Intermediate Algebra (8th Edition)
8th Edition
ISBN: 9780134178967
Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford
Publisher: PEARSON
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Chapter 3.6, Problem 20E
To determine
To graph: The function
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
Chapter 3 Solutions
Intermediate Algebra (8th Edition)
Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4
1. Graphs...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4
2. The...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 3.1 - Verbal and Writing Skills, Exercises 1-4 (5, 1) is...Ch. 3.1 - Find the missing coordinate. ( − 2 , _ _ _ _ ) is...Ch. 3.1 - Find the missing coordinate. ( − 5 , _ _ _ _ ) is...Ch. 3.1 - Find the missing coordinate.
7. is a solution of...Ch. 3.1 - Find the missing coordinate. ( _ _ _ _ _ , 2 3 )...Ch. 3.1 - Graph each equation. y = 2 x − 3Ch. 3.1 - Graph each equation.
10.
Ch. 3.1 - Graph each equation. y = 1 − 3 xCh. 3.1 - Graph each equation.
12.
Ch. 3.1 - Graph each equation.
12.
Ch. 3.1 - Graph each equation. y = 5 2 x + 1Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. Find the...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify the equation if possible. State whether...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Simplify each equation if possible. Then graph the...Ch. 3.1 - Graph each equation. Use appropriate scales on...Ch. 3.1 - Graph each equation. Use appropriate scales on...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Income of Men Versus Women The following graph...Ch. 3.1 - Prob. 42ECh. 3.1 - 43. Baseball If a baseball is thrown vertically...Ch. 3.1 - 44. Gasoline Storage Tank A full storage tank on...Ch. 3.1 - [1.3.3] Evaluate 36 ÷ ( 8 − 6 ) 2 + 3 ( − 4 )Ch. 3.1 - Prob. 46ECh. 3.1 - 47. [2.4.1.] Balloon Giveaway A novelty company is...Ch. 3.1 - Prob. 48ECh. 3.1 - Prob. 1QQCh. 3.1 - Prob. 2QQCh. 3.1 - Prob. 3QQCh. 3.1 - Prob. 4QQCh. 3.2 - Verbal and Writing Skills, Exercises 1-6 Slope...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6 A...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6 The slope...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6
4. Two...Ch. 3.2 - Verbal and Writing Skills, Exercises 1-6
5. Does...Ch. 3.2 - Prob. 6ECh. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - Find the slope, if possible, of the line passing...Ch. 3.2 - 19. Snowboarding Find the slope (grade) of a...Ch. 3.2 - 20. Grade of a Road Find the grade of a mountain...Ch. 3.2 - Rock Formation Find the slope (pitch) of a...Ch. 3.2 - Pitch of a Roof Find the slope (pitch) of a roof...Ch. 3.2 - 23. Slope of Street Baldwin Street in Dunedin, New...Ch. 3.2 - 24. Slope of a Roller Coaster Goliath at Six Flags...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Prob. 29ECh. 3.2 - Find the slope of a line parallel to the line that...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Find the slope of a line perpendicular to the line...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - A line k passes through the points ( − 3 , − 9 )...Ch. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - 40. Do the points , and C(8,1) lie on a straight...Ch. 3.2 - 41. Architect Most new buildings are required to...Ch. 3.2 - Rate of Climb of Aircraft A small Cessna plane...Ch. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 1QQCh. 3.2 - Prob. 2QQCh. 3.2 - Prob. 3QQCh. 3.2 - Prob. 4QQCh. 3.3 - Verbal and Writing Skills, Exercises 1 and 2 You...Ch. 3.3 - Verbal and Writing Skills, Exercises 1 and 2
2....Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Write an equation of the line with the given slope...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Find the slope and y-intercept of each of the...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Prob. 17ECh. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - Write each equation in slope-intercept form. Then...Ch. 3.3 - For each equation find the slope and the...Ch. 3.3 - Prob. 23ECh. 3.3 - For each equation find the slope and the...Ch. 3.3 - For each equation find the slope and the...Ch. 3.3 - Prob. 26ECh. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line that passes through...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Find an equation of the line passing through the...Ch. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Prob. 44ECh. 3.3 - Find an equation of the line satisfying the...Ch. 3.3 - Prob. 46ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 48ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 50ECh. 3.3 - Without graphing, determine whether the following...Ch. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Cost of Homes The median sale price of...Ch. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 1QQCh. 3.3 - Prob. 2QQCh. 3.3 - Prob. 3QQCh. 3.3 - Prob. 4QQCh. 3.4 - Verbal and Writing Skills, Exercises 1-6 Explain...Ch. 3.4 - Prob. 2ECh. 3.4 - Verbal and Writing Skills, Exercises 1-6 When...Ch. 3.4 - Prob. 4ECh. 3.4 - Verbal and Writing Skills, Exercises 1-6
5. When...Ch. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Graph each region.
9.
Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Graph each region. 6 y − x ≤ 12Ch. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Graph each region.
17.
Ch. 3.4 - Graph each region. x − 3 y ≥ 0Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Prob. 22ECh. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Simplify and graph each inequality in a...Ch. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 1QQCh. 3.4 - Prob. 2QQCh. 3.4 - Prob. 3QQCh. 3.4 - Prob. 4QQCh. 3.5 - Verbal and Writing Skills, Exercises 1-4 Explain...Ch. 3.5 - Prob. 2ECh. 3.5 - Verbal and Writing Skills, Exercises 1-4 What are...Ch. 3.5 - Prob. 4ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 10ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 12ECh. 3.5 - What are the domain and range of each relation? Is...Ch. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a function.Ch. 3.5 - Determine whether the graph represents a...Ch. 3.5 - Prob. 26ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 28ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 30ECh. 3.5 - Given the function defined by h ( x ) = 3 4 x + 1...Ch. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Given the function defined by r ( x ) = 2 x 2 − 4...Ch. 3.5 - Prob. 36ECh. 3.5 - Given the function defined by , find the...Ch. 3.5 - Prob. 38ECh. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - Given the function defined by t ( x ) = x 3 − 3 x...Ch. 3.5 - 42. If , find
Ch. 3.5 - 43. If , find
Ch. 3.5 - Prob. 44ECh. 3.5 - 45. If , find g (2).
Ch. 3.5 - Prob. 46ECh. 3.5 - Find the range of the function for the given...Ch. 3.5 - Prob. 48ECh. 3.5 - Find the domain of the function for the given...Ch. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 1QQCh. 3.5 - Prob. 2QQCh. 3.5 - Prob. 3QQCh. 3.5 - Prob. 4QQCh. 3.6 - Graph each function. f ( x ) = 3 4 x + 2Ch. 3.6 - Prob. 2ECh. 3.6 - Graph each function.
3.
Ch. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Wildlife Biologist Ning is a wildlife biologist...Ch. 3.6 - Insulation in a House The R value of insulation in...Ch. 3.6 - Graph each function.
9.
Ch. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Graph each function.
13.
Ch. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Graph each function.
19.
Ch. 3.6 - Prob. 20ECh. 3.6 - Graph each function.
21.
Ch. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - In each of the following problems, a table of...Ch. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - In each of the following problems, a table of...Ch. 3.6 - Prob. 32ECh. 3.6 - Computer Manufacturing The following table shows...Ch. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 1QQCh. 3.6 - Prob. 2QQCh. 3.6 - Prob. 3QQCh. 3.6 - Concept Check Explain how you would find f ( 1 4 )...Ch. 3 - Graph the straight line determined by each of the...Ch. 3 - Graph the straight line determined by each of the...Ch. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - 8. Find the slope of a line perpendicular to the...Ch. 3 - 9. A line has a slope of and a y-intercept of (0,...Ch. 3 - Find the standard form of the equation of the line...Ch. 3 - 11. Find the standard form of the equation of the...Ch. 3 - 12. Computer Company Profit A computer company's...Ch. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - Prob. 15RPCh. 3 - In exercises 13 - 16, find an equation of the line...Ch. 3 - In exercises 17 - 18, find the slope and...Ch. 3 - In exercises 17 -18, find the slope and...Ch. 3 - Prob. 19RPCh. 3 - Graph the region described by the inequality.
20....Ch. 3 - Graph the region described by the inequality. 3 x...Ch. 3 - Graph the region described by the inequality. x ≤...Ch. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - What is the domain and range of each relation? Is...Ch. 3 - What is the domain and range of each relation? Is...Ch. 3 - Determine whether the graph represents a function.Ch. 3 - Determine whether the graph represents a function.Ch. 3 - If f ( x ) = − 2 x + 10 , find f ( − 1 ) and f ( −...Ch. 3 - If h ( x ) = x 3 + 2 x 2 − 5 x + 8 , find h ( − 1...Ch. 3 - Graph each function. f ( x ) = 2 | x − 1 |Ch. 3 - Prob. 32RPCh. 3 - Prob. 33RPCh. 3 - Prob. 34RPCh. 3 - Prob. 35RPCh. 3 - Prob. 36RPCh. 3 - Complete the table of values for each...Ch. 3 - 38. Find the slope and y-intercept of .
Ch. 3 - A line n is perpendicular to the line passing...Ch. 3 - A line p is parallel to the line passing through...Ch. 3 - Find the standard form of the equation of the line...Ch. 3 - 42. Find an equation of the line parallel to and...Ch. 3 - Find the slope-intercept form of the equation of...Ch. 3 - Prob. 44RPCh. 3 - Prob. 45RPCh. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Prob. 48RPCh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Find the slope of the line passing through ( 2 , −...Ch. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Write an equation of the horizontal line passing...Ch. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - 15. If , find f .
Ch. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 1CTCh. 3 - Evaluate the expression. 3 ( 4 − 6 ) 2 + 16 + 12 ÷...Ch. 3 - Prob. 3CTCh. 3 - Prob. 4CTCh. 3 - Prob. 5CTCh. 3 - Prob. 6CTCh. 3 - Prob. 7CTCh. 3 - Prob. 8CTCh. 3 - Prob. 9CTCh. 3 - Prob. 10CTCh. 3 - Prob. 11CTCh. 3 - Prob. 12CTCh. 3 - Prob. 13CTCh. 3 - Prob. 14CTCh. 3 - Prob. 15CTCh. 3 - Prob. 16CTCh. 3 - Prob. 17CTCh. 3 - Prob. 18CTCh. 3 - Prob. 19CTCh. 3 - Prob. 20CTCh. 3 - Prob. 21CTCh. 3 - Prob. 22CTCh. 3 - Prob. 23CTCh. 3 - Prob. 24CTCh. 3 - Prob. 25CT
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