Elementary Algebra For College Students (10th Edition)
10th Edition
ISBN: 9780134759005
Author: Allen R. Angel, Dennis Runde
Publisher: PEARSON
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Textbook Question
Chapter 3, Problem 22RE
Designing a House The figure at right, above shows plans for a rectangular basement of a house. The dots represents poles in the ground and the lines represent string that has been attached to the poles. The length of the basement is to be 30 feet greater than the width. If a total of 310 feet of string was used to mark off the rooms, determine the width and length of the basement.
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Which statement is true about the graph of the equation y = csc¯¹(x)?
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There is a horizontal asymptote at y = 2.
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Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to-
one iff (f(x1),f(x2),...,f(x) } linearly independent.
(b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a
hyperplane of X.
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Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is
convex set or not, affine set or not.
Write with prove an
application of Hahn-Banach theorem.
Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)
Let M be a proper subspace of a finite dimension vector space X over a field F show that
whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M
or not.
(b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L
prove convex subset of X and hyperspace of X.
Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and
A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that
gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA.
(b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there
Xiff there
exists fE X/10) and tE F such that M=(xE X/ f(x)=t).
(c) Show that the relation equivalent is an equivalence relation on set of norms on a space
X.
Chapter 3 Solutions
Elementary Algebra For College Students (10th Edition)
Ch. 3.1 - Fill in the blanks with the appropriate word,...Ch. 3.1 - Prob. 2ESCh. 3.1 - Fill in the blanks with the appropriate word,...Ch. 3.1 - Prob. 4ESCh. 3.1 - Prob. 5ESCh. 3.1 - Prob. 6ESCh. 3.1 - Prob. 7ESCh. 3.1 - Prob. 8ESCh. 3.1 - Prob. 9ESCh. 3.1 - Prob. 10ES
Ch. 3.1 - Prob. 11ESCh. 3.1 - Prob. 12ESCh. 3.1 - Prob. 13ESCh. 3.1 - Prob. 14ESCh. 3.1 - Prob. 15ESCh. 3.1 - Prob. 16ESCh. 3.1 - Prob. 17ESCh. 3.1 - Prob. 18ESCh. 3.1 - Prob. 19ESCh. 3.1 - Prob. 20ESCh. 3.1 - Prob. 21ESCh. 3.1 - Prob. 22ESCh. 3.1 - Prob. 23ESCh. 3.1 - Prob. 24ESCh. 3.1 - Prob. 25ESCh. 3.1 - Prob. 26ESCh. 3.1 - Prob. 27ESCh. 3.1 - Prob. 28ESCh. 3.1 - Prob. 29ESCh. 3.1 - Prob. 30ESCh. 3.1 - Prob. 31ESCh. 3.1 - Prob. 32ESCh. 3.1 - Prob. 33ESCh. 3.1 - Prob. 34ESCh. 3.1 - Prob. 35ESCh. 3.1 - Prob. 36ESCh. 3.1 - Prob. 37ESCh. 3.1 - Prob. 38ESCh. 3.1 - Prob. 39ESCh. 3.1 - In Exercises 31-44, determine which unknown...Ch. 3.1 - Prob. 41ESCh. 3.1 - Prob. 42ESCh. 3.1 - Prob. 43ESCh. 3.1 - Prob. 44ESCh. 3.1 - Prob. 45ESCh. 3.1 - Prob. 46ESCh. 3.1 - Prob. 47ESCh. 3.1 - Prob. 48ESCh. 3.1 - Prob. 49ESCh. 3.1 - Prob. 50ESCh. 3.1 - Prob. 51ESCh. 3.1 - Prob. 52ESCh. 3.1 - Prob. 53ESCh. 3.1 - Prob. 54ESCh. 3.1 - Prob. 55ESCh. 3.1 - Prob. 56ESCh. 3.1 - Prob. 57ESCh. 3.1 - Prob. 58ESCh. 3.1 - Prob. 59ESCh. 3.1 - Prob. 60ESCh. 3.1 - Prob. 61ESCh. 3.1 - Prob. 62ESCh. 3.1 - Prob. 63ESCh. 3.1 - Prob. 64ESCh. 3.1 - Prob. 65ESCh. 3.1 - Prob. 66ESCh. 3.1 - Prob. 67ESCh. 3.1 - Prob. 68ESCh. 3.1 - Prob. 69ESCh. 3.1 - Prob. 70ESCh. 3.1 - Prob. 71ESCh. 3.1 - Prob. 72ESCh. 3.1 - Prob. 73ESCh. 3.1 - Prob. 74ESCh. 3.1 - Prob. 75ESCh. 3.1 - Prob. 76ESCh. 3.1 - Prob. 77ESCh. 3.1 - Prob. 78ESCh. 3.1 - Prob. 79ESCh. 3.1 - Prob. 80ESCh. 3.1 - Prob. 81ESCh. 3.1 - Prob. 82ESCh. 3.1 - Prob. 83ESCh. 3.1 - Prob. 84ESCh. 3.1 - Prob. 85ESCh. 3.1 - Prob. 86ESCh. 3.1 - Prob. 87ESCh. 3.1 - Prob. 88ESCh. 3.1 - Prob. 89ESCh. 3.1 - Prob. 90ESCh. 3.1 - Prob. 91ESCh. 3.1 - Prob. 92ESCh. 3.1 - Prob. 93ESCh. 3.1 - Prob. 94ESCh. 3.1 - Prob. 95ESCh. 3.1 - Prob. 96ESCh. 3.1 - Prob. 97ESCh. 3.1 - Prob. 98ESCh. 3.1 - Prob. 99ESCh. 3.1 - Prob. 100ESCh. 3.1 - Prob. 101ESCh. 3.1 - Prob. 102ESCh. 3.1 - Prob. 103ESCh. 3.1 - Prob. 104ESCh. 3.1 - Prob. 105ESCh. 3.1 - Prob. 106ESCh. 3.1 - Prob. 107ESCh. 3.1 - Prob. 108ESCh. 3.1 - Prob. 109ESCh. 3.1 - Prob. 110ESCh. 3.1 - In Exercises 99-132, write an equation to...Ch. 3.1 - Prob. 112ESCh. 3.1 - Prob. 113ESCh. 3.1 - Prob. 114ESCh. 3.1 - Prob. 115ESCh. 3.1 - Prob. 116ESCh. 3.1 - Prob. 117ESCh. 3.1 - Prob. 118ESCh. 3.1 - Prob. 119ESCh. 3.1 - Prob. 120ESCh. 3.1 - Prob. 121ESCh. 3.1 - Prob. 122ESCh. 3.1 - Prob. 123ESCh. 3.1 - Prob. 124ESCh. 3.1 - Prob. 125ESCh. 3.1 - Prob. 126ESCh. 3.1 - Prob. 127ESCh. 3.1 - Prob. 128ESCh. 3.1 - Prob. 129ESCh. 3.1 - Prob. 130ESCh. 3.1 - Prob. 131ESCh. 3.1 - Prob. 132ESCh. 3.1 - Time a. Write an algebraic expression for the...Ch. 3.1 - Prob. 134ESCh. 3.1 - Prob. 135ESCh. 3.1 - Prob. 136ESCh. 3.1 - Prob. 137ESCh. 3.1 - Prob. 138ESCh. 3.1 - Prob. 139ESCh. 3.1 - Solve the inequality 2x43. Graph the solution on a...Ch. 3.2 - Prob. 1ESCh. 3.2 - Prob. 2ESCh. 3.2 - Prob. 3ESCh. 3.2 - Prob. 4ESCh. 3.2 - Prob. 5ESCh. 3.2 - Prob. 6ESCh. 3.2 - Prob. 7ESCh. 3.2 - Prob. 8ESCh. 3.2 - Prob. 9ESCh. 3.2 - Prob. 10ESCh. 3.2 - Prob. 11ESCh. 3.2 - Prob. 12ESCh. 3.2 - Prob. 13ESCh. 3.2 - Prob. 14ESCh. 3.2 - Prob. 15ESCh. 3.2 - Prob. 16ESCh. 3.2 - Prob. 17ESCh. 3.2 - Prob. 18ESCh. 3.2 - Prob. 19ESCh. 3.2 - Prob. 20ESCh. 3.2 - Prob. 21ESCh. 3.2 - Prob. 22ESCh. 3.2 - Prob. 23ESCh. 3.2 - Exercises 7-32 involve determining a number or...Ch. 3.2 - Prob. 25ESCh. 3.2 - Prob. 26ESCh. 3.2 - Prob. 27ESCh. 3.2 - Prob. 28ESCh. 3.2 - Exercises 7-32 involve determining a number or...Ch. 3.2 - Prob. 30ESCh. 3.2 - Prob. 31ESCh. 3.2 - Prob. 32ESCh. 3.2 - Prob. 33ESCh. 3.2 - Prob. 34ESCh. 3.2 - Prob. 35ESCh. 3.2 - Prob. 36ESCh. 3.2 - Prob. 37ESCh. 3.2 - Prob. 38ESCh. 3.2 - Prob. 39ESCh. 3.2 - Prob. 40ESCh. 3.2 - Prob. 41ESCh. 3.2 - Prob. 42ESCh. 3.2 - Prob. 43ESCh. 3.2 - Prob. 44ESCh. 3.2 - Prob. 45ESCh. 3.2 - Prob. 46ESCh. 3.2 - Prob. 47ESCh. 3.2 - Prob. 48ESCh. 3.2 - Prob. 49ESCh. 3.2 - Prob. 50ESCh. 3.2 - Prob. 51ESCh. 3.2 - Prob. 52ESCh. 3.2 - Prob. 53ESCh. 3.2 - Prob. 54ESCh. 3.2 - Prob. 55ESCh. 3.2 - Prob. 56ESCh. 3.2 - Prob. 57ESCh. 3.2 - Prob. 58ESCh. 3.2 - Prob. 59ESCh. 3.2 - Prob. 60ESCh. 3.2 - Exercises 47-68 involve percents. Read Examples...Ch. 3.2 - Prob. 62ESCh. 3.2 - Prob. 63ESCh. 3.2 - Prob. 64ESCh. 3.2 - Prob. 65ESCh. 3.2 - Prob. 66ESCh. 3.2 - Prob. 67ESCh. 3.2 - Prob. 68ESCh. 3.2 - Prob. 69ESCh. 3.2 - Prob. 70ESCh. 3.2 - Prob. 71ESCh. 3.2 - Prob. 72ESCh. 3.2 - Prob. 73ESCh. 3.2 - Prob. 74ESCh. 3.2 - Prob. 75ESCh. 3.2 - Prob. 76ESCh. 3.3 - Prob. 1ESCh. 3.3 - Prob. 2ESCh. 3.3 - Prob. 3ESCh. 3.3 - Prob. 4ESCh. 3.3 - Prob. 5ESCh. 3.3 - Prob. 6ESCh. 3.3 - Prob. 7ESCh. 3.3 - Fill the blanks with the appropriate word, phrase,...Ch. 3.3 - Prob. 9ESCh. 3.3 - Prob. 10ESCh. 3.3 - Triangular Building This building in New York...Ch. 3.3 - Prob. 12ESCh. 3.3 - Prob. 13ESCh. 3.3 - Prob. 14ESCh. 3.3 - Prob. 15ESCh. 3.3 - Prob. 16ESCh. 3.3 - Prob. 17ESCh. 3.3 - Prob. 18ESCh. 3.3 - Prob. 19ESCh. 3.3 - Prob. 20ESCh. 3.3 - Prob. 21ESCh. 3.3 - Prob. 22ESCh. 3.3 - Prob. 23ESCh. 3.3 - Prob. 24ESCh. 3.3 - Prob. 25ESCh. 3.3 - Prob. 26ESCh. 3.3 - Prob. 27ESCh. 3.3 - Parallelogram The two smaller angles of a...Ch. 3.3 - Prob. 29ESCh. 3.3 - Prob. 30ESCh. 3.3 - Prob. 31ESCh. 3.3 - Prob. 32ESCh. 3.3 - Building a Bookcase A bookcase is have four...Ch. 3.3 - Prob. 34ESCh. 3.3 - Prob. 35ESCh. 3.3 - Prob. 36ESCh. 3.3 - Prob. 37ESCh. 3.3 - Storage Shelves Carlotta plans to build storage...Ch. 3.3 - Prob. 39ESCh. 3.3 - Prob. 40ESCh. 3.3 - Prob. 41ESCh. 3.3 - Prob. 42ESCh. 3.3 - Prob. 43ESCh. 3.3 - Prob. 44ESCh. 3.3 - Simplify 7y+x3(x2)+2y.Ch. 3.3 - Prob. 46ESCh. 3.4 - Fill in the blanks with appropriate word, phrase,...Ch. 3.4 - Fill in the blanks with appropriate word, phrase,...Ch. 3.4 - Prob. 3ESCh. 3.4 - Prob. 4ESCh. 3.4 - Prob. 5ESCh. 3.4 - Prob. 6ESCh. 3.4 - Prob. 7ESCh. 3.4 - Prob. 8ESCh. 3.4 - Prob. 9ESCh. 3.4 - Prob. 10ESCh. 3.4 - In Exercises 7-32, set up an equation that can be...Ch. 3.4 - Prob. 12ESCh. 3.4 - Prob. 13ESCh. 3.4 - Prob. 14ESCh. 3.4 - Prob. 15ESCh. 3.4 - Prob. 16ESCh. 3.4 - Prob. 17ESCh. 3.4 - Prob. 18ESCh. 3.4 - Prob. 19ESCh. 3.4 - Prob. 20ESCh. 3.4 - Prob. 21ESCh. 3.4 - Prob. 22ESCh. 3.4 - Prob. 23ESCh. 3.4 - Prob. 24ESCh. 3.4 - Prob. 25ESCh. 3.4 - Prob. 26ESCh. 3.4 - Prob. 27ESCh. 3.4 - Prob. 28ESCh. 3.4 - Prob. 29ESCh. 3.4 - Prob. 30ESCh. 3.4 - Prob. 31ESCh. 3.4 - Prob. 32ESCh. 3.4 - Prob. 33ESCh. 3.4 - Prob. 34ESCh. 3.4 - Prob. 35ESCh. 3.4 - Prob. 36ESCh. 3.4 - Prob. 37ESCh. 3.4 - Prob. 38ESCh. 3.4 - Prob. 39ESCh. 3.4 - Prob. 40ESCh. 3.4 - Prob. 41ESCh. 3.4 - Prob. 42ESCh. 3.4 - Prob. 43ESCh. 3.4 - In Exercises 33-46, set up an equation that can be...Ch. 3.4 - Prob. 45ESCh. 3.4 - Prob. 46ESCh. 3.4 - Prob. 47ESCh. 3.4 - Prob. 48ESCh. 3.4 - Prob. 49ESCh. 3.4 - Prob. 50ESCh. 3.4 - Prob. 51ESCh. 3.4 - Prob. 52ESCh. 3.4 - Prob. 53ESCh. 3.4 - Prob. 54ESCh. 3.4 - Prob. 55ESCh. 3.4 - Prob. 56ESCh. 3.4 - In Exercises 47-66, set up an equation that can be...Ch. 3.4 - Prob. 58ESCh. 3.4 - Prob. 59ESCh. 3.4 - Prob. 60ESCh. 3.4 - Prob. 61ESCh. 3.4 - Prob. 62ESCh. 3.4 - Prob. 63ESCh. 3.4 - Prob. 64ESCh. 3.4 - Prob. 65ESCh. 3.4 - Prob. 66ESCh. 3.4 - Prob. 67ESCh. 3.4 - Prob. 68ESCh. 3.4 - Discuss and answer Exercises 68 and 69 as a group....Ch. 3.4 - Prob. 70ESCh. 3.4 - Prob. 71ESCh. 3.4 - Prob. 72ESCh. 3.4 - Prob. 73ESCh. 3 - In Exercises 1-6, express each statement as an...Ch. 3 - Prob. 2MCTCh. 3 - Prob. 3MCTCh. 3 - Prob. 4MCTCh. 3 - In Exercises 1-6, express each statement as an...Ch. 3 - In Exercises 1-6, express each statement as an...Ch. 3 - Prob. 7MCTCh. 3 - Prob. 8MCTCh. 3 - Select a variable to represent one quantity and...Ch. 3 - Prob. 10MCTCh. 3 - In Exercises 10-12, write the problem as an...Ch. 3 - Prob. 12MCTCh. 3 - Prob. 13MCTCh. 3 - Prob. 14MCTCh. 3 - Prob. 15MCTCh. 3 - Prob. 16MCTCh. 3 - Prob. 17MCTCh. 3 - Prob. 18MCTCh. 3 - Prob. 19MCTCh. 3 - Prob. 20MCTCh. 3 - Prob. 1RECh. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - Prob. 10RECh. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Prob. 13RECh. 3 - In Exercises 9-18, set up an equation that can be...Ch. 3 - Prob. 15RECh. 3 - Prob. 16RECh. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Designing a House The figure at right, above shows...Ch. 3 - Rhombus The two larger angles of a rhombus are...Ch. 3 - Bookcase Wade is building a bookcase with 4...Ch. 3 - Prob. 25RECh. 3 - Trains Leaving Two trains going in opposite...Ch. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Prob. 32RECh. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Prob. 35RECh. 3 - Prob. 36RECh. 3 - Prob. 37RECh. 3 - Prob. 38RECh. 3 - Prob. 39RECh. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Speed Traveled Two brothers who are 230 miles...Ch. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 9PTCh. 3 - Prob. 10PTCh. 3 - Prob. 11PTCh. 3 - Prob. 12PTCh. 3 - Prob. 13PTCh. 3 - Prob. 14PTCh. 3 - Prob. 15PTCh. 3 - Prob. 16PTCh. 3 - Prob. 17PTCh. 3 - Prob. 18PTCh. 3 - Prob. 19PTCh. 3 - Prob. 20PTCh. 3 - Prob. 21PTCh. 3 - Prob. 22PTCh. 3 - Prob. 23PTCh. 3 - Prob. 24PTCh. 3 - Prob. 25PTCh. 3 - Prob. 1CRTCh. 3 - Prob. 2CRTCh. 3 - Prob. 3CRTCh. 3 - Prob. 4CRTCh. 3 - Prob. 5CRTCh. 3 - Prob. 6CRTCh. 3 - Prob. 7CRTCh. 3 - Prob. 8CRTCh. 3 - Prob. 9CRTCh. 3 - Prob. 10CRTCh. 3 - Prob. 11CRTCh. 3 - Prob. 12CRTCh. 3 - Prob. 13CRTCh. 3 - Prob. 14CRTCh. 3 - Prob. 15CRTCh. 3 - Prob. 16CRTCh. 3 - Prob. 17CRTCh. 3 - Prob. 18CRTCh. 3 - Prob. 19CRTCh. 3 - Quadrilateral One angle of a quadrilateral...
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