EBK COLLEGE ALGEBRA ESSENTIALS
4th Edition
ISBN: 9780100577558
Author: Blitzer
Publisher: YUZU
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Chapter P.4, Problem 39E
To determine
To find: The product of the expression
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In Exercises 83–100, use the order of operations to simplify each
expression.
83. 4(-5) – 6(-3)
84. 8(-3) – 5(-6)
85. 3(-2)? – 4(-3)²
86. 5(-3)2 – 2(-2)2
87. 82 – 16 + 2² .4 – 3
88. 10 - 100 + 52.2 - 3
5.2 - 32
10 + 2 + 3.4
90.
(12 – 3.2)
89.
[3 - (-2)
91. 8 - 3[-2(2 - 5) – 4(8 – 6)]
92. 8 - 3[-2(5 – 7) - 5(4 - 2)1
2(-2) – 4(-3)
93.
5 - 8
6(-4) – 5(-3)
94.
9 - 10
(5 – 6)? – 2|3 – 7|
95.
89 – 3.52
12 + 3.5|22 + 32|
96.
7 + 3 - 62
97. 15 - V3 - (-1) + 12 + 2.3
98. 17 - |5 - (-2)| + 12 + 2.3
99. 20 + 1 - V102 - (5 + 1)(-2)
100. 24 - V3. (5 – 2) + [-1 – (-3)|r
Chapter P Solutions
EBK COLLEGE ALGEBRA ESSENTIALS
Ch. P.1 - Evaluates 8 + 6(x 3)2 for x = 13.Ch. P.1 - Prob. 2CPCh. P.1 - Find the intersection: {3, 4, 5, 6, 7} {3, 7, 8,...Ch. P.1 - Prob. 4CPCh. P.1 - Consider the following set of numbers:...Ch. P.1 - Rewrite each expression without absolute value...Ch. P.1 - Find the distance between 4 and 5 on the real...Ch. P.1 - Simplify: 7(4x2+3x)+2(5x2+x).Ch. P.1 - Simplify: 6+4[7(x2)].Ch. P.1 - Fill in each blank so that the resulting statement...
Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Prob. 4CVCCh. P.1 - Prob. 5CVCCh. P.1 - Prob. 6CVCCh. P.1 - Prob. 7CVCCh. P.1 - Prob. 8CVCCh. P.1 - Prob. 9CVCCh. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Prob. 15CVCCh. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Fill in each blank so that the resulting statement...Ch. P.1 - Prob. 18CVCCh. P.1 - Prob. 19CVCCh. P.1 - In Exercises 116, evaluate each algebraic...Ch. P.1 - Prob. 2ECh. P.1 - In Exercises 116, evaluate each algebraic...Ch. P.1 - In Exercises 116, evaluate each algebraic...Ch. P.1 - Prob. 5ECh. P.1 - Prob. 6ECh. P.1 - Prob. 7ECh. P.1 - Prob. 8ECh. P.1 - Prob. 9ECh. P.1 - In Exercises 116, evaluate each algebraic...Ch. P.1 - Prob. 11ECh. P.1 - Prob. 12ECh. P.1 - In Exercises 116, evaluate each algebraic...Ch. P.1 - Prob. 14ECh. P.1 - Prob. 15ECh. P.1 - Prob. 16ECh. P.1 - The formula C=59(F32) expresses the relationship...Ch. P.1 - Prob. 18ECh. P.1 - Prob. 19ECh. P.1 - Prob. 20ECh. P.1 - Prob. 21ECh. P.1 - In Exercises 2128, find the intersection of the...Ch. P.1 - Prob. 23ECh. P.1 - In Exercises 2128, find the intersection of the...Ch. P.1 - In Exercises 2128, find the intersection of the...Ch. P.1 - Prob. 26ECh. P.1 - In Exercises 2128, find the intersection of the...Ch. P.1 - Prob. 28ECh. P.1 - In Exercises 2934, find the union of the sets....Ch. P.1 - Prob. 30ECh. P.1 - Prob. 31ECh. P.1 - Prob. 32ECh. P.1 - Prob. 33ECh. P.1 - In Exercises 2934, find the union of the sets....Ch. P.1 - Prob. 35ECh. P.1 - Prob. 36ECh. P.1 - Prob. 37ECh. P.1 - In Exercises 3538, list all numbers from the given...Ch. P.1 - Prob. 39ECh. P.1 - Prob. 40ECh. P.1 - Prob. 41ECh. P.1 - Give an example of a number that is a rational...Ch. P.1 - Determine whether each statement in Exercises 4350...Ch. P.1 - Determine whether each statement in Exercises 4350...Ch. P.1 - Determine whether each statement in Exercises 4350...Ch. P.1 - Prob. 46ECh. P.1 - Prob. 47ECh. P.1 - Prob. 48ECh. P.1 - Prob. 49ECh. P.1 - Prob. 50ECh. P.1 - In Exercises 5160, rewrite each expression without...Ch. P.1 - In Exercises 5160, rewrite each expression without...Ch. P.1 - Prob. 53ECh. P.1 - Prob. 54ECh. P.1 - Prob. 55ECh. P.1 - Prob. 56ECh. P.1 - Prob. 57ECh. P.1 - In Exercises 5160, rewrite each expression without...Ch. P.1 - Prob. 59ECh. P.1 - In Exercises 5160, rewrite each expression without...Ch. P.1 - Prob. 61ECh. P.1 - Prob. 62ECh. P.1 - In Exercises 6166, evaluate each algebraic...Ch. P.1 - In Exercises 6166, evaluate each algebraic...Ch. P.1 - In Exercises 6166, evaluate each algebraic...Ch. P.1 - Prob. 66ECh. P.1 - In Exercises 6774, express the distance between...Ch. P.1 - In Exercises 6774, express the distance between...Ch. P.1 - Prob. 69ECh. P.1 - Prob. 70ECh. P.1 - Prob. 71ECh. P.1 - Prob. 72ECh. P.1 - Prob. 73ECh. P.1 - In Exercises 6774, express the distance between...Ch. P.1 - Prob. 75ECh. P.1 - Prob. 76ECh. P.1 - Prob. 77ECh. P.1 - Prob. 78ECh. P.1 - Prob. 79ECh. P.1 - Prob. 80ECh. P.1 - Prob. 81ECh. P.1 - Prob. 82ECh. P.1 - In Exercises 7584, state the name of the property...Ch. P.1 - In Exercises 7584, state the name of the property...Ch. P.1 - Prob. 85ECh. P.1 - Prob. 86ECh. P.1 - In Exercises 8596, simplify each algebraic...Ch. P.1 - Prob. 88ECh. P.1 - Prob. 89ECh. P.1 - Prob. 90ECh. P.1 - Prob. 91ECh. P.1 - Prob. 92ECh. P.1 - Prob. 93ECh. P.1 - Prob. 94ECh. P.1 - Prob. 95ECh. P.1 - Prob. 96ECh. P.1 - In Exercises 97102, write each algebraic...Ch. P.1 - Prob. 98ECh. P.1 - Prob. 99ECh. P.1 - Prob. 100ECh. P.1 - Prob. 101ECh. P.1 - Prob. 102ECh. P.1 - Prob. 103ECh. P.1 - Prob. 104ECh. P.1 - Prob. 105ECh. P.1 - Prob. 106ECh. P.1 - In Exercises 103110, insert either , , or = in the...Ch. P.1 - Prob. 108ECh. P.1 - Prob. 109ECh. P.1 - Prob. 110ECh. P.1 - Prob. 111ECh. P.1 - Prob. 112ECh. P.1 - Prob. 113ECh. P.1 - Prob. 114ECh. P.1 - Prob. 115ECh. P.1 - In Exercises 111120, use the order of operations...Ch. P.1 - In Exercises 111120, use the order of operations...Ch. P.1 - Prob. 118ECh. P.1 - Prob. 119ECh. P.1 - Prob. 120ECh. P.1 - In Exercises 121128, write each English phrase as...Ch. P.1 - Prob. 122ECh. P.1 - Prob. 123ECh. P.1 - Prob. 124ECh. P.1 - Prob. 125ECh. P.1 - Prob. 126ECh. P.1 - In Exercises 121128, write each English phrase as...Ch. P.1 - Prob. 128ECh. P.1 - Application Exercises The maximum heart rate, in...Ch. P.1 - Prob. 130ECh. P.1 - Prob. 131ECh. P.1 - Prob. 132ECh. P.1 - Prob. 133ECh. P.1 - Prob. 134ECh. P.1 - Prob. 135ECh. P.1 - Prob. 136ECh. P.1 - Prob. 137ECh. P.1 - Prob. 138ECh. P.1 - Prob. 139ECh. P.1 - Prob. 140ECh. P.1 - An effective way to understand something is to...Ch. P.1 - Prob. 142ECh. P.1 - Prob. 143ECh. P.1 - Make Sense? In Exercises 144147, determine whether...Ch. P.1 - Make Sense? In Exercises 144147, determine whether...Ch. P.1 - Make Sense? In Exercises 144147, determine whether...Ch. P.1 - Prob. 147ECh. P.1 - Prob. 148ECh. P.1 - In Exercises 148-155, determine whether each...Ch. P.1 - Prob. 150ECh. P.1 - Prob. 151ECh. P.1 - Prob. 152ECh. P.1 - Prob. 153ECh. P.1 - Prob. 154ECh. P.1 - In Exercises 148155, determine whether each...Ch. P.1 - Prob. 156ECh. P.1 - Prob. 157ECh. P.1 - Prob. 158ECh. P.1 - Exercises 159161 will help you prepare for the...Ch. P.1 - Exercises 159161 will help you prepare for the...Ch. P.1 - Exercises 159161 will help you prepare for the...Ch. P.2 - Multiply each expression using the product rule:...Ch. P.2 - Divide each expression using the quotient rule:...Ch. P.2 - Prob. 3CPCh. P.2 - Prob. 4CPCh. P.2 - Prob. 5CPCh. P.2 - Simplify: a.(2y)5 b.(x53)3.Ch. P.2 - Prob. 7CPCh. P.2 - Prob. 8CPCh. P.2 - Prob. 9CPCh. P.2 - Prob. 10CPCh. P.2 - Prob. 11CPCh. P.2 - Prob. 12CPCh. P.2 - Prob. 1CVCCh. P.2 - Prob. 2CVCCh. P.2 - Prob. 3CVCCh. P.2 - Prob. 4CVCCh. P.2 - Fill in each blank so that the resulting statement...Ch. P.2 - Prob. 6CVCCh. P.2 - Prob. 7CVCCh. P.2 - Prob. 8CVCCh. P.2 - Prob. 9CVCCh. P.2 - Prob. 10CVCCh. P.2 - Prob. 1ECh. P.2 - Prob. 2ECh. P.2 - Prob. 3ECh. P.2 - Prob. 4ECh. P.2 - Prob. 5ECh. P.2 - Prob. 6ECh. P.2 - Prob. 7ECh. P.2 - Evaluate each exponential expression in Exercises...Ch. P.2 - Prob. 9ECh. P.2 - Prob. 10ECh. P.2 - Prob. 11ECh. P.2 - Prob. 12ECh. P.2 - Prob. 13ECh. P.2 - Prob. 14ECh. P.2 - Prob. 15ECh. P.2 - Prob. 16ECh. P.2 - Prob. 17ECh. P.2 - Prob. 18ECh. P.2 - Prob. 19ECh. P.2 - Prob. 20ECh. P.2 - Prob. 21ECh. P.2 - Prob. 22ECh. P.2 - Prob. 23ECh. P.2 - Prob. 24ECh. P.2 - Prob. 25ECh. P.2 - Prob. 26ECh. P.2 - Prob. 27ECh. P.2 - Prob. 28ECh. P.2 - Prob. 29ECh. P.2 - Prob. 30ECh. P.2 - Prob. 31ECh. P.2 - Prob. 32ECh. P.2 - Simplify each exponential expression in Exercises...Ch. P.2 - Prob. 34ECh. P.2 - Prob. 35ECh. P.2 - Prob. 36ECh. P.2 - Prob. 37ECh. P.2 - Simplify each exponential expression in Exercises...Ch. P.2 - Prob. 39ECh. P.2 - Prob. 40ECh. P.2 - Simplify each exponential expression in Exercises...Ch. P.2 - Prob. 42ECh. P.2 - Prob. 43ECh. P.2 - Prob. 44ECh. P.2 - Prob. 45ECh. P.2 - Prob. 46ECh. P.2 - Prob. 47ECh. P.2 - Prob. 48ECh. P.2 - Prob. 49ECh. P.2 - Prob. 50ECh. P.2 - Prob. 51ECh. P.2 - Prob. 52ECh. P.2 - Simplify each exponential expression in Exercises...Ch. P.2 - Prob. 54ECh. P.2 - Prob. 55ECh. P.2 - Prob. 56ECh. P.2 - Prob. 57ECh. P.2 - Prob. 58ECh. P.2 - Prob. 59ECh. P.2 - Prob. 60ECh. P.2 - Prob. 61ECh. P.2 - Prob. 62ECh. P.2 - Prob. 63ECh. P.2 - Prob. 64ECh. P.2 - Prob. 65ECh. P.2 - Prob. 66ECh. P.2 - Prob. 67ECh. P.2 - Prob. 68ECh. P.2 - Prob. 69ECh. P.2 - Prob. 70ECh. P.2 - Prob. 71ECh. P.2 - In Exercises 6576, write each number in decimal...Ch. P.2 - Prob. 73ECh. P.2 - Prob. 74ECh. P.2 - Prob. 75ECh. P.2 - Prob. 76ECh. P.2 - In Exercises 7786, write each number in scientific...Ch. P.2 - Prob. 78ECh. P.2 - In Exercises 7786, write each number in scientific...Ch. P.2 - In Exercises 7786, write each number in scientific...Ch. P.2 - In Exercises 7786, write each number in scientific...Ch. P.2 - Prob. 82ECh. P.2 - Prob. 83ECh. P.2 - Prob. 84ECh. P.2 - Prob. 85ECh. P.2 - Prob. 86ECh. P.2 - Prob. 87ECh. P.2 - Prob. 88ECh. P.2 - Prob. 89ECh. P.2 - Prob. 90ECh. P.2 - Prob. 91ECh. P.2 - Prob. 92ECh. P.2 - Prob. 93ECh. P.2 - In Exercises 87106, perform the indicated...Ch. P.2 - Prob. 95ECh. P.2 - Prob. 96ECh. P.2 - Prob. 97ECh. P.2 - Prob. 98ECh. P.2 - Prob. 99ECh. P.2 - Prob. 100ECh. P.2 - Prob. 101ECh. P.2 - Prob. 102ECh. P.2 - In Exercises 87106, perform the indicated...Ch. P.2 - In Exercises 87106, perform the indicated...Ch. P.2 - Prob. 105ECh. P.2 - Prob. 106ECh. P.2 - Prob. 107ECh. P.2 - Prob. 108ECh. P.2 - Prob. 109ECh. P.2 - Prob. 110ECh. P.2 - In Exercises 107114, simplify each exponential...Ch. P.2 - Prob. 112ECh. P.2 - Prob. 113ECh. P.2 - Prob. 114ECh. P.2 - Prob. 115ECh. P.2 - Prob. 116ECh. P.2 - Prob. 117ECh. P.2 - Prob. 118ECh. P.2 - Prob. 119ECh. P.2 - Prob. 120ECh. P.2 - Prob. 121ECh. P.2 - Prob. 122ECh. P.2 - Prob. 123ECh. P.2 - Explain the product rule for exponents. Use 2325...Ch. P.2 - Prob. 125ECh. P.2 - Prob. 126ECh. P.2 - Prob. 127ECh. P.2 - Prob. 128ECh. P.2 - Prob. 129ECh. P.2 - Prob. 130ECh. P.2 - Prob. 131ECh. P.2 - Prob. 132ECh. P.2 - Prob. 133ECh. P.2 - Prob. 134ECh. P.2 - Prob. 135ECh. P.2 - Prob. 136ECh. P.2 - Prob. 137ECh. P.2 - Prob. 138ECh. P.2 - Prob. 139ECh. P.2 - Prob. 140ECh. P.2 - Prob. 141ECh. P.2 - Prob. 142ECh. P.2 - Prob. 143ECh. P.2 - The mad Dr. Frankenstein has gathered enough bits...Ch. P.2 - If bA = MN, bC = M, and bD = N, what is the...Ch. P.2 - Prob. 146ECh. P.2 - Prob. 148ECh. P.2 - Exercises 145147 will help you prepare for the...Ch. P.2 - Prob. 150ECh. P.3 - Evaluate: a. 81 b. 9 c. 125 d. 36+64 e. 36+64Ch. P.3 - Prob. 2CPCh. P.3 - Prob. 3CPCh. P.3 - Prob. 4CPCh. P.3 - Prob. 5CPCh. P.3 - Prob. 6CPCh. P.3 - Rationalize the denominator:84+5Ch. P.3 - Prob. 8CPCh. P.3 - Subtract: 3813433.Ch. P.3 - Prob. 10CPCh. P.3 - Prob. 11CPCh. P.3 - Prob. 12CPCh. P.3 - Prob. 13CPCh. P.3 - Fill in each blank so that the resulting statement...Ch. P.3 - Prob. 2CVCCh. P.3 - Prob. 3CVCCh. P.3 - Prob. 4CVCCh. P.3 - Prob. 5CVCCh. P.3 - Fill in each blank so that the resulting statement...Ch. P.3 - Prob. 7CVCCh. P.3 - Prob. 8CVCCh. P.3 - Fill in each blank so that the resulting statement...Ch. P.3 - Prob. 10CVCCh. P.3 - Prob. 11CVCCh. P.3 - Prob. 12CVCCh. P.3 - Prob. 13CVCCh. P.3 - Prob. 14CVCCh. P.3 - Prob. 1ECh. P.3 - Prob. 2ECh. P.3 - Prob. 3ECh. P.3 - Prob. 4ECh. P.3 - Prob. 5ECh. P.3 - Prob. 6ECh. P.3 - Prob. 7ECh. P.3 - Prob. 8ECh. P.3 - Evaluate each expression in Exercises 112, or...Ch. P.3 - Prob. 10ECh. P.3 - Prob. 11ECh. P.3 - Prob. 12ECh. P.3 - Prob. 13ECh. P.3 - Prob. 14ECh. P.3 - Prob. 15ECh. P.3 - Prob. 16ECh. P.3 - Use the product rule to simplify the expressions...Ch. P.3 - Use the product rule to simplify the expressions...Ch. P.3 - Use the product rule to simplify the expressions...Ch. P.3 - Prob. 20ECh. P.3 - Prob. 21ECh. P.3 - Prob. 22ECh. P.3 - Prob. 23ECh. P.3 - Prob. 24ECh. P.3 - Prob. 25ECh. P.3 - Prob. 26ECh. P.3 - Prob. 27ECh. P.3 - Prob. 28ECh. P.3 - Use the quotient rule to simplify the expressions...Ch. P.3 - Prob. 30ECh. P.3 - Prob. 31ECh. P.3 - Prob. 32ECh. P.3 - Prob. 33ECh. P.3 - Prob. 34ECh. P.3 - Prob. 35ECh. P.3 - Prob. 36ECh. P.3 - In Exercises 3344, add or subtract terms whenever...Ch. P.3 - In Exercises 3344, add or subtract terms whenever...Ch. P.3 - Prob. 39ECh. P.3 - Prob. 40ECh. P.3 - In Exercises 3344, add or subtract terms whenever...Ch. P.3 - Prob. 42ECh. P.3 - Prob. 43ECh. P.3 - In Exercises 3344, add or subtract terms whenever...Ch. P.3 - Prob. 45ECh. P.3 - Prob. 46ECh. P.3 - Prob. 47ECh. P.3 - Prob. 48ECh. P.3 - Prob. 49ECh. P.3 - Prob. 50ECh. P.3 - Prob. 51ECh. P.3 - Prob. 52ECh. P.3 - Prob. 53ECh. P.3 - Prob. 54ECh. P.3 - Prob. 55ECh. P.3 - Prob. 56ECh. P.3 - Prob. 57ECh. P.3 - Prob. 58ECh. P.3 - Evaluate each expression in Exercises 5566, or...Ch. P.3 - Prob. 60ECh. P.3 - Evaluate each expression in Exercises 5566, or...Ch. P.3 - Prob. 62ECh. P.3 - Prob. 63ECh. P.3 - Prob. 64ECh. P.3 - Prob. 65ECh. P.3 - Prob. 66ECh. P.3 - Prob. 67ECh. P.3 - Prob. 68ECh. P.3 - Prob. 69ECh. P.3 - Prob. 70ECh. P.3 - Prob. 71ECh. P.3 - Prob. 72ECh. P.3 - Simplify the radical expressions in Exercises 6774...Ch. P.3 - Prob. 74ECh. P.3 - Prob. 75ECh. P.3 - Prob. 76ECh. P.3 - Prob. 77ECh. P.3 - Prob. 78ECh. P.3 - Prob. 79ECh. P.3 - Prob. 80ECh. P.3 - Prob. 81ECh. P.3 - Prob. 82ECh. P.3 - Prob. 83ECh. P.3 - In Exercises 8390, evaluate each expression...Ch. P.3 - Prob. 85ECh. P.3 - Prob. 86ECh. P.3 - Prob. 87ECh. P.3 - Prob. 88ECh. P.3 - Prob. 89ECh. P.3 - Prob. 90ECh. P.3 - In Exercises 91100, simplify using properties of...Ch. P.3 - Prob. 92ECh. P.3 - Prob. 93ECh. P.3 - In Exercises 91100, simplify using properties of...Ch. P.3 - Prob. 95ECh. P.3 - Prob. 96ECh. P.3 - Prob. 97ECh. P.3 - Prob. 98ECh. P.3 - Prob. 99ECh. P.3 - Prob. 100ECh. P.3 - Prob. 101ECh. P.3 - Prob. 102ECh. P.3 - In Exercises 101108, simplify by reducing the...Ch. P.3 - Prob. 104ECh. P.3 - Prob. 105ECh. P.3 - Prob. 106ECh. P.3 - Prob. 107ECh. P.3 - Prob. 108ECh. P.3 - Prob. 109ECh. P.3 - Prob. 110ECh. P.3 - Prob. 111ECh. P.3 - Prob. 112ECh. P.3 - Prob. 113ECh. P.3 - Prob. 114ECh. P.3 - Prob. 115ECh. P.3 - Prob. 116ECh. P.3 - The early Greeks believed that the most pleasing...Ch. P.3 - Prob. 118ECh. P.3 - Prob. 119ECh. P.3 - Prob. 120ECh. P.3 - Prob. 121ECh. P.3 - Prob. 122ECh. P.3 - Prob. 123ECh. P.3 - Prob. 124ECh. P.3 - Prob. 125ECh. P.3 - Prob. 126ECh. P.3 - Prob. 127ECh. P.3 - Prob. 129ECh. P.3 - Prob. 130ECh. P.3 - Prob. 131ECh. P.3 - Critical Thinking Exercises Make Sense? In...Ch. P.3 - Prob. 133ECh. P.3 - Prob. 134ECh. P.3 - Prob. 135ECh. P.3 - Prob. 136ECh. P.3 - Prob. 137ECh. P.3 - Prob. 138ECh. P.3 - Prob. 139ECh. P.3 - Prob. 140ECh. P.3 - Prob. 141ECh. P.3 - Prob. 142ECh. P.3 - Exercises 142144 will help you prepare for the...Ch. P.3 - Exercises 142144 will help you prepare for the...Ch. P.4 - Perform the indicated operations and simplify: a....Ch. P.4 - Prob. 2CPCh. P.4 - Multiply: (7x 5)(4x 3).Ch. P.4 - Prob. 4CPCh. P.4 - Prob. 5CPCh. P.4 - Prob. 6CPCh. P.4 - Subtract: (x3 4x2y + 5xy2 y3) (x3 6x2y + y3).Ch. P.4 - Prob. 8CPCh. P.4 - Prob. 1CVCCh. P.4 - Fill in each blank so that the resulting statement...Ch. P.4 - Prob. 3CVCCh. P.4 - Prob. 4CVCCh. P.4 - Fill in each blank so that the resulting statement...Ch. P.4 - Prob. 6CVCCh. P.4 - Prob. 7CVCCh. P.4 - Prob. 8CVCCh. P.4 - Prob. 9CVCCh. P.4 - Prob. 10CVCCh. P.4 - Prob. 11CVCCh. P.4 - Prob. 12CVCCh. P.4 - Prob. 13CVCCh. P.4 - Prob. 14CVCCh. P.4 - Prob. 1ECh. P.4 - Prob. 2ECh. P.4 - Prob. 3ECh. P.4 - Prob. 4ECh. P.4 - Prob. 5ECh. P.4 - Prob. 6ECh. P.4 - Prob. 7ECh. P.4 - Prob. 8ECh. P.4 - EXERCISE SET P.4 In Exercises 914, perform the...Ch. P.4 - Prob. 10ECh. P.4 - Prob. 11ECh. P.4 - Prob. 12ECh. P.4 - Prob. 13ECh. P.4 - Prob. 14ECh. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - Prob. 16ECh. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - Prob. 18ECh. P.4 - Prob. 19ECh. P.4 - Prob. 20ECh. P.4 - Prob. 21ECh. P.4 - Prob. 22ECh. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - Prob. 25ECh. P.4 - Prob. 26ECh. P.4 - Prob. 27ECh. P.4 - Prob. 28ECh. P.4 - Prob. 29ECh. P.4 - Prob. 30ECh. P.4 - Prob. 31ECh. P.4 - Prob. 32ECh. P.4 - Prob. 33ECh. P.4 - Prob. 34ECh. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - Prob. 36ECh. P.4 - Prob. 37ECh. P.4 - Prob. 38ECh. P.4 - Prob. 39ECh. P.4 - Prob. 40ECh. P.4 - Prob. 41ECh. P.4 - Prob. 42ECh. P.4 - Prob. 43ECh. P.4 - Prob. 44ECh. P.4 - Prob. 45ECh. P.4 - Prob. 46ECh. P.4 - Prob. 47ECh. P.4 - Prob. 48ECh. P.4 - Prob. 49ECh. P.4 - Prob. 50ECh. P.4 - Prob. 51ECh. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - EXERCISE SET P.4 In Exercises 1558, find each...Ch. P.4 - Prob. 54ECh. P.4 - Prob. 55ECh. P.4 - Prob. 56ECh. P.4 - Prob. 57ECh. P.4 - Prob. 58ECh. P.4 - Prob. 59ECh. P.4 - Prob. 60ECh. P.4 - Prob. 61ECh. P.4 - EXERCISE SET P.4 In Exercises 5966, perform the...Ch. P.4 - Prob. 63ECh. P.4 - Prob. 64ECh. P.4 - Prob. 65ECh. P.4 - Prob. 66ECh. P.4 - Prob. 67ECh. P.4 - Prob. 68ECh. P.4 - Prob. 69ECh. P.4 - Prob. 70ECh. P.4 - Prob. 71ECh. P.4 - EXERCISE SET P.4 In Exercises 6782, find each...Ch. P.4 - EXERCISE SET P.4 In Exercises 6782, find each...Ch. P.4 - Prob. 74ECh. P.4 - Prob. 75ECh. P.4 - Prob. 76ECh. P.4 - Prob. 77ECh. P.4 - Prob. 78ECh. P.4 - Prob. 79ECh. P.4 - Prob. 80ECh. P.4 - Prob. 81ECh. P.4 - Prob. 82ECh. P.4 - Prob. 83ECh. P.4 - Prob. 84ECh. P.4 - Prob. 85ECh. P.4 - Prob. 86ECh. P.4 - Prob. 87ECh. P.4 - Prob. 88ECh. P.4 - Prob. 89ECh. P.4 - Prob. 90ECh. P.4 - Prob. 91ECh. P.4 - Prob. 92ECh. P.4 - Prob. 93ECh. P.4 - Prob. 94ECh. P.4 - Prob. 95ECh. P.4 - Prob. 96ECh. P.4 - Prob. 97ECh. P.4 - Prob. 98ECh. P.4 - Prob. 99ECh. P.4 - Prob. 100ECh. P.4 - Prob. 101ECh. P.4 - Prob. 102ECh. P.4 - Prob. 103ECh. P.4 - Prob. 104ECh. P.4 - Make Sense? In Exercises 103106, determine whether...Ch. P.4 - Prob. 106ECh. P.4 - Prob. 107ECh. P.4 - In Exercises 107110, determine whether each...Ch. P.4 - Prob. 109ECh. P.4 - Prob. 110ECh. P.4 - Prob. 111ECh. P.4 - Prob. 112ECh. P.4 - Prob. 113ECh. P.4 - Express the area of the plane figure shown as a...Ch. P.4 - Prob. 115ECh. P.4 - Exercises 115117 will help you prepare for the...Ch. P.4 - Prob. 117ECh. P.5 - Factor: a.10x34x2 b.2x(x7)+3(x7).Ch. P.5 - Prob. 2CPCh. P.5 - Prob. 3CPCh. P.5 - Prob. 4CPCh. P.5 - Prob. 5CPCh. P.5 - Prob. 6CPCh. P.5 - Prob. 7CPCh. P.5 - Prob. 8CPCh. P.5 - Prob. 9CPCh. P.5 - Prob. 10CPCh. P.5 - Prob. 11CPCh. P.5 - Prob. 12CPCh. P.5 - Prob. 13CPCh. P.5 - Prob. 1CVCCh. P.5 - Fill in each blank by writing the letter of the...Ch. P.5 - Prob. 3CVCCh. P.5 - Prob. 4CVCCh. P.5 - Prob. 5CVCCh. P.5 - Prob. 6CVCCh. P.5 - Prob. 7CVCCh. P.5 - Prob. 8CVCCh. P.5 - Prob. 1ECh. P.5 - Prob. 2ECh. P.5 - Prob. 3ECh. P.5 - Prob. 4ECh. P.5 - Prob. 5ECh. P.5 - Prob. 6ECh. P.5 - Prob. 7ECh. P.5 - Prob. 8ECh. P.5 - Prob. 9ECh. P.5 - Prob. 10ECh. P.5 - Prob. 11ECh. P.5 - Prob. 12ECh. P.5 - Prob. 13ECh. P.5 - Prob. 14ECh. P.5 - Prob. 15ECh. P.5 - Prob. 16ECh. P.5 - Prob. 17ECh. P.5 - Prob. 18ECh. P.5 - Prob. 19ECh. P.5 - Prob. 20ECh. P.5 - Prob. 21ECh. P.5 - Prob. 22ECh. P.5 - Prob. 23ECh. P.5 - Prob. 24ECh. P.5 - Prob. 25ECh. P.5 - Prob. 26ECh. P.5 - Prob. 27ECh. P.5 - Prob. 28ECh. P.5 - Prob. 29ECh. P.5 - Prob. 30ECh. P.5 - Prob. 31ECh. P.5 - Prob. 32ECh. P.5 - Prob. 33ECh. P.5 - Prob. 34ECh. P.5 - Prob. 35ECh. P.5 - Prob. 36ECh. P.5 - In Exercises 1738, factor each trinomial, or state...Ch. P.5 - Prob. 38ECh. P.5 - Prob. 39ECh. P.5 - Prob. 40ECh. P.5 - Prob. 41ECh. P.5 - Prob. 42ECh. P.5 - Prob. 43ECh. P.5 - Prob. 44ECh. P.5 - Prob. 45ECh. P.5 - Prob. 46ECh. P.5 - Prob. 47ECh. P.5 - Prob. 48ECh. P.5 - Prob. 49ECh. P.5 - Prob. 50ECh. P.5 - Prob. 51ECh. P.5 - Prob. 52ECh. P.5 - Prob. 53ECh. P.5 - Prob. 54ECh. P.5 - Prob. 55ECh. P.5 - Prob. 56ECh. P.5 - Prob. 57ECh. P.5 - Prob. 58ECh. P.5 - Prob. 59ECh. P.5 - Prob. 60ECh. P.5 - Prob. 61ECh. P.5 - Prob. 62ECh. P.5 - Prob. 63ECh. P.5 - Prob. 64ECh. P.5 - Prob. 65ECh. P.5 - Prob. 66ECh. P.5 - Prob. 67ECh. P.5 - Prob. 68ECh. P.5 - Prob. 69ECh. P.5 - Prob. 70ECh. P.5 - Prob. 71ECh. P.5 - Prob. 72ECh. P.5 - Prob. 73ECh. P.5 - Prob. 74ECh. P.5 - Prob. 75ECh. P.5 - Prob. 76ECh. P.5 - Prob. 77ECh. P.5 - Prob. 78ECh. P.5 - Prob. 79ECh. P.5 - Prob. 80ECh. P.5 - Prob. 81ECh. P.5 - In Exercises 6592, factor completely, or state...Ch. P.5 - Prob. 83ECh. P.5 - Prob. 84ECh. P.5 - Prob. 85ECh. P.5 - Prob. 86ECh. P.5 - Prob. 87ECh. P.5 - Prob. 88ECh. P.5 - Prob. 89ECh. P.5 - Prob. 90ECh. P.5 - Prob. 91ECh. P.5 - Prob. 92ECh. P.5 - Prob. 93ECh. P.5 - Prob. 94ECh. P.5 - Prob. 95ECh. P.5 - Prob. 96ECh. P.5 - In Exercises 93102, factor and simplify each...Ch. P.5 - Prob. 98ECh. P.5 - Prob. 99ECh. P.5 - Prob. 100ECh. P.5 - Prob. 101ECh. P.5 - Prob. 102ECh. P.5 - Prob. 103ECh. P.5 - In Exercises 103-114, factor completely. 104....Ch. P.5 - Prob. 105ECh. P.5 - Prob. 106ECh. P.5 - Prob. 107ECh. P.5 - Prob. 108ECh. P.5 - Prob. 109ECh. P.5 - Prob. 110ECh. P.5 - Prob. 111ECh. P.5 - Prob. 112ECh. P.5 - Prob. 113ECh. P.5 - In Exercises 103114, factor completely....Ch. P.5 - Prob. 115ECh. P.5 - Prob. 116ECh. P.5 - Prob. 117ECh. P.5 - In Exercises 117120, a. Write an expression for...Ch. P.5 - Prob. 119ECh. P.5 - Prob. 120ECh. P.5 - Prob. 121ECh. P.5 - Prob. 122ECh. P.5 - Prob. 123ECh. P.5 - Prob. 124ECh. P.5 - Explain how to factor 3x2 + 10x + 8.Ch. P.5 - Prob. 126ECh. P.5 - Prob. 127ECh. P.5 - Prob. 128ECh. P.5 - Prob. 129ECh. P.5 - Make Sense? In Exercises 130133, determine whether...Ch. P.5 - Prob. 131ECh. P.5 - Prob. 132ECh. P.5 - Prob. 133ECh. P.5 - Prob. 134ECh. P.5 - Prob. 135ECh. P.5 - Prob. 136ECh. P.5 - Prob. 137ECh. P.5 - Prob. 138ECh. P.5 - Prob. 139ECh. P.5 - In Exercises 138141, factor completely. 140. x4 ...Ch. P.5 - Prob. 141ECh. P.5 - Prob. 142ECh. P.5 - In Exercises 142143, find all integers b so that...Ch. P.5 - Prob. 144ECh. P.5 - In Exercises 145146, perform the indicated...Ch. P.6 - Find all the numbers that must be excluded from...Ch. P.6 - Simplify: a. x3+3x2x+3 b. x21x2+2x+1.Ch. P.6 - Prob. 3CPCh. P.6 - Divide: x22x+1x3+xx2+x23x2+3.Ch. P.6 - Prob. 5CPCh. P.6 - Prob. 6CPCh. P.6 - Find the least common denominator of...Ch. P.6 - Subtract: xx210x+25x42x10.Ch. P.6 - Prob. 9CPCh. P.6 - Prob. 10CPCh. P.6 - Prob. 1CVCCh. P.6 - Prob. 2CVCCh. P.6 - Prob. 3CVCCh. P.6 - Prob. 4CVCCh. P.6 - Prob. 5CVCCh. P.6 - Prob. 6CVCCh. P.6 - Prob. 7CVCCh. P.6 - Prob. 8CVCCh. P.6 - Prob. 9CVCCh. P.6 - Prob. 10CVCCh. P.6 - In Exercises 16, find all numbers that must be...Ch. P.6 - Prob. 2ECh. P.6 - Prob. 3ECh. P.6 - Prob. 4ECh. P.6 - Prob. 5ECh. P.6 - In Exercises 16, find all numbers that must be...Ch. P.6 - Prob. 7ECh. P.6 - Prob. 8ECh. P.6 - In Exercises 714, simplify each rational...Ch. P.6 - Prob. 10ECh. P.6 - Prob. 11ECh. P.6 - Prob. 12ECh. P.6 - In Exercises 714, simplify each rational...Ch. P.6 - Prob. 14ECh. P.6 - Prob. 15ECh. P.6 - Prob. 16ECh. P.6 - Prob. 17ECh. P.6 - Prob. 18ECh. P.6 - Prob. 19ECh. P.6 - Prob. 20ECh. P.6 - Prob. 21ECh. P.6 - Prob. 22ECh. P.6 - Prob. 23ECh. P.6 - Prob. 24ECh. P.6 - In Exercises 1532, multiply or divide as...Ch. P.6 - Prob. 26ECh. P.6 - In Exercises 1532, multiply or divide as...Ch. P.6 - Prob. 28ECh. P.6 - Prob. 29ECh. P.6 - Prob. 30ECh. P.6 - Prob. 31ECh. P.6 - Prob. 32ECh. P.6 - Prob. 33ECh. P.6 - Prob. 34ECh. P.6 - Prob. 35ECh. P.6 - In Exercises 3358, add or subtract as indicated....Ch. P.6 - Prob. 37ECh. P.6 - Prob. 38ECh. P.6 - Prob. 39ECh. P.6 - Prob. 40ECh. P.6 - Prob. 41ECh. P.6 - Prob. 42ECh. P.6 - Prob. 43ECh. P.6 - Prob. 44ECh. P.6 - Prob. 45ECh. P.6 - Prob. 46ECh. P.6 - Prob. 47ECh. P.6 - Prob. 48ECh. P.6 - In Exercises 3358, add or subtract as indicated....Ch. P.6 - Prob. 50ECh. P.6 - Prob. 51ECh. P.6 - Prob. 52ECh. P.6 - Prob. 53ECh. P.6 - Prob. 54ECh. P.6 - Prob. 55ECh. P.6 - Prob. 56ECh. P.6 - Prob. 57ECh. P.6 - Prob. 58ECh. P.6 - Prob. 59ECh. P.6 - Prob. 60ECh. P.6 - Prob. 61ECh. P.6 - Prob. 62ECh. P.6 - Prob. 63ECh. P.6 - Prob. 64ECh. P.6 - Prob. 65ECh. P.6 - Prob. 66ECh. P.6 - Prob. 67ECh. P.6 - Prob. 68ECh. P.6 - Prob. 69ECh. P.6 - In Exercises 5972, simplify each complex rational...Ch. P.6 - Prob. 71ECh. P.6 - Prob. 72ECh. P.6 - Prob. 73ECh. P.6 - Prob. 74ECh. P.6 - Prob. 75ECh. P.6 - Prob. 76ECh. P.6 - Prob. 77ECh. P.6 - Prob. 78ECh. P.6 - Prob. 79ECh. P.6 - Prob. 80ECh. P.6 - The rational expression 130x100x describes the...Ch. P.6 - Prob. 82ECh. P.6 - Prob. 83ECh. P.6 - Prob. 84ECh. P.6 - Prob. 85ECh. P.6 - What is a rational expression?Ch. P.6 - Prob. 87ECh. P.6 - Prob. 88ECh. P.6 - Prob. 89ECh. P.6 - Prob. 90ECh. P.6 - Prob. 91ECh. P.6 - Prob. 92ECh. P.6 - Prob. 93ECh. P.6 - Prob. 94ECh. P.6 - Explain the error in Exercises 9597. Then rewrite...Ch. P.6 - Explain the error in Exercises 9597. Then rewrite...Ch. P.6 - Explain the error in Exercises 9597. Then rewrite...Ch. P.6 - Prob. 98ECh. P.6 - Make Sense? In Exercises 98101, determine whether...Ch. P.6 - Prob. 100ECh. P.6 - Prob. 101ECh. P.6 - Prob. 102ECh. P.6 - Prob. 103ECh. P.6 - In Exercises 102105, determine whether each...Ch. P.6 - In Exercises 102105, determine whether each...Ch. P.6 - Prob. 106ECh. P.6 - Prob. 107ECh. P.6 - Prob. 108ECh. P.6 - Prob. 109ECh. P.6 - Prob. 110ECh. P.6 - Prob. 111ECh. P.6 - If y=|x+1|, find the value of y that corresponds...Ch. P - In Exercises 125, simplify the given expression or...Ch. P - In Exercises 125, simplify the given expression or...Ch. P - In Exercises 125, simplify the given expression or...Ch. P - Prob. 4MCCh. P - Prob. 5MCCh. P - Prob. 6MCCh. P - Prob. 7MCCh. P - Prob. 8MCCh. P - Prob. 9MCCh. P - Prob. 10MCCh. P - In Exercises 125, simplify the given expression or...Ch. P - Prob. 12MCCh. P - Prob. 13MCCh. P - Prob. 14MCCh. P - Prob. 15MCCh. P - Prob. 16MCCh. P - Prob. 17MCCh. P - Prob. 18MCCh. P - Prob. 19MCCh. P - Prob. 20MCCh. P - Prob. 21MCCh. P - Prob. 22MCCh. P - Prob. 23MCCh. P - Prob. 24MCCh. P - Prob. 25MCCh. P - Prob. 26MCCh. P - Prob. 27MCCh. P - Prob. 28MCCh. P - Prob. 29MCCh. P - Prob. 30MCCh. P - Prob. 31MCCh. P - In Exercises 12, evaluate each algebraic...Ch. P - Prob. 2RECh. P - Prob. 3RECh. P - Prob. 4RECh. P - Prob. 5RECh. P - Prob. 6RECh. P - Prob. 7RECh. P - Prob. 8RECh. P - In Exercises 911, rewrite each expression without...Ch. P - Prob. 10RECh. P - Prob. 11RECh. P - Prob. 12RECh. P - Prob. 13RECh. P - Prob. 14RECh. P - Prob. 15RECh. P - Prob. 16RECh. P - Prob. 17RECh. P - Prob. 18RECh. P - Prob. 19RECh. P - Prob. 20RECh. P - Prob. 21RECh. P - Prob. 22RECh. P - Prob. 23RECh. P - Prob. 24RECh. P - Prob. 25RECh. P - Prob. 26RECh. P - Prob. 27RECh. P - Prob. 28RECh. P - Prob. 29RECh. P - Prob. 30RECh. P - Prob. 31RECh. P - Prob. 32RECh. P - Prob. 33RECh. P - Prob. 34RECh. P - Prob. 35RECh. P - Prob. 36RECh. P - Prob. 37RECh. P - Prob. 38RECh. P - Prob. 39RECh. P - Prob. 40RECh. P - Prob. 41RECh. P - Prob. 42RECh. P - Prob. 43RECh. P - Prob. 44RECh. P - Prob. 45RECh. P - Prob. 46RECh. P - Prob. 47RECh. P - Prob. 48RECh. P - Prob. 49RECh. P - Prob. 50RECh. P - Prob. 51RECh. P - Prob. 52RECh. P - Prob. 53RECh. P - Prob. 54RECh. P - Prob. 55RECh. P - Prob. 56RECh. P - Prob. 57RECh. P - Prob. 58RECh. P - Prob. 59RECh. P - Prob. 60RECh. P - Prob. 61RECh. P - Prob. 62RECh. P - Prob. 63RECh. P - Prob. 64RECh. P - Prob. 65RECh. P - Prob. 66RECh. P - Prob. 67RECh. P - Prob. 68RECh. P - Prob. 69RECh. P - Prob. 70RECh. P - Prob. 71RECh. P - Prob. 72RECh. P - Prob. 73RECh. P - Prob. 74RECh. P - Prob. 75RECh. P - Prob. 76RECh. P - Prob. 77RECh. P - Prob. 78RECh. P - Prob. 79RECh. P - Prob. 80RECh. P - Prob. 81RECh. P - Prob. 82RECh. P - Prob. 83RECh. P - Prob. 84RECh. P - Prob. 85RECh. P - Prob. 86RECh. P - Prob. 87RECh. P - Prob. 88RECh. P - Prob. 89RECh. P - Prob. 90RECh. P - In Exercises 89105, factor completely, or state...Ch. P - Prob. 92RECh. P - Prob. 93RECh. P - In Exercises 89105, factor completely, or state...Ch. P - Prob. 95RECh. P - Prob. 96RECh. P - Prob. 97RECh. P - Prob. 98RECh. P - Prob. 99RECh. P - Prob. 100RECh. P - Prob. 101RECh. P - In Exercises 89105, factor completely, or state...Ch. P - Prob. 103RECh. P - Prob. 104RECh. P - Prob. 105RECh. P - Prob. 106RECh. P - Prob. 107RECh. P - Prob. 108RECh. P - Prob. 109RECh. P - Prob. 110RECh. P - Prob. 111RECh. P - Prob. 112RECh. P - Prob. 113RECh. P - Prob. 114RECh. P - Prob. 115RECh. P - Prob. 116RECh. P - Prob. 117RECh. P - Prob. 118RECh. P - Prob. 119RECh. P - Prob. 120RECh. P - Prob. 121RECh. P - In Exercises 118, simplify the given expression or...Ch. P - Prob. 2TCh. P - Prob. 3TCh. P - Prob. 4TCh. P - Prob. 5TCh. P - Prob. 6TCh. P - Prob. 7TCh. P - Prob. 8TCh. P - Prob. 9TCh. P - Prob. 10TCh. P - Prob. 11TCh. P - Prob. 12TCh. P - Prob. 13TCh. P - Prob. 14TCh. P - Prob. 15TCh. P - Prob. 16TCh. P - Prob. 17TCh. P - Prob. 18TCh. P - Prob. 19TCh. P - In Exercises 1924, factor completely, or state...Ch. P - Prob. 21TCh. P - Prob. 22TCh. P - Prob. 23TCh. P - Prob. 24TCh. P - Prob. 25TCh. P - Prob. 26TCh. P - Prob. 27TCh. P - Prob. 28TCh. P - Prob. 29TCh. P - Prob. 30TCh. P - Prob. 31TCh. P - Prob. 32T
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- Questions 7 and 8 refer to the following definition. 6. 12 11 10 11 Square 1 Square 2 The number inside a square is the sum of all the digits outside the square. For square 1, the middle num- ber is 5 + 6 +7+1 +1= 20. %3D 7. What is the number in the center of square 2? (A) 2 (B) 11 (C) 38 (D) 83 (E) 6,600 20arrow_forwardLINEAR ALGEBRAarrow_forwardIn Exercises 75–81, find each product. 75. (3x – 2)(4x² + 3x – 5) 77. (4x + 5)(4r – 5) 79. (3x - 4)2 81. (5x – 2) 76. (3x - 5)(2x + 1) 78. (2x + 5) 80. (2x + 1)arrow_forward
- Write and evaluate an expression of the form C(n, r) that represents each number of combinations of r cubes that can be taken from the eight cubes shown. (a) r = 1 (b) r = 2 (c) r = 3 (d) r = 4 (e) r = 5 (f) r = 6 (g) r = 7 (h) r = 8 II II II IIarrow_forwardSimplify the given figurearrow_forwardScreen Full Page 12. Find the pattern when the squares of the Fibonacci numbers are added: a. Complete the table for the first six rows: The squares of Fibonacci Numbers Pattern Sum (F1)2 (F1)2 + (F2)2 = 12 = 12 + 12 = 1 = 2 = 1 x1 = F1 x F2 = 1 x 2 = F2 x F3 = 1+1 (F1)² + (F2)² + (F3)² = 12 + 12 + 22 = 1+1+4 = 6 = 2 x 2 = _x _ %D = %3D %3D Complete the blanks and the next three rows. Hint: look for two special numbers that multiply to get the sum. b. Explain the pattern of the answers in words. Hint: relate the two multiplied numbers to the numbers you just added. TIP: Look for a pattern that goes across (F1)2 + (F2)? Look for how these NOT how each old answer is related to the new answer. = 12 + 12 = 1+1 = 2 = 1 x 2 = F2 × F3 are related to these. c. Use the pattern to predict the sum when 1² + 1² + 2² + 32 + 5² + ... + 233² is added. Your answer should show that you know how to get the answer using the pattern, without having to actually add up all the numbers! Hint: which subscript…arrow_forward
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