{"id":235,"date":"2023-06-21T13:22:47","date_gmt":"2023-06-21T13:22:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-15\/"},"modified":"2023-07-03T20:30:13","modified_gmt":"2023-07-03T20:30:13","slug":"summary-review-15","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-15\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"\n\n<h2>Key Concepts<\/h2>\n<ul>\n \t<li>Formulas for specific types of applications containing more than one variable may be solved for an unknown variable by substituting known values and solving the formula for the unknown variable.<\/li>\n \t<li>Functions containing radicals may be graphed by substituting input values and solving for the coordinating output value to create a graph of points existing on the graph. After plotting enough points to obtain the shape of the graph, draw a smooth curve between them.<\/li>\n \t<li>Work [latex]W[\/latex], rate [latex]r[\/latex], and time [latex]t[\/latex] may be related by the formulas [latex]W=rt,\\text{ }t=\\dfrac{W}{r}\\text{, and }r=\\dfrac{W}{t}[\/latex]<\/li>\n \t<li>Proportions, equations of the form [latex]\\dfrac{a}{b}=\\dfrac{c}{d}[\/latex], are helpful for setting up relationships in applications. Solve by cross-multiplying or by multiplying both sides of the equation by the reciprocal of one.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n \t<dt><strong>proportion<\/strong><\/dt>\n \t<dd>a statement of the equality of two ratios<\/dd>\n \t<dt><strong>radical formula<\/strong><\/dt>\n \t<dd>an equation used in certain applications that contains at least one radical expression (a variable expression using a radical such as a square or cube root)<\/dd>\n \t<dt><strong>rational formula<\/strong><\/dt>\n \t<dd>an equation used in certain applications that contains at least one rational expression (a variable expression in fraction form)<\/dd>\n<\/dl>\n\n","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>Formulas for specific types of applications containing more than one variable may be solved for an unknown variable by substituting known values and solving the formula for the unknown variable.<\/li>\n<li>Functions containing radicals may be graphed by substituting input values and solving for the coordinating output value to create a graph of points existing on the graph. After plotting enough points to obtain the shape of the graph, draw a smooth curve between them.<\/li>\n<li>Work [latex]W[\/latex], rate [latex]r[\/latex], and time [latex]t[\/latex] may be related by the formulas [latex]W=rt,\\text{ }t=\\dfrac{W}{r}\\text{, and }r=\\dfrac{W}{t}[\/latex]<\/li>\n<li>Proportions, equations of the form [latex]\\dfrac{a}{b}=\\dfrac{c}{d}[\/latex], are helpful for setting up relationships in applications. Solve by cross-multiplying or by multiplying both sides of the equation by the reciprocal of one.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl>\n<dt><strong>proportion<\/strong><\/dt>\n<dd>a statement of the equality of two ratios<\/dd>\n<dt><strong>radical formula<\/strong><\/dt>\n<dd>an equation used in certain applications that contains at least one radical expression (a variable expression using a radical such as a square or cube root)<\/dd>\n<dt><strong>rational formula<\/strong><\/dt>\n<dd>an equation used in certain applications that contains at least one rational expression (a variable expression in fraction form)<\/dd>\n<\/dl>\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-235\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <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":395986,"menu_order":29,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"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-235","chapter","type-chapter","status-publish","hentry"],"part":202,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/235","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions"}],"predecessor-version":[{"id":580,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/235\/revisions\/580"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/202"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/235\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/media?parent=235"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=235"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/contributor?post=235"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/wp-json\/wp\/v2\/license?post=235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}