{"id":1764,"date":"2019-08-08T18:45:02","date_gmt":"2019-08-08T22:45:02","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1764"},"modified":"2019-08-09T12:29:06","modified_gmt":"2019-08-09T16:29:06","slug":"answer-key-10-3","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-10-3\/","title":{"raw":"Answer Key 10.3","rendered":"Answer Key 10.3"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\dfrac{30}{2}&=&15 \\\\ \\\\\r\n15^2&=&225 \\\\\r\n\\therefore x^2&-&30x+225\\text{ or }(x-15)^2\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\dfrac{24}{2}&=&12 \\\\ \\\\\r\n12^2&=&144 \\\\\r\n\\therefore a^2&-&24a+144\\text{ or }(a-12)^2\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\dfrac{36}{2}&=&18 \\\\ \\\\\r\n18^2&=&324 \\\\\r\n\\therefore m^2&-&36m+324\\text{ or }(m-18)^2\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n\\dfrac{34}{2}&=&17 \\\\ \\\\\r\n17^2&=&289 \\\\\r\n\\therefore x^2&-&34x+289\\text{ or }(x-17)^2\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\dfrac{15}{2}&=&7.5 \\\\ \\\\\r\n7.5^2&=&56.25 \\\\\r\n\\therefore x^2&-&15x+56.25\\text{ or }\\left(x-\\dfrac{15}{2}\\right)^2\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{19}{2}&=&\\dfrac{19}{2} \\\\ \\\\\r\n\\left(\\dfrac{19}{2}\\right)^2&=&\\dfrac{361}{4} \\\\\r\n\\therefore r^2&-&19r+\\dfrac{361}{4}\\text{ or } \\left(r-\\dfrac{19}{2}\\right)^2\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{1}{2}&& \\\\ \\\\\r\n\\left(\\dfrac{1}{2}\\right)^2&=&\\dfrac{1}{4} \\\\\r\n\\therefore y^2&-&y+\\dfrac{1}{4}\\text{ or } \\left(y-\\dfrac{1}{2}\\right)^2\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{17}{2}&& \\\\ \\\\\r\n\\left(\\dfrac{17}{2}\\right)^2&=&\\dfrac{289}{4} \\\\\r\n\\therefore p^2&-&17p+\\dfrac{289}{4}\\text{ or }\\left(p-\\dfrac{17}{2}\\right)^2\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrlrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx^2&-&16x&+&55&=&0&& \\\\\r\n&&&-&55&&-55&& \\\\\r\n\\midrule\r\n&&x^2&-&16x&=&-55&& \\\\ \\\\\r\nx^2&-&16x&+&64&=&64&-&55 \\\\\r\n&&(x&-&8)^2&=&9&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(x-8)^2}=\\sqrt{9}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nx&-&8&=&\\pm &3& \\\\\r\n&+&8&&+ &8& \\\\\r\n\\midrule\r\n&&x&=&8&\\pm &3 \\\\\r\n&&x&=&5,&11 &\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nn^2&-&4n&-&12&=&0&& \\\\\r\n&&&+&12&&+12&& \\\\\r\n\\midrule\r\n&&n^2&-&4n&=&12&& \\\\ \\\\\r\nn^2&-&4n&+&4&=&12&+&4 \\\\\r\n&&(n&-&2)^2&=&16&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(n-2)^2}=\\pm \\sqrt{16}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nn&-&2&=&\\pm &4& \\\\\r\n&+&2&&+&2& \\\\\r\n\\midrule\r\n&&n&=&2&\\pm &4 \\\\\r\n&&n&=&6,&-2&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nv^2&-&4v&-&21&=&0&& \\\\\r\n&&&+&21&&+21&& \\\\\r\n\\midrule\r\n&&v^2&-&4v&=&21&& \\\\ \\\\\r\nv^2&-&4v&+&4&=&21&+&4 \\\\\r\n&&(v&-&2)^2&=&25&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(v-2)^2}=\\sqrt{25}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nv&-&2&=&\\pm &5& \\\\\r\n&+&2&&+&2& \\\\\r\n\\midrule\r\n&&v&=&2&\\pm &5 \\\\\r\n&&v&=&7,&-3&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\nb^2&+&8b&+&7&=&0&& \\\\\r\n&&&-&7&&-7&& \\\\\r\n\\midrule\r\n&&b^2&+&8b&=&-7&& \\\\ \\\\\r\nb^2&+&8b&+&16&=&-7&+&16 \\\\\r\n&&(b&+&4)^2&=&9&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(b+4)^2}=\\sqrt{9}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nb&+&4&=&\\pm&3& \\\\\r\n&-&4&&-&4& \\\\\r\n\\midrule\r\n&&b&=&-4&\\pm &3 \\\\\r\n&&b&=&-7,&-1&\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\\r\nx^2&-&8x&+&16&=&-6&+&16 \\\\\r\n&&(x&-&4)^2&=&10&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(x-4)^2}=\\sqrt{10}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nx&-&4&=&\\pm&\\sqrt{10}& \\\\\r\n&+&4&&+&4& \\\\\r\n\\midrule\r\n&&x&=&4&\\pm&\\sqrt{10}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\\r\nx^2&&&-&13&=&4x&& \\\\\r\n&-&4x&+&13&&-4x&+&13 \\\\\r\n\\midrule\r\nx^2&-&4x&+&4&=&13&+&4 \\\\\r\n&&(x&-&2)^2&=&17&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(x-2)^2}=\\sqrt{17}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nx&-&2&=&\\pm&\\sqrt{17}& \\\\\r\n&+&2&&+&2& \\\\\r\n\\midrule\r\n&&x&=&2&\\pm&\\sqrt{17}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\dfrac{3}{3}(k^2&+&8k)&=&\\dfrac{-1}{3}&& \\\\ \\\\\r\n&&k^2&+&8k&=&-\\dfrac{1}{3}&& \\\\ \\\\\r\nk^2&+&8k&+&16&=&-\\dfrac{1}{3}&+&16 \\\\ \\\\\r\n&&(k&+&4)^2&=&15\\dfrac{2}{3}&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(k+4)^2}=\\sqrt{15\\dfrac{2}{3}}\\)\r\n\r\n\\(\\begin{array}{rrrrrrr}\r\nk&+&4&=&\\pm &\\sqrt{\\dfrac{47}{3}}& \\\\\r\n&-&4&&-&4& \\\\\r\n\\midrule\r\n&&k&=&-4&\\pm &\\sqrt{\\dfrac{47}{3}}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\dfrac{4}{4}(a^2&+&9a)&=&\\dfrac{-2}{4}&& \\\\ \\\\\r\na^2&+&9a&+&20.25&=&-\\dfrac{1}{2}&+&20.25 \\\\ \\\\\r\n&&(a&+&4.5)^2&=&19.75&&\r\n\\end{array}\\)\r\n\r\n\\(\\sqrt{(a+4.5)^2}=\\pm \\sqrt{19.75}\\)\r\n\r\n\\(\\begin{array}{rrrrrcl}\r\na&+&4.5&=&\\pm&\\sqrt{19.75}& \\\\\r\n&-&4.5&&-&4.5& \\\\\r\n\\midrule\r\n&&a&=&-4.5&\\pm&\\sqrt{19.75}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\begin{array}{rrl}<\/li>\n
    2. \"\begin{array}{rrl}<\/li>\n
    3. \"\begin{array}{rrl}<\/li>\n
    4. \"\begin{array}{rrl}<\/li>\n
    5. \"\begin{array}{rrl}<\/li>\n
    6. \"\begin{array}{rrl}<\/li>\n
    7. \"\begin{array}{rrl}<\/li>\n
    8. \"\begin{array}{rrl}<\/li>\n
    9. \"\begin{array}{rrrrrlrrr}\n

      \"\sqrt{(x-8)^2}=\sqrt{9}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    10. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(n-2)^2}=\pm \sqrt{16}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    11. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(v-2)^2}=\sqrt{25}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    12. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(b+4)^2}=\sqrt{9}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    13. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(x-4)^2}=\sqrt{10}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    14. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(x-2)^2}=\sqrt{17}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    15. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(k+4)^2}=\sqrt{15\dfrac{2}{3}}\"<\/p>\n

      \"\begin{array}{rrrrrrr}<\/li>\n

    16. \"\begin{array}{rrrrrrrrr}\n

      \"\sqrt{(a+4.5)^2}=\pm \sqrt{19.75}\"<\/p>\n

      \"\begin{array}{rrrrrcl}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":90,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1764","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":4,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1764\/revisions"}],"predecessor-version":[{"id":1768,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1764\/revisions\/1768"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1764\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1764"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1764"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1764"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}