{"id":1766,"date":"2015-11-12T18:30:45","date_gmt":"2015-11-12T18:30:45","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1766"},"modified":"2015-11-12T18:30:45","modified_gmt":"2015-11-12T18:30:45","slug":"key-concepts-glossary-31","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/key-concepts-glossary-31\/","title":{"raw":"Key Concepts &amp; Glossary","rendered":"Key Concepts &amp; Glossary"},"content":{"raw":"<h2>Key Concepts<\/h2>\n<ul><li>There are three possible types of solutions to a system of equations representing a line and a parabola: (1) no solution, the line does not intersect the parabola; (2) one solution, the line is tangent to the parabola; and (3) two solutions, the line intersects the parabola in two points.<\/li>\n\t<li>There are three possible types of solutions to a system of equations representing a circle and a line: (1) no solution, the line does not intersect the circle; (2) one solution, the line is tangent to the parabola; (3) two solutions, the line intersects the circle in two points.<\/li>\n\t<li>There are five possible types of solutions to the system of nonlinear equations representing an ellipse and a circle:\n(1) no solution, the circle and the ellipse do not intersect; (2) one solution, the circle and the ellipse are tangent to each other; (3) two solutions, the circle and the ellipse intersect in two points; (4) three solutions, the circle and ellipse intersect in three places; (5) four solutions, the circle and the ellipse intersect in four points.<\/li>\n\t<li>An inequality is graphed in much the same way as an equation, except for &gt; or &lt;, we draw a dashed line and shade the region containing the solution set.<\/li>\n\t<li>Inequalities are solved the same way as equalities, but solutions to systems of inequalities must satisfy both inequalities.<\/li>\n<\/ul><h2>Glossary<\/h2>\n<dl id=\"fs-id1165132944813\" class=\"definition\"><dt>feasible region<\/dt><dd id=\"fs-id1165132944818\">the solution to a system of nonlinear inequalities that is the region of the graph where the shaded regions of each inequality intersect<\/dd><\/dl><dl id=\"fs-id1165132944823\" class=\"definition\"><dt>nonlinear inequality<\/dt><dd id=\"fs-id1165132944828\">an inequality containing a nonlinear expression<\/dd><\/dl><dl id=\"fs-id1165132944832\" class=\"definition\"><dt>system of nonlinear equations<\/dt><dd id=\"fs-id1165137681182\">a system of equations containing at least one equation that is of degree larger than one<\/dd><\/dl><dl id=\"fs-id1165137681185\" class=\"definition\"><dt>system of nonlinear inequalities<\/dt><dd id=\"fs-id1165137681190\">a system of two or more inequalities in two or more variables containing at least one inequality that is not linear<\/dd><\/dl>","rendered":"<h2>Key Concepts<\/h2>\n<ul>\n<li>There are three possible types of solutions to a system of equations representing a line and a parabola: (1) no solution, the line does not intersect the parabola; (2) one solution, the line is tangent to the parabola; and (3) two solutions, the line intersects the parabola in two points.<\/li>\n<li>There are three possible types of solutions to a system of equations representing a circle and a line: (1) no solution, the line does not intersect the circle; (2) one solution, the line is tangent to the parabola; (3) two solutions, the line intersects the circle in two points.<\/li>\n<li>There are five possible types of solutions to the system of nonlinear equations representing an ellipse and a circle:<br \/>\n(1) no solution, the circle and the ellipse do not intersect; (2) one solution, the circle and the ellipse are tangent to each other; (3) two solutions, the circle and the ellipse intersect in two points; (4) three solutions, the circle and ellipse intersect in three places; (5) four solutions, the circle and the ellipse intersect in four points.<\/li>\n<li>An inequality is graphed in much the same way as an equation, except for &gt; or &lt;, we draw a dashed line and shade the region containing the solution set.<\/li>\n<li>Inequalities are solved the same way as equalities, but solutions to systems of inequalities must satisfy both inequalities.<\/li>\n<\/ul>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1165132944813\" class=\"definition\">\n<dt>feasible region<\/dt>\n<dd id=\"fs-id1165132944818\">the solution to a system of nonlinear inequalities that is the region of the graph where the shaded regions of each inequality intersect<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132944823\" class=\"definition\">\n<dt>nonlinear inequality<\/dt>\n<dd id=\"fs-id1165132944828\">an inequality containing a nonlinear expression<\/dd>\n<\/dl>\n<dl id=\"fs-id1165132944832\" class=\"definition\">\n<dt>system of nonlinear equations<\/dt>\n<dd id=\"fs-id1165137681182\">a system of equations containing at least one equation that is of degree larger than one<\/dd>\n<\/dl>\n<dl id=\"fs-id1165137681185\" class=\"definition\">\n<dt>system of nonlinear inequalities<\/dt>\n<dd id=\"fs-id1165137681190\">a system of two or more inequalities in two or more variables containing at least one inequality that is not linear<\/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-1766\">\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>Precalculus. <strong>Authored by<\/strong>: OpenStax College. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/Preface\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/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":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Precalculus\",\"author\":\"OpenStax College\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1\/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-1766","chapter","type-chapter","status-publish","hentry"],"part":1751,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1766","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":1,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1766\/revisions"}],"predecessor-version":[{"id":2262,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1766\/revisions\/2262"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1751"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1766\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/media?parent=1766"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1766"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1766"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/wp-json\/wp\/v2\/license?post=1766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}