{"id":3252,"date":"2019-11-19T14:28:22","date_gmt":"2019-11-19T19:28:22","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3252"},"modified":"2019-12-29T19:43:56","modified_gmt":"2019-12-30T00:43:56","slug":"midterm-two-version-a-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-two-version-a-answer-key\/","title":{"raw":"Midterm 2: Version A Answer Key","rendered":"Midterm 2: Version A Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \r\n\r\n\r\n\r\n\r\n
    \\(x+2y=-5\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n\\(-\\dfrac{5}{2}\\)<\/td>\r\n<\/tr>\r\n
    \u22125<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n
    \\(x-y=-2\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n2<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Bar<\/li>\r\n \t
  2. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrl}\r\n&(4x&-&3y&=&13)(2) \\\\\r\n&(5x&-&2y&=&\\phantom{1}4)(-3) \\\\ \\\\\r\n&8x&-&6y&=&\\phantom{-}26 \\\\\r\n+&-15x&+&6y&=&-12 \\\\\r\n\\midrule\r\n&&&-7x&=&\\phantom{-}14 \\\\ \\\\\r\n&&&x&=&\\dfrac{14}{-7}\\text{ or }-2\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrcrl}\r\n\\\\\r\n5x&-&2y&=&\\phantom{+1}4 \\\\\r\n5(-2)&-&2y&=&\\phantom{+1}4 \\\\\r\n-10&-&2y&=&\\phantom{+1}4 \\\\\r\n+10&&&&+10 \\\\\r\n\\midrule\r\n&&-2y&=&\\phantom{+}14 \\\\ \\\\\r\n&&y&=&\\dfrac{14}{-2}\\text{ or }-7\r\n\\end{array}\r\n\\end{array}\\)\r\n\\((-2,-7)\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x&-&2y&=&-5 \\\\\r\n&(2x&+&y&=&\\phantom{-}5)(2) \\\\ \\\\\r\n&x&-&2y&=&-5 \\\\\r\n+&4x&+&2y&=&10 \\\\\r\n\\midrule\r\n&&&5x&=&5 \\\\\r\n&&&x&=&1 \\\\ \\\\\r\n\\therefore &2(1)&+&y&=&\\phantom{-}5 \\\\\r\n&-2&&&&-2 \\\\\r\n\\midrule\r\n&&&y&=&\\phantom{-}3\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(x&+&y&+&2z&=&0)(-2) \\\\ \\\\\r\n&-2x&-&2y&-&4z&=&0 \\\\\r\n+&2x&&&+&z&=&1 \\\\\r\n\\midrule\r\n&&&-2y&-&3z&=&1 \\\\ \\\\\r\n&&&(-2y&-&3z&=&1)(3) \\\\\r\n&&&(3y&+&4z&=&0)(2) \\\\ \\\\\r\n&&&-6y&-&9z&=&3 \\\\\r\n&&+&6y&+&8z&=&0 \\\\\r\n\\midrule\r\n&&&&&-z&=&3 \\\\\r\n&&&&&z&=&-3 \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrcrl}\r\n\\\\ \\\\\r\n3y&+&4z&=&0 \\\\\r\n3y&+&4(-3)&=&0 \\\\\r\n3y&-&12&=&0 \\\\\r\n&&3y&=&12 \\\\\r\n&&y&=&4 \\\\ \\\\\r\n2x&+&z&=&1 \\\\\r\n2x&+&(-3)&=&1 \\\\\r\n&&2x&=&4 \\\\\r\n&&x&=&2 \\\\\r\n\\end{array}\r\n\\end{array}\\)\r\n\\((2,4,-3)\\)<\/li>\r\n \t
  5. \\(28-\\{5x-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+5x^2\\)\r\n\\(28-\\{5x-1\\}+5x^2\\)\r\n\\(28-5x+1+5x^2\\)\r\n\\(5x^2-5x+29\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrrcrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&a&-&3&& \\\\\r\n\\times &a&-&3&& \\\\\r\n\\midrule\r\n&a^2&-&3a&& \\\\\r\n+&&-&3a&+&9 \\\\\r\n\\midrule\r\n&a^2&-&6a&+&9 \\\\ \\\\\r\n&a^2&-&6a&+&9 \\\\\r\n\\times&&&&&4a^2 \\\\\r\n\\midrule\r\n&4a^4&-&24a^3&+&36a^2 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&+&2x&+&3&&&& \\\\\r\n\\times&x^2&+&2x&+&3&&&& \\\\\r\n\\midrule\r\n&x^4&+&2x^3&+&3x^2&&&& \\\\\r\n&&&2x^3&+&4x^2&+&6x&& \\\\\r\n+&&&&&3x^2&+&6x&+&9 \\\\\r\n\\midrule\r\n&x^4&+&4x^3&+&10x^2&+&12x&+&9\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\polylongdiv{2x^3-7x^2+15}{x-2}\\)<\/li>\r\n \t
  9. \\(a(2b+3c)-2(2b+3c)\\)\r\n\\((2b+3c)(a-2)\\)<\/li>\r\n \t
  10. \\(a^2-5ab+3ab-15b^2\\)\r\n\\(a(a-5b)+3b(a-5b)\\)\r\n\\((a-5b)(a+3b)\\)<\/li>\r\n \t
  11. \\(x^2(x+1)-9(x+1)\\)\r\n\\((x^2-9)(x+1)\\)\r\n\\((x+3)(x-3)(x+1)\\)<\/li>\r\n \t
  12. \\((x)^3-(4y)^3\\)\r\n\\((x-4y)(x^2+4xy+16y^2)\\)<\/li>\r\n \t
  13. \\(\\phantom{1}\\)\r\n\\(B+S=35\\Rightarrow B=35-S \\\\ \\)\r\n\\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrrr}\r\n&B&-&10&=&2(S&-&10) \\\\\r\n&35-S&-&10&=&2S&-&20 \\\\\r\n&25&-&S&=&2S&-&20 \\\\\r\n+&20&+&S&&S&+&20 \\\\\r\n\\midrule\r\n&&&45&=&3S&&\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\nS&=&\\dfrac{45}{3}\\text{ or }15 \\\\ \\\\\r\n\\therefore B&=&35-S \\\\\r\nB&=&35-15 \\\\\r\nB&=&20 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\phantom{1}\\)\r\n\\(D+Q=20\\Rightarrow Q=20-D \\\\ \\)\r\n\\(\\begin{array}{ll}\r\n\\begin{array}{rrlrr}\r\n10D&+&25Q&=&275 \\\\\r\n10D&+&25(20-D)&=&275 \\\\\r\n10D&+&500-25D&=&275 \\\\\r\n&-&500&&-500 \\\\\r\n\\midrule\r\n&&\\phantom{500}-15D&=&-225\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\nD&=&\\dfrac{-225}{-15}\\text{ or }15 \\\\ \\\\\r\n\\therefore Q&=&20-D \\\\\r\nQ&=&20-15 \\\\\r\nQ&=&5 \\\\\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\phantom{1}\\)\r\n\\(A+B=50\\Rightarrow A=50-B \\\\ \\)\r\n\\(\\begin{array}{rrrrrrl}\r\n(3.95A&+&3.70(50&-&A)&=&191.25)(100) \\\\ \\\\\r\n395A&+&370(50&-&A)&=&19125 \\\\\r\n395A&+&18500&-&370A&=&19125 \\\\\r\n&-&18500&&&&-18500 \\\\\r\n\\midrule\r\n&&&&25A&=&625 \\\\ \\\\\r\n&&&&A&=&\\dfrac{625}{25}\\text{ or 25 kg} \\\\ \\\\\r\n&&&&B&=&50-25 \\\\\r\n&&&&B&=&25 \\text{ kg} \\\\\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

    <\/h1>","rendered":"
      \n
    1. \n\n\n\n\n\n
      \"x+2y=-5\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n\"-\dfrac{5}{2}\"<\/td>\n<\/tr>\n
      \u22125<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
      \"x-y=-2\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n2<\/td>\n<\/tr>\n
      \u22122<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Bar<\/li>\n

    2. \"\begin{array}{ll}
      \n\"(-2,-7)\"<\/li>\n
    3. \"\begin{array}{rrrrrl}<\/li>\n
    4. \"\begin{array}{ll}
      \n\"(2,4,-3)\"<\/li>\n
    5. \"28-\{5x-\cancel{\left[6x-3(5-2x)\right]^0}1\}+5x^2\"
      \n\"28-\{5x-1\}+5x^2\"
      \n\"28-5x+1+5x^2\"
      \n\"5x^2-5x+29\"<\/li>\n
    6. \"\begin{array}{rrrcrl}<\/li>\n
    7. \"\begin{array}{rrrrrlrrrr}<\/li>\n
    8. \"\polylongdiv{2x^3-7x^2+15}{x-2}\"<\/li>\n
    9. \"a(2b+3c)-2(2b+3c)\"
      \n\"(2b+3c)(a-2)\"<\/li>\n
    10. \"a^2-5ab+3ab-15b^2\"
      \n\"a(a-5b)+3b(a-5b)\"
      \n\"(a-5b)(a+3b)\"<\/li>\n
    11. \"x^2(x+1)-9(x+1)\"
      \n\"(x^2-9)(x+1)\"
      \n\"(x+3)(x-3)(x+1)\"<\/li>\n
    12. \"(x)^3-(4y)^3\"
      \n\"(x-4y)(x^2+4xy+16y^2)\"<\/li>\n
    13. \"\phantom{1}\"
      \n\"B+S=35\Rightarrow B=35-S \\\"
      \n\"\begin{array}{ll}<\/li>\n
    14. \"\phantom{1}\"
      \n\"D+Q=20\Rightarrow Q=20-D \\\"
      \n\"\begin{array}{ll}<\/li>\n
    15. \"\phantom{1}\"
      \n\"A+B=50\Rightarrow A=50-B \\\"
      \n\"\begin{array}{rrrrrrl}<\/li>\n<\/ol>\n

      <\/h1>\n","protected":false},"author":14,"menu_order":64,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3252","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3252","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":6,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3252\/revisions"}],"predecessor-version":[{"id":3743,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3252\/revisions\/3743"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3252\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3252"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3252"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3252"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}