Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)
8th Edition
ISBN: 9780134578507
Author: John Tobey Jr., Jeffrey Slater, Jenny Crawford, Jamie Blair
Publisher: PEARSON
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Textbook Question
Chapter 6.1, Problem 56E
Tropical Fish The total number of fish will depend on the size of a pond or aquarium. At the Reading Mandarin Restaurant a total of 90 tropical fish were placed in an aquarium. For the next 12 months the total number of fish could be predicted by the equation
where P is the number of fish and x is the number of months since the fish were placed in the aquarium.
One year after the fish are first placed in me aquarium, what is me total
number of fish? Round your answer to the nearest whole number.
Using your answers for exercises 51 to 54, graph the function
P(a).
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1.2.19. Let and s be natural numbers. Let G be the simple graph with vertex set
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Question 3
over a field K.
In this question, MË(K) denotes the set of n × n matrices
(a) Suppose that A Є Mn(K) is an invertible matrix. Is it always true that A is
equivalent to A-¹? Justify your answer.
(b) Let B be given by
8
B = 0 7 7
0 -7 7
Working over the field F2 with 2 elements, compute the rank of B as an element
of M2(F2).
(c) Let
1
C
-1 1
[4]
[6]
and consider C as an element of M3(Q). Determine the minimal polynomial
mc(x) and hence, or otherwise, show that C can not be diagonalised.
[7]
(d) Show that C in (c) considered as an element of M3(R) can be diagonalised. Write
down all the eigenvalues. Show your working.
[8]
R denotes the field of real numbers, Q denotes the field of rationals, and
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results from lectures.
Question 1
For each non-negative integer m, let R[x]m denote the
vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m.
x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent
(a) Let vi = x, V2 =
list in R[x] 3.
(b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4)
is a basis of R[x] 3.
[8]
[6]
(c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a
linear map.
[6]
(d) Write down the matrix for the map ƒ defined in (c) with respect to the basis
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[5]
Chapter 6 Solutions
Intermediate Algebra Books a la Carte Edition PLUS MyLab Math (8th Edition)
Ch. 6.1 - Find the domain of each of the following rational...Ch. 6.1 - Find the domain of each of the following rational...Ch. 6.1 - Find the domain of each of the following rational...Ch. 6.1 - Prob. 4ECh. 6.1 - Simplify completely. − 18 x 4 y 12 x 2 y 6Ch. 6.1 - Simplify completely. − 7 x y 2 28 x 5 yCh. 6.1 - Prob. 7ECh. 6.1 - Simplify completely. 24 x 2 − 4 x 4 x 2 − 8 xCh. 6.1 - Simplify completely. 8 x 2 28 x 2 + 4 xCh. 6.1 - Simplify completely. 30 x 2 6 x 2 + 18 x
Ch. 6.1 - Simplify completely.
11.
Ch. 6.1 - Simplify completely. 6 m 2 n 4 + 2 m n 3 4 m n 2 −...Ch. 6.1 - Simplify completely.
13.
Ch. 6.1 - Simplify completely. 6 x 2 − 15 x 3 xCh. 6.1 - Simplify completely.
15.
Ch. 6.1 - Simplify completely. x + 2 7 x 2 − 28Ch. 6.1 - Simplify completely.
17.
Ch. 6.1 - Simplify completely.
18.
Ch. 6.1 - Simplify completely 2 y 2 + y − 10 4 − y 2Ch. 6.1 - Simplify completely.
20.
Ch. 6.1 - Multiply.
21.
Ch. 6.1 - Multiply. 24 x 4 y 2 − 12 x 5 y ⋅ 8 x 3 30 x 2 yCh. 6.1 - Multiply. 3 a 2 a 2 + 4 a + 4 ⋅ a 2 − 4 3 aCh. 6.1 - Multiply.
24.
Ch. 6.1 - Multiply.
25.
Ch. 6.1 - Multiply.
26.
Ch. 6.1 - Multiply. x 2 − 3 x y − 10 y 2 x + y ⋅ x 2 + 7 x y...Ch. 6.1 - Multiply.
28.
Ch. 6.1 - Multiply. y 2 − y − 12 2 y 2 + y − 1 ⋅ 2 x y 2 + 7...Ch. 6.1 - Multiply.
30.
Ch. 6.1 - Multiply.
31.
Ch. 6.1 - Prob. 32ECh. 6.1 - Divide. 2 m n − m 15 m 3 ÷ 2 n − 1 3 m 2Ch. 6.1 - Prob. 34ECh. 6.1 - Divide.
35.
Ch. 6.1 - Divide. a 2 − 3 a a 2 − 9 ÷ a 3 − a 2 4 a 2 − a −...Ch. 6.1 - Divide. x 2 − x y − 6 y 2 x 2 + 2 ÷ ( x 2 + 2 x y...Ch. 6.1 - Divide. x 2 − 5 x + 4 2 x − 8 ÷ ( 3 x 2 − 3 x )Ch. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - Perform the operation indicated When no operation...Ch. 6.1 - Prob. 44ECh. 6.1 - Perform the operation indicated When no operation...Ch. 6.1 - Prob. 46ECh. 6.1 - Perform the operation indicated When no operation...Ch. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Tropical Fish The total number of fish will depend...Ch. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - Tropical Fish The total number of fish will depend...Ch. 6.1 - Tropical Fish The total number of fish will depend...Ch. 6.1 - 57. [2.6.3] Solve.
Ch. 6.1 - 58. [5.1.6] Multiply.
Ch. 6.1 - 59. [1.2.2] Motorcyclist Deaths Between 2008 and...Ch. 6.1 - Prob. 1QQCh. 6.1 - Prob. 2QQCh. 6.1 - Prob. 3QQCh. 6.1 - Prob. 4QQCh. 6.2 - Verbal and Writing Skills, Exercises 1 and 2
1....Ch. 6.2 - Prob. 2ECh. 6.2 - Find the LCD. 3 x − 1 , 4 x 2 − 2 x + 1Ch. 6.2 - Prob. 4ECh. 6.2 - Find the LCD.
5.
Ch. 6.2 - Prob. 6ECh. 6.2 - Find the LCD. 3 x ( 2 x + 5 ) 3 , x − 2 ( x + 1...Ch. 6.2 - Prob. 8ECh. 6.2 - Find the LCD. 2 y 2 x 2 + x , 11 x y 15 x 2 − x...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Add or subtract and simplify your answers.
13.
Ch. 6.2 - Prob. 14ECh. 6.2 - Add or subtract and simplify your answers. 3 x 2 −...Ch. 6.2 - Prob. 16ECh. 6.2 - Add or subtract and simplify your answers.
17.
Ch. 6.2 - Prob. 18ECh. 6.2 - Add or subtract and simplify your answers. − 5 y y...Ch. 6.2 - Prob. 20ECh. 6.2 - Add or subtract and simplify your answers.
21.
Ch. 6.2 - Prob. 22ECh. 6.2 - Add or subtract and simplify your answers. 5 x − 4...Ch. 6.2 - Prob. 24ECh. 6.2 - Add or subtract and simplify your answers.
25.
Ch. 6.2 - Add or subtract and simplify your answers.
26.
Ch. 6.2 - Add or subtract and simplify your answers. 4 y y 2...Ch. 6.2 - Prob. 28ECh. 6.2 - Add or subtract and simplify your answers. a + 2 +...Ch. 6.2 - Prob. 30ECh. 6.2 - 31. Artificial Lung If an artificial lung company...Ch. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - 34. Artificial Heart Determine the daily profit of...Ch. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - 37. [2.5.1] Purchase Price of Automobiles Jamie,...Ch. 6.2 - Prob. 38ECh. 6.2 - Prob. 1QQCh. 6.2 - Prob. 2QQCh. 6.2 - Prob. 3QQCh. 6.2 - Prob. 4QQCh. 6.3 - Simplify the complex fractions by any method.
1.
Ch. 6.3 - Prob. 2ECh. 6.3 - Simplify the complex fractions by any method. − 4...Ch. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Simplify the complex fractions by any method. 3 2...Ch. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Simplify the complex fractions by any method.
19....Ch. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 1QQCh. 6.3 - Prob. 2QQCh. 6.3 - Prob. 3QQCh. 6.3 - Prob. 4QQCh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 2ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 4ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 9ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 14ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 16ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 18ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 22ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 24ECh. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Solve the equations and check your solutions. If...Ch. 6.4 - Prob. 28ECh. 6.4 - Verbal and Writing Skills In what situations will...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Factor completely. [5.7.1] 2 x 2 + 20 x + 50Ch. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Factor completely. [5.2.2] Divide. ( 2 x 3 − 3 x 2...Ch. 6.4 - Prob. 1QQCh. 6.4 - Prob. 2QQCh. 6.4 - Prob. 3QQCh. 6.4 - Prob. 4QQCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Solve for the indicated variable.
3.
Ch. 6.5 - Solve for the indicated variable 1 f = 1 a + 1 b ;...Ch. 6.5 - Solve for the indicated variable. V l h = w ; ...Ch. 6.5 - Solve for the indicated variable r = I p t ; for...Ch. 6.5 - Solve for the indicated variable.
7.
Ch. 6.5 - Solve for the indicated variable.
8.
Ch. 6.5 - Solve for the indicated variable r 3 V = 3 4 π ; ...Ch. 6.5 - Solve for the indicated variable
10.
Ch. 6.5 - Solve for the indicated variable. F = k q 1 q 2 r...Ch. 6.5 - Solve for the indicated variable. F = k q 1 q 2 r...Ch. 6.5 - Solve for the indicated variable. Q R 1 S 1 = Q R...Ch. 6.5 - Solve for the indicated variable. Q R 1 S 1 = Q R...Ch. 6.5 - Prob. 15ECh. 6.5 - Prob. 16ECh. 6.5 - Prob. 17ECh. 6.5 - Prob. 18ECh. 6.5 - Prob. 19ECh. 6.5 - Prob. 20ECh. 6.5 - Prob. 21ECh. 6.5 - Prob. 22ECh. 6.5 - Prob. 23ECh. 6.5 - Prob. 24ECh. 6.5 - Prob. 25ECh. 6.5 - Prob. 26ECh. 6.5 - Prob. 27ECh. 6.5 - Prob. 28ECh. 6.5 - Prob. 29ECh. 6.5 - Prob. 30ECh. 6.5 - Map Scale On a map of Nigeria, the cities of Benin...Ch. 6.5 - Prob. 32ECh. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - In exercises 35-50, round your answers to the...Ch. 6.5 - Prob. 36ECh. 6.5 - Prob. 37ECh. 6.5 - Prob. 38ECh. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - Prob. 42ECh. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - Prob. 45ECh. 6.5 - Prob. 46ECh. 6.5 - Prob. 47ECh. 6.5 - Prob. 48ECh. 6.5 - In exercises 35-50, round your answers to the...Ch. 6.5 - Prob. 50ECh. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Prob. 53ECh. 6.5 - Prob. 54ECh. 6.5 - Prob. 55ECh. 6.5 - Prob. 56ECh. 6.5 - Prob. 1QQCh. 6.5 - Prob. 2QQCh. 6.5 - Prob. 3QQCh. 6.5 - Prob. 4QQCh. 6 - Simplify.
1.
Ch. 6 - Prob. 2RPCh. 6 - Prob. 3RPCh. 6 - Prob. 4RPCh. 6 - Prob. 5RPCh. 6 - Prob. 6RPCh. 6 - Prob. 7RPCh. 6 - Prob. 8RPCh. 6 - Simplify.
9.
Ch. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 12RPCh. 6 - Prob. 13RPCh. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 16RPCh. 6 - Prob. 17RPCh. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - Prob. 23RPCh. 6 - Prob. 24RPCh. 6 - Prob. 25RPCh. 6 - Prob. 26RPCh. 6 - Prob. 27RPCh. 6 - Prob. 28RPCh. 6 - Prob. 29RPCh. 6 - Prob. 30RPCh. 6 - Prob. 31RPCh. 6 - Prob. 32RPCh. 6 - Prob. 33RPCh. 6 - Prob. 34RPCh. 6 - Prob. 35RPCh. 6 - Prob. 36RPCh. 6 - Prob. 37RPCh. 6 - Prob. 38RPCh. 6 - Prob. 39RPCh. 6 - Prob. 40RPCh. 6 - Prob. 41RPCh. 6 - Prob. 42RPCh. 6 - Prob. 43RPCh. 6 - Prob. 44RPCh. 6 - Prob. 45RPCh. 6 - Prob. 46RPCh. 6 - Prob. 47RPCh. 6 - Prob. 48RPCh. 6 - Solve the following exercises. If necessary, round...Ch. 6 - Prob. 50RPCh. 6 - Solve the following exercises. If necessary, round...Ch. 6 - Prob. 52RPCh. 6 - Prob. 53RPCh. 6 - Prob. 54RPCh. 6 - Prob. 55RPCh. 6 - Prob. 1TCh. 6 - Prob. 2TCh. 6 - Prob. 3TCh. 6 - Prob. 4TCh. 6 - Prob. 5TCh. 6 - Prob. 6TCh. 6 - Prob. 7TCh. 6 - Prob. 8TCh. 6 - Prob. 9TCh. 6 - Prob. 10TCh. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - Prob. 13TCh. 6 - Prob. 14TCh. 6 - Prob. 15TCh. 6 - Prob. 16TCh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Prob. 4CTCh. 6 - Prob. 5CTCh. 6 - Prob. 6CTCh. 6 - Prob. 7CTCh. 6 - Prob. 8CTCh. 6 - Prob. 9CTCh. 6 - Prob. 10CTCh. 6 - Prob. 11CTCh. 6 - Prob. 12CTCh. 6 - Prob. 13CTCh. 6 - Prob. 14CTCh. 6 - Prob. 15CTCh. 6 - Prob. 16CTCh. 6 - Prob. 17CTCh. 6 - Prob. 18CTCh. 6 - Prob. 19CTCh. 6 - Prob. 20CTCh. 6 - Prob. 21CTCh. 6 - Prob. 22CTCh. 6 - Prob. 23CTCh. 6 - Prob. 24CTCh. 6 - Prob. 25CTCh. 6 - Prob. 26CTCh. 6 - Prob. 27CTCh. 6 - Prob. 28CTCh. 6 - Prob. 29CTCh. 6 - The mayor of Chicago decided that in the coming...
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