{"id":1399,"date":"2024-05-10T23:32:04","date_gmt":"2024-05-10T23:32:04","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=1399"},"modified":"2024-12-04T15:22:57","modified_gmt":"2024-12-04T15:22:57","slug":"module-5-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/module-5-background-youll-need-2\/","title":{"raw":"Function Basic: Background You'll Need 2","rendered":"Function Basic: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Calculate an algebraic expression using given numbers for the variables<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<div class=\"page\" title=\"Page 30\">\r\n<div class=\"layoutArea\">\r\n<div class=\"column\">\r\n<h2>Algebraic Expressions<\/h2>\r\nAn <strong>algebraic expression<\/strong> is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division. For example, [latex]3x + 2y - 7[\/latex] is an algebraic expression that contains two variables [latex]x[\/latex] and [latex]y[\/latex] and three constants [latex]3[\/latex], [latex]2[\/latex], and [latex]7[\/latex].\r\n<div class=\"page\" title=\"Page 30\">\r\n<div class=\"layoutArea\">\r\n<div class=\"column\">\r\n\r\nAny variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression.\r\n\r\n<section class=\"textbox questionHelp\"><strong>How To: Evaluate Algebraic Expressions<\/strong>Use the following steps to evaluate an algebraic expression:\r\n<ol>\r\n \t<li>Replace each variable in the expression with the given value<\/li>\r\n \t<li>Simplify the resulting expression using the order of operations<\/li>\r\n<\/ol>\r\nNote: If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.\r\n\r\n<\/section><section class=\"textbox example\">Evaluate each expression for the given values.\r\n<ol>\r\n \t<li>[latex]x+5[\/latex] for [latex]x=-5[\/latex]\r\n[reveal-answer q=\"880683\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"880683\"]Substitute [latex]-5[\/latex] for [latex]x[\/latex].<center>[latex]\\begin{align}x+5 &amp;=\\left(-5\\right)+5 \\\\ &amp;=0\\end{align}[\/latex]<\/center>[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\dfrac{t}{2t - 1}[\/latex] for [latex]t=10[\/latex]\r\n[reveal-answer q=\"764987\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"764987\"]Substitute [latex] 10[\/latex] for [latex]t[\/latex].<center>[latex]\\begin{align}\\dfrac{t}{2t-1} &amp; =\\dfrac{\\left(10\\right)}{2\\left(10\\right)-1} \\\\ &amp; =\\dfrac{10}{20-1} \\\\ &amp; =\\dfrac{10}{19}\\end{align}[\/latex]<\/center>[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\dfrac{4}{3}\\pi {r}^{3}[\/latex] for [latex]r=5[\/latex]\r\n[reveal-answer q=\"590356\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"590356\"]Substitute [latex]5[\/latex] for [latex]r[\/latex].<center>[latex]\\begin{align}\\frac{4}{3}\\pi r^{3} &amp; =\\frac{4}{3}\\pi\\left(5\\right)^{3} \\\\ &amp; =\\frac{4}{3}\\pi\\left(125\\right) \\\\ &amp; =\\frac{500}{3}\\pi\\end{align}[\/latex]<\/center>[\/hidden-answer]<\/li>\r\n \t<li>[latex]a+ab+b[\/latex] for [latex]a=11,b=-8[\/latex]\r\n[reveal-answer q=\"911479\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"911479\"]Substitute [latex]11[\/latex] for [latex]a[\/latex] and \u20138 for [latex]b[\/latex].<center>[latex]\\begin{align}a+ab+b &amp; =\\left(11\\right)+\\left(11\\right)\\left(-8\\right)+\\left(-8\\right) \\\\ &amp; =11-8-8 \\\\ &amp; =-85\\end{align}[\/latex]<\/center>[\/hidden-answer]<\/li>\r\n \t<li>[latex]\\sqrt{2{m}^{3}{n}^{2}}[\/latex] for [latex]m=2,n=3[\/latex]\r\n[reveal-answer q=\"929252\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"929252\"]Substitute [latex]2[\/latex] for [latex]m[\/latex] and [latex]3[\/latex] for [latex]n[\/latex].<center>[latex]\\begin{align}\\sqrt{2m^{3}n^{2}} &amp; =\\sqrt{2\\left(2\\right)^{3}\\left(3\\right)^{2}} \\\\ &amp; =\\sqrt{2\\left(8\\right)\\left(9\\right)} \\\\ &amp; =\\sqrt{144} \\\\ &amp; =12\\end{align}[\/latex]<\/center>[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6621[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6622[\/ohm2_question]<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6753[\/ohm2_question]<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-root=\"1\">Calculate an algebraic expression using given numbers for the variables<\/span><\/li>\n<\/ul>\n<\/section>\n<div class=\"page\" title=\"Page 30\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<h2>Algebraic Expressions<\/h2>\n<p>An <strong>algebraic expression<\/strong> is a collection of constants and variables joined together by the algebraic operations of addition, subtraction, multiplication, and division. For example, [latex]3x + 2y - 7[\/latex] is an algebraic expression that contains two variables [latex]x[\/latex] and [latex]y[\/latex] and three constants [latex]3[\/latex], [latex]2[\/latex], and [latex]7[\/latex].<\/p>\n<div class=\"page\" title=\"Page 30\">\n<div class=\"layoutArea\">\n<div class=\"column\">\n<p>Any variable in an algebraic expression may take on or be assigned different values. When that happens, the value of the algebraic expression changes. To evaluate an algebraic expression means to determine the value of the expression for a given value of each variable in the expression.<\/p>\n<section class=\"textbox questionHelp\"><strong>How To: Evaluate Algebraic Expressions<\/strong>Use the following steps to evaluate an algebraic expression:<\/p>\n<ol>\n<li>Replace each variable in the expression with the given value<\/li>\n<li>Simplify the resulting expression using the order of operations<\/li>\n<\/ol>\n<p>Note: If the algebraic expression contains more than one variable, replace each variable with its assigned value and simplify the expression as before.<\/p>\n<\/section>\n<section class=\"textbox example\">Evaluate each expression for the given values.<\/p>\n<ol>\n<li>[latex]x+5[\/latex] for [latex]x=-5[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q880683\">Show Answer<\/button><\/p>\n<div id=\"q880683\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]-5[\/latex] for [latex]x[\/latex].<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{align}x+5 &=\\left(-5\\right)+5 \\\\ &=0\\end{align}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\dfrac{t}{2t - 1}[\/latex] for [latex]t=10[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q764987\">Show Answer<\/button><\/p>\n<div id=\"q764987\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]10[\/latex] for [latex]t[\/latex].<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{align}\\dfrac{t}{2t-1} & =\\dfrac{\\left(10\\right)}{2\\left(10\\right)-1} \\\\ & =\\dfrac{10}{20-1} \\\\ & =\\dfrac{10}{19}\\end{align}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\dfrac{4}{3}\\pi {r}^{3}[\/latex] for [latex]r=5[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q590356\">Show Answer<\/button><\/p>\n<div id=\"q590356\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]5[\/latex] for [latex]r[\/latex].<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{align}\\frac{4}{3}\\pi r^{3} & =\\frac{4}{3}\\pi\\left(5\\right)^{3} \\\\ & =\\frac{4}{3}\\pi\\left(125\\right) \\\\ & =\\frac{500}{3}\\pi\\end{align}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/li>\n<li>[latex]a+ab+b[\/latex] for [latex]a=11,b=-8[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q911479\">Show Answer<\/button><\/p>\n<div id=\"q911479\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]11[\/latex] for [latex]a[\/latex] and \u20138 for [latex]b[\/latex].<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{align}a+ab+b & =\\left(11\\right)+\\left(11\\right)\\left(-8\\right)+\\left(-8\\right) \\\\ & =11-8-8 \\\\ & =-85\\end{align}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/li>\n<li>[latex]\\sqrt{2{m}^{3}{n}^{2}}[\/latex] for [latex]m=2,n=3[\/latex]\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q929252\">Show Answer<\/button><\/p>\n<div id=\"q929252\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]2[\/latex] for [latex]m[\/latex] and [latex]3[\/latex] for [latex]n[\/latex].<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{align}\\sqrt{2m^{3}n^{2}} & =\\sqrt{2\\left(2\\right)^{3}\\left(3\\right)^{2}} \\\\ & =\\sqrt{2\\left(8\\right)\\left(9\\right)} \\\\ & =\\sqrt{144} \\\\ & =12\\end{align}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6621\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6621&theme=lumen&iframe_resize_id=ohm6621&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6622\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6622&theme=lumen&iframe_resize_id=ohm6622&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6753\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6753&theme=lumen&iframe_resize_id=ohm6753&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":12,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":116,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1399"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":12,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1399\/revisions"}],"predecessor-version":[{"id":6628,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1399\/revisions\/6628"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/116"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1399\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=1399"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1399"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=1399"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=1399"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}