In the following exercises, solve the problem....Ch. 12.3 - In the following exercises, solve the problem....Ch. 12.3 - In the following exercises, solve the problem....Ch. 12.3 - In the following exercises, solve the problem....Ch. 12.3 - In your own words, explain how to determine...Ch. 12.3 - In your own words, explain how to find the general...Ch. 12.3 - In your own words, explain the difference between...Ch. 12.3 - In your own words, explain how to determine if an...Ch. 12.4 - Use Pascal’s Triangle to expand (x+y)5.Ch. 12.4 - Use Pascal’s Triangle to expand (p+q)7.Ch. 12.4 - Use Pascal’s Triangle to expand (x+2)4.Ch. 12.4 - Use Pascal’s Triangle to expand (x+1)6.Ch. 12.4 - Use Pascal’s Triangle to expand (2x3)4.Ch. 12.4 - Use Pascal’s Triangle to expand (2x1)6.Ch. 12.4 - Evaluate each binomial coefficient: (a)(61)...Ch. 12.4 - Evaluate each binomial coefficient: (a)(21) (b)(...Ch. 12.4 - Use the Binomial Theorem to expand (x+y)5.Ch. 12.4 - Use the Binomial Theorem to expand (m+n)6.Ch. 12.4 - Use the Binomial Theorem to expand (x3)5.Ch. 12.4 - Use the Binomial Theorem to expand (y1)6.Ch. 12.4 - Use the Binomial Theorem to expand (3x2y)5.Ch. 12.4 - Use the Binomial Theorem to Expand (4x3y)4.Ch. 12.4 - Find the third term of (x+y)6.Ch. 12.4 - Find the fifth term of (a+b)8.Ch. 12.4 - Find the coefficient of the x5 term of (x+4)8.Ch. 12.4 - Find the coefficient of the x4 term of (x+2)7.Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, expand each binomial...Ch. 12.4 - In the following exercises, evaluate. 210. (a)...Ch. 12.4 - In the following exercises, evaluate. 211. (a)...Ch. 12.4 - In the following exercises, evaluate. 212. (a)...Ch. 12.4 - In the following exercises, evaluate. 213. (a)...Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, expand each binomial....Ch. 12.4 - In the following exercises, find the indicated...Ch. 12.4 - In the following exercises, find the indicated...Ch. 12.4 - In the following exercises, find the indicated...Ch. 12.4 - In the following exercises, find the indicated...Ch. 12.4 - In the following exercises, find the coefficient...Ch. 12.4 - In the following exercises, find the coefficient...Ch. 12.4 - In the following exercises, find the coefficient...Ch. 12.4 - the following exercises, find the coefficient of...Ch. 12.4 - In the following exercises, find the coefficient...Ch. 12.4 - the following exercises, find the coefficient of...Ch. 12.4 - your own words explain how to find the rows of the...Ch. 12.4 - In your own words, explain the pattern of...Ch. 12.4 - In your own words, explain the difference between...Ch. 12.4 - your own words, explain how to find a specific...Ch. 12 - In the following exercises, write the first five...Ch. 12 - the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, find a general term...Ch. 12 - In the following exercises, find a general term...Ch. 12 - In the following exercises, find a general term...Ch. 12 - In the following exercises, find a general term...Ch. 12 - In the following exercises, find a general term...Ch. 12 - In the following exercises, using factorial...Ch. 12 - In the following exercises, using factorial...Ch. 12 - In the following exercises, using factorial...Ch. 12 - In the following exercises, expand the partial sum...Ch. 12 - In the following exercises, expand the partial sum...Ch. 12 - In the following exercises, expand the partial sum...Ch. 12 - In the following exercises, expand the partial sum...Ch. 12 - In the following exercises, write each sum using...Ch. 12 - In the following exercises, write each sum using...Ch. 12 - In the following exercises, write each sum using...Ch. 12 - In the following exercises, determine if each...Ch. 12 - In the following exercises, determine if each...Ch. 12 - In the following exercises, determine if each...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, find the term...Ch. 12 - In the following exercises, find the term...Ch. 12 - In the following exercises, find the term...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the first term...Ch. 12 - In the following exercises, find the first term...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find each sum. 277....Ch. 12 - In the following exercises, find each sum. 278....Ch. 12 - In the following exercises, find each sum. 279....Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find the sum of the...Ch. 12 - In the following exercises, find the sum 294....Ch. 12 - In the following exercises, find the sum 295....Ch. 12 - In the following exercises, find the sum of each...Ch. 12 - In the following exercises, find the sum of each...Ch. 12 - In the following exercises, write each repeating...Ch. 12 - In the following exercises, write each repeating...Ch. 12 - In the following exercises, solve the problem....Ch. 12 - In the following exercises, solve the problem....Ch. 12 - In the following exercises, expand each binomial...Ch. 12 - In the following exercises, expand each binomial...Ch. 12 - In the following exercises, expand each binomial...Ch. 12 - In the following exercises, expand each binomial...Ch. 12 - äIn the following exercises, expand each binomial...Ch. 12 - In the following exercises, evaluate. 307. 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(a)...Ch. 12 - In the following exercises, expand each binomial,...Ch. 12 - In the following exercises, expand each binomial,...Ch. 12 - In the following exercises, expand each binomial,...Ch. 12 - In the following exercises, expand each binomial,...Ch. 12 - In the following exercises, expand each binomial,...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the indicated...Ch. 12 - In the following exercises, find the coefficient...Ch. 12 - In the following exercises, find the coefficient...Ch. 12 - In the following exercises, find the coefficient...Ch. 12 - In the following exercises, write the first five...Ch. 12 - In the following exercises, write the first five...Ch. 12 - Find a general term for the sequence,...Ch. 12 - Expand the partial sum and find its value. i=14(...Ch. 12 - Write the following using summation notation....Ch. 12 - Write the first five terms of the arithmetic...Ch. 12 - Find the twentieth term of an arithmetic sequence...Ch. 12 - Find the twenty-third term of an arithmetic...Ch. 12 - Find the first term and common difference of an...Ch. 12 - Find the sum of the first 25 terms of the...Ch. 12 - Find the sum of the first 50 terms of the...Ch. 12 - Find the sum. i=140(5i21)Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - In the following exercises, determine if the...Ch. 12 - the following exercises, determine if the sequence...Ch. 12 - In the following exercises, find the sum. 338....Ch. 12 - In the following exercises, find the sum. 339....Ch. 12 - In the following exercises, find the sum. 340....Ch. 12 - In the following exercises, find the sum. 341....Ch. 12 - In the following exercises, find the sum. 342....Ch. 12 - In the following exercises, find the sum. 343....Ch. 12 - In the following exercises, find the sum. 344....
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Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
College Algebra
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ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Intermediate Algebra
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ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Binomial Theorem Introduction to Raise Binomials to High Powers; Author: ProfRobBob;https://www.youtube.com/watch?v=G8dHmjgzVFM;License: Standard YouTube License, CC-BY