PREALGEBRA
PREALGEBRA
15th Edition
ISBN: 9781938168994
Author: OpenStax
Publisher: OpenStax
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 3.3, Problem 3.65TI

TRY IT :: 3.65

Model the expression:

6 − ( − 4 )

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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]
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Chapter 3 Solutions

PREALGEBRA

Ch. 3.1 - TRY IT:: 3.1 Plot the numbers on a number line. a....Ch. 3.1 - TRY IT:: 3.2 Plot the numbers on a number line. a....Ch. 3.1 - TRY IT:: 3 Order each of the following pairs of...Ch. 3.1 - TRY IT:: 3.4 Order each of the following pairs of...Ch. 3.1 - TRYIT:: 3.5 Find the opposite of each number: a. 4...Ch. 3.1 - TRY IT:: 3.6 Find the opposite of each number: a....Ch. 3.1 - Try IT:: 3.7 Simplify: (1)Ch. 3.1 - Try IT:: 3.8 Simplify: (5)Ch. 3.1 - TRY IT:: 3.9 Evaluate n: a. when n=4 b. when n=4Ch. 3.1 - TRY IT:: 3.10 Evaluate: m: a. when m=11 b. when...
Ch. 3.1 - Try IT:: 3.11 Simplify: a. |12| b. |28|Ch. 3.1 - TRYIT:: 3.12 Simplify: a.|9| b.(b)-|37|Ch. 3.1 - TRYIT:: 3.13 Evaluate: a. |x|when x=17 b. |y|when...Ch. 3.1 - TRY IT:: 3.14 a. |y|when y=23 b. |y|when y=21 c....Ch. 3.1 - TRY IT:: 3.15 Fill in <, >, or = for each of the...Ch. 3.1 - TRY IT:: 3.16 Fill in <, >, or = for each of the...Ch. 3.1 - TRY IT:: 3.17 Simplify: a. |129| b. 3|6|Ch. 3.1 - TRY IT:: 3.18 Simplify: a. |2716| b. 9|7|Ch. 3.1 - TRY IT:: 3.19 Simplify: |1+8||2+5|Ch. 3.1 - TRY IT:: 3.20 Simplify: |95||76|Ch. 3.1 - TRY IT:: 3.21 Simplify: 19|114(31)|Ch. 3.1 - TRY IT:: 3.22 Simplify: 9|84(75)|Ch. 3.1 - TRY IT:: 3.23 Translate each phrase into an...Ch. 3.1 - TRY IT:: 3.24 Translate each phrase into an...Ch. 3.1 - TRY IT:: 3.25 Translate into an expression with...Ch. 3.1 - TRY IT:: 3.26 Translate into an expression with...Ch. 3.1 - In the following exercises, locate and label the...Ch. 3.1 - In the following exercises, locate and label the...Ch. 3.1 - In the following exercises, locate and label the...Ch. 3.1 - In the following exercises, locate and label the...Ch. 3.1 - In the following exercises, order each of the...Ch. 3.1 - In the following exercises, order each of the...Ch. 3.1 - In the following exercises, order each of the...Ch. 3.1 - In the following exercises, order each of the...Ch. 3.1 - In the following exercises, find the opposite of...Ch. 3.1 - In the following exercises, find the opposite of...Ch. 3.1 - In the following exercises, find the opposite of...Ch. 3.1 - In the following exercises, find the opposite of...Ch. 3.1 - In the following exercises, simplify. -(-4)Ch. 3.1 - In the following exercises, simplify. -(-8)Ch. 3.1 - In the following exercises, simplify. -(-15)Ch. 3.1 - In the following exercises, simplify. -(-11)Ch. 3.1 - In the following exercises, evaluate. mwhen a. m=3...Ch. 3.1 - In the following exercises, evaluate. pwhen a. p=6...Ch. 3.1 - In the following exercises, evaluate. cwhen a....Ch. 3.1 - In the following exercises, evaluate. dwhen a....Ch. 3.1 - In the following exercises, simplify each absolute...Ch. 3.1 - In the following exercises, simplify each absolute...Ch. 3.1 - In the following exercises, simplify each absolute...Ch. 3.1 - In the following exercises, simplify each absolute...Ch. 3.1 - In the following exercises, evaluate each absolute...Ch. 3.1 - In the following exercises, evaluate each absolute...Ch. 3.1 - In the following exercises, evaluate each absolute...Ch. 3.1 - In the following exercises, evaluate each absolute...Ch. 3.1 - In the following exercises, fill in <, >, or = to...Ch. 3.1 - In the following exercises, fill in <, >, or = to...Ch. 3.1 - In the following exercises, fill in <, >, or = to...Ch. 3.1 - In the following exercises, fill in <, >, or = to...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - wIn the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - In the following exercises, simplify each...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Translate each phrase into an expression with...Ch. 3.1 - Elevation The highest elevation in the United...Ch. 3.1 - Extreme temperatures The highest recorded...Ch. 3.1 - State budgets In June, 2011, the state of...Ch. 3.1 - College enrollments Across the United States,...Ch. 3.1 - Give an example of a negative number from your...Ch. 3.1 - What are the three uses of the “-” sign in...Ch. 3.2 - TRY IT :: 3.27 Model the expression. 2+4Ch. 3.2 - TRY IT : : 3.28 Model the expression. 2+5Ch. 3.2 - TRY IT :: 3.29 Model the expression. 2+(4)Ch. 3.2 - TRY IT :: 3.30 Model the expression. 2+(5)Ch. 3.2 - TRY IT :: 3.31 Model the expression, and then...Ch. 3.2 - TRY IT :: 3.32 Model the expression, and then...Ch. 3.2 - TRY IT :: 3.33 Model the expression, and then...Ch. 3.2 - TRY IT :: 3.34 Model the expression: (2)+5Ch. 3.2 - TRY IT :: 3.35 Model each addition. a. 3+4 b. 1+4...Ch. 3.2 - TRY IT :: 3.36 a. 5+1 b. 3+7 c. 2+(8) d. 3+(4)Ch. 3.2 - TRY IT :: 3.37 Simplify each expression: a....Ch. 3.2 - TRY IT :: 3.38 Simplify each expression: a. 55+9...Ch. 3.2 - TRY IT :: 3.39 Simplify each expression: 31+(19)Ch. 3.2 - TRY IT :: 3.40 Simplify each expression: 42+(28)Ch. 3.2 - TRY IT :: 3.41 Simplify each expression: 2+5(4+7)Ch. 3.2 - TRY IT :: 3.42 Simplify each expression: 4+2(3+5)Ch. 3.2 - TRY IT :: 3.43 Evaluate each expression for the...Ch. 3.2 - TRY IT :: 3.44 Evaluate each expression for the...Ch. 3.2 - TRY IT :: 3.45 When n=8, Evaluate a. n+2 b. n+2Ch. 3.2 - TRY IT :: 3.46 When y=9, evaluate a. y+8 b. y+8Ch. 3.2 - TRY IT :: 3.47 Evaluate the expression: a+2bwhen...Ch. 3.2 - TRY IT :: 3.48 Evaluate the expression: 5p+qwhen...Ch. 3.2 - TRY IT :: 3.49 Evaluate: (x+y)2when x=15and y=29.Ch. 3.2 - TRY IT :: 3.50 Evaluate: (x+y)3when x=8and y=10.Ch. 3.2 - TRY IT :: 3.51 Translate and simplify the...Ch. 3.2 - TRY IT :: 3.52 Translate and simplify the...Ch. 3.2 - TRY IT :: 3.53 Translate and simplify: the sum of...Ch. 3.2 - TRY IT :: 3.54 Translate and simplify: the sum of...Ch. 3.2 - TRY IT :: 3.55 The temperature in Chicago at 5...Ch. 3.2 - TRY IT :: 3.56 A scuba diver was swimming 16 feet...Ch. 3.2 - TRY IT :: 3.57 The Bears took possession of the...Ch. 3.2 - TRY IT:: 3.58 The Chargers began with the football...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, model the expression...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - yIn the following exercises, simplify each...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - In the following exercises, simplify each...Ch. 3.2 - 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Temperature The...Ch. 3.2 - In the following exercises, solve. Temperature The...Ch. 3.2 - In the following exercises, solve. Credit Cards...Ch. 3.2 - In the following exercises, solve. Credit Cards...Ch. 3.2 - In the following exercises, solve. Weight Loss...Ch. 3.2 - In the following exercises, solve. Weight Loss...Ch. 3.2 - In the following exercises, solve. Football The...Ch. 3.2 - In the following exercises, solve. Football The...Ch. 3.2 - In the following exercises, solve. Calories...Ch. 3.2 - In the following exercises, solve. Calories Ozzie...Ch. 3.2 - In the following exercises, solve. Stock Market...Ch. 3.2 - In the following exercises, solve. Stock Market...Ch. 3.2 - In the following exercises, solve. Explain why the...Ch. 3.2 - In the following exercises, solve. Give an example...Ch. 3.3 - TRY IT :: 3.59 Model the expression: 64Ch. 3.3 - wTRY IT :: 3.60 Model the expression: 74Ch. 3.3 - TRY IT :: 3.61 Model the expression: 6(4)Ch. 3.3 - TRY IT :: 3.62 Model the expression: 7(4)Ch. 3.3 - TRY IT :: 3.63 Model the expression: 64Ch. 3.3 - TRY IT :: 3.64 Model the expression: 74Ch. 3.3 - TRY IT :: 3.65 Model the expression: 6(4)Ch. 3.3 - TRY IT :: 3.66 Model the expression: 7(4)Ch. 3.3 - TRY IT :: 3.67 Model each subtraction. a. 7(8) b....Ch. 3.3 - yTRY IT :: 3.68 Model each subtraction. a. 4(6) b....Ch. 3.3 - TRY IT :: 3.69 Model each subtraction expression....Ch. 3.3 - TRY IT :: 3.70 Model each subtraction expression....Ch. 3.3 - TRY IT :: 3.71 Simplify each expression: a.sw...Ch. 3.3 - TRY IT :: 3.72 Simplify each expression: a. 157and...Ch. 3.3 - TRY IT :: 3.73 Simplify each expression: a....Ch. 3.3 - TRY IT :: 3.74 Simplify each expression: a....Ch. 3.3 - TRY IT :: 3.75 Simplify the expression: 67(38)Ch. 3.3 - TRY IT :: 3.76 Simplify the expression: 83(57)Ch. 3.3 - TRY IT :: 3.77 Simplify the expression: 8(31)9Ch. 3.3 - TRY IT :: 3.78 Simplify the expression: 12(96)14Ch. 3.3 - TRY IT :: 3.79 Simplify the expression: 629189.Ch. 3.3 - TRY IT :: 3.80 Simplify the expression: 253749Ch. 3.3 - TRY IT :: 3.81 Evaluate each expression: y7when a....Ch. 3.3 - TRY IT :: 3.82 Evaluate each expression: m3when a....Ch. 3.3 - TRY IT :: 3.83 Evaluate each expression: 17kwhen...Ch. 3.3 - TRY IT :: 3.84 Evaluate each expression: sw 5bwhen...Ch. 3.3 - TRY IT :: 3.85 Translate and simplify: a. the...Ch. 3.3 - TRY IT :: 3.86 Translate and simplify: a. the...Ch. 3.3 - TRY IT :: 3.87 The temperature in Anchorage,...Ch. 3.3 - TRY IT :: 3.88 The temperature in Denver was -6...Ch. 3.3 - TRY IT :: 3.89 One day, John hiked to the 10,023...Ch. 3.3 - TRY IT :: 3.90 The submarine Nautilus is at 340...Ch. 3.3 - TRY IT :: 3.91 Araceli has $75 in her checking...Ch. 3.3 - TRY IT :: 3.92 Genevieve’s bank account was...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, model each expression...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - In the following exercises, simplify each...Ch. 3.3 - 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TRY IT :: 3.101 Simplify: 8(3)+5(7)4Ch. 3.4 - TRY IT :: 3.102 Simplify: 9(3)+7(8)1Ch. 3.4 - TRY IT :: 3.103 Simplify: a.(3)4 b. 34Ch. 3.4 - TRY IT :: 3.104 Simplify: a. (7)2 b.72Ch. 3.4 - TRY IT :: 3.105 Simplify: 174(811)Ch. 3.4 - TRY IT :: 3.106 Simplify: 166(713)Ch. 3.4 - TRY IT :: 3.107 Simplify: sw 12(9)(3)3Ch. 3.4 - TRY IT :: 3.108 Simplify: 18(4)(2)3Ch. 3.4 - TRY IT :: 3.109 Simplify: 273+(5)(6)Ch. 3.4 - TRY IT :: 3.110 Simplify: 324+(2)(7)Ch. 3.4 - TRY IT :: 3.111 Evaluate: 3x22x+6when x=3Ch. 3.4 - TRY IT :: 3.112 Evaluate: 4x2x5when x=2Ch. 3.4 - TRY IT :: 3.113 Evaluate: 7x+6y12when x=2and y=3Ch. 3.4 - TRY IT :: 3.114 Evaluate: 8x6y+13when x=3and y=5Ch. 3.4 - TRY IT :: 3.115 Translate to an algebraic...Ch. 3.4 - TRY IT :: 3.116 Translate to an algebraic...Ch. 3.4 - TRY IT :: 3.117 Translate to an algebraic...Ch. 3.4 - TRY IT :: 3.118 Translate to an algebraic...Ch. 3.4 - In the following exercises, multiply each pair of...Ch. 3.4 - In the following exercises, multiply each pair of...Ch. 3.4 - In the following exercises, multiply each pair of...Ch. 3.4 - In the following exercises, multiply each pair of...Ch. 3.4 - In the following exercises, multiply each pair of...Ch. 3.4 - 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