{"id":3336,"date":"2019-11-19T15:06:33","date_gmt":"2019-11-19T20:06:33","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3336"},"modified":"2019-11-19T15:13:14","modified_gmt":"2019-11-19T20:13:14","slug":"midterm-3-version-e","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-3-version-e\/","title":{"raw":"Midterm 3: Version E Answer Key","rendered":"Midterm 3: Version E Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\dfrac{\\cancel{12}1\\cancel{m^3}}{\\cancel{5}1\\cancel{n^2}}\\cdot \\dfrac{\\cancel{15}\\cancel{3}1\\cancel{n^3}}{\\cancel{36}\\cancel{3}1\\cancel{m^6}}\\cdot \\dfrac{\\cancel{8}4m^{\\cancel{4}}}{\\cancel{6}3n^{\\cancel{2}}}\\Rightarrow \\dfrac{4m}{3n}\\)<\/li>\r\n \t
  2. \\(\\dfrac{\\cancel{x}1\\cancel{(x+2)}}{\\cancel{(x+2)}\\cancel{(x+7)}}\\cdot \\dfrac{\\cancel{2}1\\cancel{(x+7)}}{\\cancel{2}1x^{\\cancel{3}2}}=\\dfrac{1}{x^2}\\)<\/li>\r\n \t
  3. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x-3}{7}-\\dfrac{x-15}{28}=\\dfrac{3}{4}\\right)(28) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrrl}\r\n4(x&-&3)&-&(x&-&15)&=&3(7) \\\\\r\n4x&-&12&-&x&+&15&=&21 \\\\\r\n&+&12&&&-&15&&-15+12 \\\\\r\n\\midrule\r\n&&&&&&3x&=&18 \\\\\r\n&&&&&&x&=&6\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{l}\r\n\\dfrac{\\left(\\dfrac{x^2}{y^2}-36\\right)y^3}{\\left(\\dfrac{x+6y}{y^3}\\right)y^3}\\Rightarrow \\dfrac{x^2y-36y^3}{x+6y}\\Rightarrow \\dfrac{y(x^2-36y^2)}{x+6y}\\Rightarrow \\dfrac{y(x-6y)\\cancel{(x+6y)}}{\\cancel{(x+6y)}} \\\\ \\\\\r\n\\Rightarrow y(x-6y)\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\sqrt{x^6\\cdot x\\cdot y^4\\cdot y}+2xy\\sqrt{36\\cdot x\\cdot y^4\\cdot y}-\\sqrt{x\\cdot y^2\\cdot y} \\\\ \\\\\r\nx^3y^2\\sqrt{xy}+2xy\\cdot 6y^2\\sqrt{xy}-y\\sqrt{xy} \\\\ \\\\\r\nx^3y^2\\sqrt{xy}+12xy^3\\sqrt{xy}-y\\sqrt{xy} \\\\ \\\\\r\n\\sqrt{xy}(x^3y^2+12xy^3-y)\r\n\\end{array}\\)<\/li>\r\n \t
  6. \\(\\dfrac{\\sqrt{7}}{3-\\sqrt{7}}\\cdot \\dfrac{3+\\sqrt{7}}{3+\\sqrt{7}}\\Rightarrow \\dfrac{3\\sqrt{7}+7}{9-7}\\Rightarrow \\dfrac{3\\sqrt{7}+7}{2}\\)<\/li>\r\n \t
  7. \\(\\left(\\dfrac{\\cancel{x^0}1y^4}{z^{-12}}\\right)^{\\frac{1}{4}}\\Rightarrow \\dfrac{y^{4\\cdot \\frac{1}{4}}}{z^{-12\\cdot \\frac{1}{4}}}\\Rightarrow \\dfrac{y^1}{z^{-3}}\\Rightarrow yz^3\\)<\/li>\r\n \t
  8. \\(\\phantom{1}\\)\r\n\\((\\sqrt{4x-5})^2=(\\sqrt{2x+3})^2 \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrr}\r\n&4x&-&5&=&2x&+&3 \\\\\r\n-&2x&+&5&&-2x&+&5 \\\\\r\n\\midrule\r\n&&&2x&=&8&& \\\\\r\n&&&x&=&4&&\r\n\\end{array}\\)<\/li>\r\n \t
  9. \\(\\phantom{1}\\)\r\n
      \r\n \t
    1. \\(\\left(\\dfrac{x^2}{3}=27\\right)(3)\\Rightarrow x^2=81 \\Rightarrow x=\\pm 9\\)<\/li>\r\n \t
    2. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n27x^2+3x&=&0 \\\\\r\n3x(9x+1)&=&0 \\\\\r\nx&=&0, -\\dfrac{1}{9}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    3. \\(\\phantom{1}\\)\r\n
        \r\n \t
      1. \\(\\begin{array}{rrl}\r\n\\\\\r\n(x-12)(x+1)&=&0 \\\\\r\nx&=&12, -1\r\n\\end{array}\\)<\/li>\r\n \t
      2. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\nx^2+13x+12&=&0 \\\\\r\n(x+12)(x+1)&=&0 \\\\\r\nx&=&-1, -12\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
      3. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{2}{x}=\\dfrac{2x}{3x+8}\\right)(x)(3x+8) \\\\ \\)\r\n\\(\\begin{array}{ll}\r\n\\begin{array}{rrl}\r\n2(3x+8)&=&2x^2 \\\\\r\n6x+16&=&2x^2 \\\\\r\n0&=&2x^2-6x-16 \\\\\r\n0&=&2(x^2-3x-8)\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{l}\r\n\\\\ \\\\ \\\\\r\n\\dfrac{-(-3)\\pm \\sqrt{(-3)^2-4(1)(-8)}}{2(1)} \\\\ \\\\\r\n\\dfrac{3\\pm \\sqrt{9+32}}{2} \\\\ \\\\\r\n\\dfrac{3\\pm \\sqrt{41}}{2}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
      4. \\(\\begin{array}{rrl}\r\n\\\\ \\\\\r\n(x^2-64)(x^2+1)&=&0 \\\\\r\n(x-8)(x+8)(x^2+1)&=&0 \\\\\r\nx&=&\\pm 8\r\n\\end{array}\\)<\/li>\r\n \t
      5. \\(\\begin{array}{rrcrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&A&=&20&+&P&&&& \\\\ \\\\\r\n&&L(L&-&5)&=&20&+&2(L&-&5)&+&2L \\\\\r\nL^2&-&5L&&&=&20&+&2L&-&10&+&2L \\\\\r\n&-&4L&-&10&&-10&-&4L&&&& \\\\\r\n\\midrule\r\nL^2&-&9L&-&10&=&0&&&&&& \\\\\r\n(L&-&10)(L&+&1)&=&0&&&&&& \\\\\r\n&&&&L&=&10,&\\cancel{-1}&&&&& \\\\ \\\\\r\n&&&&W&=&L&-&5&&&& \\\\\r\n&&&&W&=&10&-&5&&&& \\\\\r\n&&&&W&=&5&&&&&&\r\n\\end{array}\\)<\/li>\r\n \t
      6. \\(\\phantom{1}\\)\r\n\\(x, x+2, x+4 \\\\ \\)\r\n\\(\\begin{array}{rrcrrrrrcrr}\r\n&&x(x&+&4)&=&35&+&10(x&+&2) \\\\\r\nx^2&+&4x&&&=&35&+&10x&+&20 \\\\\r\n&-&10x&-&55&&-55&-&10x&& \\\\\r\n\\midrule\r\nx^2&-&6x&-&55&=&0&&&& \\\\\r\n(x&-&11)(x&+&5)&=&0&&&& \\\\\r\n&&&&x&=&11,&-5&&&\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\n\\(\\text{numbers are }11,13,15\\text{ or }-5,-3,-1\\)<\/li>\r\n \t
      7. \\(\\begin{array}{rrrrrrcrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&d_{\\text{d}}&=&d_{\\text{u}}&+&9&& \\\\ \\\\\r\n&3(5&+&r)&=&4(5&-&r)&+&9 \\\\\r\n&15&+&3r&=&20&-&4r&+&9 \\\\\r\n-&15&+&4r&&-15&+&4r&& \\\\\r\n\\midrule\r\n&&&7r&=&14&&&& \\\\\r\n&&&r&=&2&\\text{km\/h}&&&\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
          \n
        1. \"\dfrac{\cancel{12}1\cancel{m^3}}{\cancel{5}1\cancel{n^2}}\cdot \dfrac{\cancel{15}\cancel{3}1\cancel{n^3}}{\cancel{36}\cancel{3}1\cancel{m^6}}\cdot \dfrac{\cancel{8}4m^{\cancel{4}}}{\cancel{6}3n^{\cancel{2}}}\Rightarrow \dfrac{4m}{3n}\"<\/li>\n
        2. \"\dfrac{\cancel{x}1\cancel{(x+2)}}{\cancel{(x+2)}\cancel{(x+7)}}\cdot \dfrac{\cancel{2}1\cancel{(x+7)}}{\cancel{2}1x^{\cancel{3}2}}=\dfrac{1}{x^2}\"<\/li>\n
        3. \"\phantom{1}\"
          \n\"\left(\dfrac{x-3}{7}-\dfrac{x-15}{28}=\dfrac{3}{4}\right)(28) \\\"
          \n\"\begin{array}{rrrrrrrrl}<\/li>\n
        4. \"\begin{array}{l}<\/li>\n
        5. \"\begin{array}{l}<\/li>\n
        6. \"\dfrac{\sqrt{7}}{3-\sqrt{7}}\cdot \dfrac{3+\sqrt{7}}{3+\sqrt{7}}\Rightarrow \dfrac{3\sqrt{7}+7}{9-7}\Rightarrow \dfrac{3\sqrt{7}+7}{2}\"<\/li>\n
        7. \"\left(\dfrac{\cancel{x^0}1y^4}{z^{-12}}\right)^{\frac{1}{4}}\Rightarrow \dfrac{y^{4\cdot \frac{1}{4}}}{z^{-12\cdot \frac{1}{4}}}\Rightarrow \dfrac{y^1}{z^{-3}}\Rightarrow yz^3\"<\/li>\n
        8. \"\phantom{1}\"
          \n\"(\sqrt{4x-5})^2=(\sqrt{2x+3})^2 \\\"
          \n\"\begin{array}{rrrrrrrr}<\/li>\n
        9. \"\phantom{1}\"\n
            \n
          1. \"\left(\dfrac{x^2}{3}=27\right)(3)\Rightarrow x^2=81 \Rightarrow x=\pm 9\"<\/li>\n
          2. \"\begin{array}{rrl}<\/li>\n<\/ol>\n<\/li>\n
          3. \"\phantom{1}\"\n
              \n
            1. \"\begin{array}{rrl}<\/li>\n
            2. \"\begin{array}{rrl}<\/li>\n<\/ol>\n<\/li>\n
            3. \"\phantom{1}\"
              \n\"\left(\dfrac{2}{x}=\dfrac{2x}{3x+8}\right)(x)(3x+8) \\\"
              \n\"\begin{array}{ll}<\/li>\n
            4. \"\begin{array}{rrl}<\/li>\n
            5. \"\begin{array}{rrcrrrrrrrrrr}<\/li>\n
            6. \"\phantom{1}\"
              \n\"x, x+2, x+4 \\\"
              \n\"\begin{array}{rrcrrrrrcrr}
              \n\"\phantom{1}\"
              \n\"\text{numbers are }11,13,15\text{ or }-5,-3,-1\"<\/li>\n
            7. \"\begin{array}{rrrrrrcrrr}<\/li>\n<\/ol>\n","protected":false},"author":14,"menu_order":101,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3336","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3336","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\/14"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3336\/revisions"}],"predecessor-version":[{"id":3349,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3336\/revisions\/3349"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3336\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3336"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3336"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3336"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3336"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}