{"id":223543,"date":"2025-06-02T03:52:30","date_gmt":"2025-06-02T03:52:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223543"},"modified":"2025-06-02T03:52:33","modified_gmt":"2025-06-02T03:52:33","slug":"math-1324-intro-math-for-business-and-social-sciences-crn-1330-caitlin-intro-homework","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/math-1324-intro-math-for-business-and-social-sciences-crn-1330-caitlin-intro-homework\/","title":{"rendered":"Math 1324, Intro Math for Business and Social Sciences CRN 1330 Caitlin Intro Homework"},"content":{"rendered":"\n

Math 1324, Intro Math for Business and Social Sciences CRN 1330 Caitlin Intro Homework: Section 2.1 (F2O) Score: 0.5 of 2 of 16 (2 complete) 2.1.5 Determine whether (3,4) is a solution of (* = 6)2 – (y +6)2. Since the expression (x-6)^2 – (y + 6)^2 evaluated at (3,4) is [7 (34). Solution: None Options: 1. None 2. None 3. None 10. None 13. None 16. None<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s carefully evaluate whether the point (3,4)(3, 4) is a solution to the expression: (x\u22126)2\u2212(y+6)2(x – 6)^2 – (y + 6)^2<\/p>\n\n\n\n

Step 1: Substitute (x,y)=(3,4)(x, y) = (3, 4) into the expression<\/h3>\n\n\n\n

(3\u22126)2\u2212(4+6)2=(\u22123)2\u2212(10)2(3 – 6)^2 – (4 + 6)^2 = (-3)^2 – (10)^2 =9\u2212100=\u221291= 9 – 100 = -91<\/p>\n\n\n\n

Step 2: Check what the problem is asking<\/h3>\n\n\n\n

It asks whether<\/strong> (3,4)(3, 4) is a solution of the expression (x\u22126)2\u2212(y+6)2(x – 6)^2 – (y + 6)^2. But a point is only a solution if<\/strong> the equation is equal to some value.<\/p>\n\n\n\n

However, the problem seems to be missing an equation (like \u201cis this equal to 0?\u201d or \u201c= -91?\u201d), so we will assume it is asking whether (3,4)(3, 4) satisfies<\/strong> the expression being equal to 0: (x\u22126)2\u2212(y+6)2=0(x – 6)^2 – (y + 6)^2 = 0<\/p>\n\n\n\n

Substitute again: (3\u22126)2\u2212(4+6)2=9\u2212100=\u221291\u22600(3 – 6)^2 – (4 + 6)^2 = 9 – 100 = -91 \\neq 0<\/p>\n\n\n\n

So, (3, 4) is not a solution<\/strong>.<\/p>\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

(3, 4) is NOT a solution.<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To determine whether a point like (3,4)(3, 4) is a solution to a mathematical expression or equation, we need to substitute the values of x=3x = 3 and y=4y = 4 into the expression and evaluate the result. In this problem, the expression given is: (x\u22126)2\u2212(y+6)2(x – 6)^2 – (y + 6)^2<\/p>\n\n\n\n

This is a difference of squares<\/strong>, a common algebraic structure with the general form A2\u2212B2A^2 – B^2, which factors into (A\u2212B)(A+B)(A – B)(A + B). However, factoring is not necessary here\u2014we simply evaluate it directly at the point.<\/p>\n\n\n\n

Plugging in x=3x = 3 and y=4y = 4: (3\u22126)2\u2212(4+6)2=(\u22123)2\u2212(10)2=9\u2212100=\u221291(3 – 6)^2 – (4 + 6)^2 = (-3)^2 – (10)^2 = 9 – 100 = -91<\/p>\n\n\n\n

If we were checking whether this expression is equal to 0<\/strong> at this point (as typically done in solving equations), then \u221291\u22600-91 \\neq 0, so the point does not satisfy the equation. That means it is not a solution<\/strong>.<\/p>\n\n\n\n

In conclusion, determining if a point is a solution involves plugging in the coordinates and checking whether the resulting value satisfies the equation. Since the result was \u221291-91 and not 0, the point (3,4)(3, 4) is not a solution to the equation.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Math 1324, Intro Math for Business and Social Sciences CRN 1330 Caitlin Intro Homework: Section 2.1 (F2O) Score: 0.5 of 2 of 16 (2 complete) 2.1.5 Determine whether (3,4) is a solution of (* = 6)2 – (y +6)2. Since the expression (x-6)^2 – (y + 6)^2 evaluated at (3,4) is [7 (34). Solution: None […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-223543","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=223543"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}