{"id":234,"date":"2015-09-18T20:12:48","date_gmt":"2015-09-18T20:12:48","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=234"},"modified":"2015-10-30T18:55:59","modified_gmt":"2015-10-30T18:55:59","slug":"solutions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/solutions\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"<h2>Solutions to Try Its<\/h2>\r\n1. a.\u00a0[latex]\\frac{11}{1}[\/latex]\r\nb. [latex]\\frac{3}{1}[\/latex]\r\nc. [latex]-\\frac{4}{1}[\/latex]\r\n\r\n2. a.\u00a04 (or 4.0), terminating\r\nb. [latex]0.\\overline{615384}[\/latex], repeating\r\nc. \u20130.85, terminating\r\n\r\n3. a.\u00a0rational and repeating\r\nb. rational and terminating\r\nc. irrational\r\nd. rational and repeating\r\ne. irrational\r\n\r\n4. a.\u00a0positive, irrational; right\r\nb. negative, rational; left\r\nc. positive, rational; right\r\nd. negative, irrational; left\r\ne. positive, rational; right\r\n\r\n5.\r\n<table summary=\"A table with six rows and six columns. The first entry of the first row is empty, but the rest read: N, W, I, Q, and Q'. (These are the sets of numbers.) The first entry of the second row reads: negative thirty-five over seven. Then the fourth and fifth columns are marked. The first entry of the third row reads: zero. Then the third, fourth, and fifth columns are marked. The first entry of the fourth row reads: square root of one hundred sixty-nine. Then the second, third, fourth, and fifth columns are marked. The first entry of the fifth row reads: square root of twenty-four. Then only the sixth column is marked. The first entry of the sixth row reads: 4.763763763\u2026. Then only the fifth column is marked\">\r\n<thead>\r\n<tr>\r\n<th><\/th>\r\n<th><em>N<\/em><\/th>\r\n<th><em>W<\/em><\/th>\r\n<th><em>I<\/em><\/th>\r\n<th><em>Q<\/em><\/th>\r\n<th><em>Q'<\/em><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>a. [latex]-\\frac{35}{7}[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b. 0<\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c. [latex]\\sqrt{169}[\/latex]<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d. [latex]\\sqrt{24}[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>e. [latex]4.763763763\\dots[\/latex]<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>X<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n6.\u00a0a. 10\r\nb. 2\r\nc. 4.5\r\nd. 25\r\ne. 26\r\n\r\n7. a.\u00a0commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;\r\nb. 33, distributive property;\r\nc. 26, distributive property;\r\nd. [latex]\\frac{4}{9}[\/latex], commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;\r\ne. 0, distributive property, inverse property of addition, identity property of addition\r\n\r\n8.\r\n<table summary=\"A table with four rows and three columns. The first entry of the first row is empty, the second column entry reads: Constants and the third reads: Variables. The first entry of the second row reads: two times pi times r times the quantity r plus h in parenthesis. The second column entry reads: two, pi. The third column entry reads: r, h. The first entry of the third row reads: two times the quantity L plus W in parenthesis. The second column entry reads: two. The third column entry reads: L, W. The first entry of the fourth row reads: four times y cubed plus y. The second column entry reads: four. The third column entry reads: y.\">\r\n<thead>\r\n<tr>\r\n<th><\/th>\r\n<th>Constants<\/th>\r\n<th>Variables<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>a. [latex]2\\pi r\\left(r+h\\right)[\/latex]<\/td>\r\n<td>[latex]2,\\pi [\/latex]<\/td>\r\n<td>[latex]r,h[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b. 2(L + W)<\/td>\r\n<td>2<\/td>\r\n<td>L, W<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c. [latex]4{y}^{3}+y[\/latex]<\/td>\r\n<td>4<\/td>\r\n<td>[latex]y[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n9. a.\u00a05\r\nb. 11\r\nc. 9\r\nd. 26\r\n\r\n10. a.\u00a04\r\nb. 11\r\nc. [latex]\\frac{121}{3}\\pi [\/latex]\r\nd. 1728\r\ne. 3\r\n\r\n11.\u00a01,152 cm<sup>2<\/sup>\r\n\r\n12.\u00a0a. [latex]-2y - 2z\\text{ or }-2\\left(y+z\\right)[\/latex]\r\nb. [latex]\\frac{2}{t}-1[\/latex]\r\nc. [latex]3pq - 4p+q[\/latex]\r\nd. [latex]7r - 2s+6[\/latex]\r\n\r\n13.\u00a0[latex]A=P\\left(1+rt\\right)[\/latex]\r\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.\r\n\r\n3.\u00a0The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.\r\n\r\n5.\u00a0[latex]-6[\/latex]\r\n\r\n7.\u00a0[latex]-2[\/latex]\r\n\r\n9.\u00a0[latex]-9[\/latex]\r\n\r\n11.\u00a09\r\n\r\n13.\u00a04\r\n\r\n15.\u00a04\r\n\r\n17.\u00a00\r\n\r\n19.\u00a09\r\n\r\n21.\u00a025\r\n\r\n23.\u00a0[latex]-6[\/latex]\r\n\r\n25.\u00a017\r\n\r\n27.\u00a04\r\n\r\n29.\u00a0[latex]-4[\/latex]\r\n\r\n31.\u00a0[latex]-6[\/latex]\r\n\r\n33.\u00a0[latex]\\pm 1[\/latex]\r\n\r\n35.\u00a02\r\n\r\n37.\u00a02\r\n\r\n39.\u00a0[latex]-14y - 11[\/latex]\r\n\r\n41.\u00a0[latex]-4b+1[\/latex]\r\n\r\n43.\u00a0[latex]43z - 3[\/latex]\r\n\r\n45.\u00a0[latex]9y+45[\/latex]\r\n\r\n47.\u00a0[latex]-6b+6[\/latex]\r\n\r\n49.\u00a0[latex]\\frac{16x}{3}\\\\[\/latex]\r\n\r\n51.\u00a0[latex]9x[\/latex]\r\n\r\n53.\u00a0[latex]\\frac{1}{2}\\left(40 - 10\\right)+5[\/latex]\r\n\r\n55.\u00a0irrational number\r\n\r\n57.\u00a0[latex]g+400 - 2\\left(600\\right)=1200[\/latex]\r\n\r\n59.\u00a0inverse property of addition\r\n\r\n61.\u00a068.4\r\n\r\n63.\u00a0true\r\n\r\n65.\u00a0irrational\r\n\r\n67.\u00a0rational","rendered":"<h2>Solutions to Try Its<\/h2>\n<p>1. a.\u00a0[latex]\\frac{11}{1}[\/latex]<br \/>\nb. [latex]\\frac{3}{1}[\/latex]<br \/>\nc. [latex]-\\frac{4}{1}[\/latex]<\/p>\n<p>2. a.\u00a04 (or 4.0), terminating<br \/>\nb. [latex]0.\\overline{615384}[\/latex], repeating<br \/>\nc. \u20130.85, terminating<\/p>\n<p>3. a.\u00a0rational and repeating<br \/>\nb. rational and terminating<br \/>\nc. irrational<br \/>\nd. rational and repeating<br \/>\ne. irrational<\/p>\n<p>4. a.\u00a0positive, irrational; right<br \/>\nb. negative, rational; left<br \/>\nc. positive, rational; right<br \/>\nd. negative, irrational; left<br \/>\ne. positive, rational; right<\/p>\n<p>5.<\/p>\n<table summary=\"A table with six rows and six columns. The first entry of the first row is empty, but the rest read: N, W, I, Q, and Q'. (These are the sets of numbers.) The first entry of the second row reads: negative thirty-five over seven. Then the fourth and fifth columns are marked. The first entry of the third row reads: zero. Then the third, fourth, and fifth columns are marked. The first entry of the fourth row reads: square root of one hundred sixty-nine. Then the second, third, fourth, and fifth columns are marked. The first entry of the fifth row reads: square root of twenty-four. Then only the sixth column is marked. The first entry of the sixth row reads: 4.763763763\u2026. Then only the fifth column is marked\">\n<thead>\n<tr>\n<th><\/th>\n<th><em>N<\/em><\/th>\n<th><em>W<\/em><\/th>\n<th><em>I<\/em><\/th>\n<th><em>Q<\/em><\/th>\n<th><em>Q&#8217;<\/em><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>a. [latex]-\\frac{35}{7}[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>b. 0<\/td>\n<td><\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>c. [latex]\\sqrt{169}[\/latex]<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>d. [latex]\\sqrt{24}[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<\/tr>\n<tr>\n<td>e. [latex]4.763763763\\dots[\/latex]<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<td>X<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>6.\u00a0a. 10<br \/>\nb. 2<br \/>\nc. 4.5<br \/>\nd. 25<br \/>\ne. 26<\/p>\n<p>7. a.\u00a0commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;<br \/>\nb. 33, distributive property;<br \/>\nc. 26, distributive property;<br \/>\nd. [latex]\\frac{4}{9}[\/latex], commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;<br \/>\ne. 0, distributive property, inverse property of addition, identity property of addition<\/p>\n<p>8.<\/p>\n<table summary=\"A table with four rows and three columns. The first entry of the first row is empty, the second column entry reads: Constants and the third reads: Variables. The first entry of the second row reads: two times pi times r times the quantity r plus h in parenthesis. The second column entry reads: two, pi. The third column entry reads: r, h. The first entry of the third row reads: two times the quantity L plus W in parenthesis. The second column entry reads: two. The third column entry reads: L, W. The first entry of the fourth row reads: four times y cubed plus y. The second column entry reads: four. The third column entry reads: y.\">\n<thead>\n<tr>\n<th><\/th>\n<th>Constants<\/th>\n<th>Variables<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>a. [latex]2\\pi r\\left(r+h\\right)[\/latex]<\/td>\n<td>[latex]2,\\pi[\/latex]<\/td>\n<td>[latex]r,h[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>b. 2(L + W)<\/td>\n<td>2<\/td>\n<td>L, W<\/td>\n<\/tr>\n<tr>\n<td>c. [latex]4{y}^{3}+y[\/latex]<\/td>\n<td>4<\/td>\n<td>[latex]y[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>9. a.\u00a05<br \/>\nb. 11<br \/>\nc. 9<br \/>\nd. 26<\/p>\n<p>10. a.\u00a04<br \/>\nb. 11<br \/>\nc. [latex]\\frac{121}{3}\\pi[\/latex]<br \/>\nd. 1728<br \/>\ne. 3<\/p>\n<p>11.\u00a01,152 cm<sup>2<\/sup><\/p>\n<p>12.\u00a0a. [latex]-2y - 2z\\text{ or }-2\\left(y+z\\right)[\/latex]<br \/>\nb. [latex]\\frac{2}{t}-1[\/latex]<br \/>\nc. [latex]3pq - 4p+q[\/latex]<br \/>\nd. [latex]7r - 2s+6[\/latex]<\/p>\n<p>13.\u00a0[latex]A=P\\left(1+rt\\right)[\/latex]<\/p>\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.\u00a0irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.<\/p>\n<p>3.\u00a0The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.<\/p>\n<p>5.\u00a0[latex]-6[\/latex]<\/p>\n<p>7.\u00a0[latex]-2[\/latex]<\/p>\n<p>9.\u00a0[latex]-9[\/latex]<\/p>\n<p>11.\u00a09<\/p>\n<p>13.\u00a04<\/p>\n<p>15.\u00a04<\/p>\n<p>17.\u00a00<\/p>\n<p>19.\u00a09<\/p>\n<p>21.\u00a025<\/p>\n<p>23.\u00a0[latex]-6[\/latex]<\/p>\n<p>25.\u00a017<\/p>\n<p>27.\u00a04<\/p>\n<p>29.\u00a0[latex]-4[\/latex]<\/p>\n<p>31.\u00a0[latex]-6[\/latex]<\/p>\n<p>33.\u00a0[latex]\\pm 1[\/latex]<\/p>\n<p>35.\u00a02<\/p>\n<p>37.\u00a02<\/p>\n<p>39.\u00a0[latex]-14y - 11[\/latex]<\/p>\n<p>41.\u00a0[latex]-4b+1[\/latex]<\/p>\n<p>43.\u00a0[latex]43z - 3[\/latex]<\/p>\n<p>45.\u00a0[latex]9y+45[\/latex]<\/p>\n<p>47.\u00a0[latex]-6b+6[\/latex]<\/p>\n<p>49.\u00a0[latex]\\frac{16x}{3}\\\\[\/latex]<\/p>\n<p>51.\u00a0[latex]9x[\/latex]<\/p>\n<p>53.\u00a0[latex]\\frac{1}{2}\\left(40 - 10\\right)+5[\/latex]<\/p>\n<p>55.\u00a0irrational number<\/p>\n<p>57.\u00a0[latex]g+400 - 2\\left(600\\right)=1200[\/latex]<\/p>\n<p>59.\u00a0inverse property of addition<\/p>\n<p>61.\u00a068.4<\/p>\n<p>63.\u00a0true<\/p>\n<p>65.\u00a0irrational<\/p>\n<p>67.\u00a0rational<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-234\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":10,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-234","chapter","type-chapter","status-publish","hentry"],"part":214,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/234","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/234\/revisions"}],"predecessor-version":[{"id":495,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/234\/revisions\/495"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/214"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/234\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=234"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=234"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=234"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=234"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}