{"id":3256,"date":"2019-11-19T14:29:01","date_gmt":"2019-11-19T19:29:01","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3256"},"modified":"2019-12-29T19:45:00","modified_gmt":"2019-12-30T00:45:00","slug":"midterm-two-version-c-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-two-version-c-answer-key\/","title":{"raw":"Midterm 2: Version C Answer Key","rendered":"Midterm 2: Version C Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \r\n\r\n\r\n\r\n\r\n\r\n
    \\(2x-y-2=0\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n
    1<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n\r\n\r\n
    \\(2x+3y+6=0\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n
    \u22123<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    \u22126<\/td>\r\n2<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Graph<\/li>\r\n \t
  2. \\(\\phantom{1}\\)\r\n\\(x+y=2\\Rightarrow x=2-y \\\\ \\)\r\n\\(\\begin{array}{rrrrrrl}\r\n3(2&-&y)&-&4y&=&13 \\\\\r\n6&-&3y&-&4y&=&13 \\\\\r\n-6&&&&&&-6 \\\\\r\n\\midrule\r\n&&&&-7y&=&\\phantom{-}7 \\\\\r\n&&&&y&=&-1 \\\\ \\\\\r\n&&&&x&=&2--1 \\\\\r\n&&&&x&=&3\r\n\\end{array}\\)\r\n\\((3,-1)\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&4x&-&3y&=&6 \\\\\r\n+&4x&+&3y&=&2 \\\\\r\n\\midrule\r\n&&&8x&=&8 \\\\\r\n&&&x&=&1 \\\\ \\\\\r\n&3y&+&4(1)&=&2 \\\\\r\n&&-&4&&-4 \\\\\r\n\\midrule\r\n&&&3y&=&-2 \\\\ \\\\\r\n&&&y&=&-\\dfrac{2}{3}\r\n\\end{array}\\)\r\n\\(\\left(1,-\\dfrac{2}{3}\\right)\\)<\/li>\r\n \t
  4. \\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\left[1\\right]&(x&+&y&+&z&=&\\phantom{-}6)(-2) \\\\\r\n\\left[2\\right]&&&(-2x&+&z&=&-3)(-1) \\\\ \\\\\r\n\\left[1\\right]&-2x&-&2y&-&2z&=&-12 \\\\\r\n+&&&2y&+&4z&=&\\phantom{-}10 \\\\\r\n\\midrule\r\n&&&-2x&+&2z&=&-2 \\\\\r\n+&&\\left[2\\right]&2x&-&z&=&\\phantom{-}3 \\\\\r\n\\midrule\r\n&&&&&z&=&1 \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2y&+&4z&=&10 \\\\\r\n2y&+&4(1)&=&10 \\\\\r\n&-&4&&-4 \\\\\r\n\\midrule\r\n&&2y&=&6 \\\\\r\n&&y&=&3 \\\\ \\\\\r\n-2x&+&z&=&-3 \\\\\r\n-2x&+&1&=&-3 \\\\\r\n&-&1&&-1 \\\\\r\n\\midrule\r\n&&-2x&=&-4 \\\\\r\n&&x&=&2 \\\\\r\n\\end{array}\r\n\\end{array}\\)\r\n\\((2,3,1)\\)<\/li>\r\n \t
  5. \\(36+\\{\\cancel{-2x-\\left[6x-3(5-2x)\\right]\\}^0}1+6x^3\\)\r\n\\(36+1+6x^3\\Rightarrow 6x^3+37\\)<\/li>\r\n \t
  6. \\(6a^2b(a^2-9)\\)\r\n\\(6a^4b-54a^2b\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&+&3x&+&5&&&& \\\\\r\n\\times &x^2&+&3x&+&5&&&& \\\\\r\n\\midrule\r\n&x^4&+&3x^3&+&5x^2&&&& \\\\\r\n&&&3x^3&+&9x^2&+&15x&& \\\\\r\n+&&&&&5x^2&+&15x&+&25 \\\\\r\n\\midrule\r\n&x^4&+&6x^3&+&19x^2&+&30x&+&25\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\polylongdiv{2x^4+x^3+4x^2-4x-5}{2x+1}\\)<\/li>\r\n \t
  9. \\(x^2-x+18x-18\\)\r\n\\(x(x-1)+18(x-1)\\)\r\n\\((x-1)(x+18)\\)<\/li>\r\n \t
  10. \\(2(a^2-2ab-15b^2)\\)\r\n\\(2(a^2-5ab+3ab-15b^2)\\)\r\n\\(2\\left[a(a-5b)+3b(a-5b)\\right]\\)\r\n\\(2(a-5b)(a+3b)\\)<\/li>\r\n \t
  11. \\((2x)^3-y^3\\)\r\n\\((2x-y)(4x^2+2xy+y^2)\\)<\/li>\r\n \t
  12. \\((4y^2-x^2)(4y^2+x^2)\\)\r\n\\((2y-x)(2y+x)(4y^2+x^2)\\)<\/li>\r\n \t
  13. \\(\\phantom{1}\\)\r\n\\(B+S=30\\Rightarrow B=30-S \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\nB&-&10&=&4(S&-&10) \\\\\r\n30-S&-&10&=&4S&-&40 \\\\\r\n+S&+&40&&+S&+&40 \\\\\r\n\\midrule\r\n&&60&=&5S&& \\\\ \\\\\r\n&&S&=&\\dfrac{60}{5}&=&12 \\\\ \\\\\r\n&&\\therefore B&=&30&-&S \\\\\r\n&&B&=&30&-&12 \\\\\r\n&&B&=&18&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(D&+&N&=&\\phantom{1}18)(-1) \\\\\r\n&(10D&+&5N&=&120)(\\div 5) \\\\ \\\\\r\n&-D&-&N&=&-18 \\\\\r\n+&2D&+&N&=&\\phantom{-}24 \\\\\r\n\\midrule\r\n&&&D&=&6 \\\\ \\\\\r\n\\therefore &D&+&N&=&18 \\\\\r\n&6&+&N&=&18 \\\\\r\n&-6&&&&-6 \\\\\r\n\\midrule\r\n&&&N&=&12\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\phantom{1}\\)\r\n\\(\\text{if }x=5\\%, \\text{ then }10-x=30\\% \\\\ \\)\r\n\\(\\begin{array}{rrrrcrl}\r\n5x&+&30(10&-&x)&=&25(10) \\\\\r\n5x&+&300&-&30x&=&\\phantom{-}250 \\\\\r\n&-&300&&&&-300 \\\\\r\n\\midrule\r\n&&&&-25x&=&-50 \\\\ \\\\\r\n&&&&x&=&\\dfrac{-50}{-25}\\text{ or 2 L of 5\\%} \\\\ \\\\\r\n&&10&-&x&=&\\text{8 L of 30\\%}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

    <\/h1>","rendered":"
      \n
    1. \n\n\n\n\n\n\n
      \"2x-y-2=0\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n\u22122<\/td>\n<\/tr>\n
      1<\/td>\n0<\/td>\n<\/tr>\n
      2<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
      \"2x+3y+6=0\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n\u22122<\/td>\n<\/tr>\n
      \u22123<\/td>\n0<\/td>\n<\/tr>\n
      \u22126<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. \"\phantom{1}\"
      \n\"x+y=2\Rightarrow x=2-y \\\"
      \n\"\begin{array}{rrrrrrl}
      \n\"(3,-1)\"<\/li>\n
    3. \"\begin{array}{rrrrrr}
      \n\"\left(1,-\dfrac{2}{3}\right)\"<\/li>\n
    4. \"\begin{array}{ll}
      \n\"(2,3,1)\"<\/li>\n
    5. \"36+\{\cancel{-2x-\left[6x-3(5-2x)\right]\}^0}1+6x^3\"
      \n\"36+1+6x^3\Rightarrow 6x^3+37\"<\/li>\n
    6. \"6a^2b(a^2-9)\"
      \n\"6a^4b-54a^2b\"<\/li>\n
    7. \"\begin{array}{rrrrrlrrrr}<\/li>\n
    8. \"\polylongdiv{2x^4+x^3+4x^2-4x-5}{2x+1}\"<\/li>\n
    9. \"x^2-x+18x-18\"
      \n\"x(x-1)+18(x-1)\"
      \n\"(x-1)(x+18)\"<\/li>\n
    10. \"2(a^2-2ab-15b^2)\"
      \n\"2(a^2-5ab+3ab-15b^2)\"
      \n\"2\left[a(a-5b)+3b(a-5b)\right]\"
      \n\"2(a-5b)(a+3b)\"<\/li>\n
    11. \"(2x)^3-y^3\"
      \n\"(2x-y)(4x^2+2xy+y^2)\"<\/li>\n
    12. \"(4y^2-x^2)(4y^2+x^2)\"
      \n\"(2y-x)(2y+x)(4y^2+x^2)\"<\/li>\n
    13. \"\phantom{1}\"
      \n\"B+S=30\Rightarrow B=30-S \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    14. \"\begin{array}{rrrrrl}<\/li>\n
    15. \"\phantom{1}\"
      \n\"\text{if }x=5\%, \text{ then }10-x=30\% \\\"
      \n\"\begin{array}{rrrrcrl}<\/li>\n<\/ol>\n

      <\/h1>\n","protected":false},"author":14,"menu_order":66,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3256","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3256","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":8,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3256\/revisions"}],"predecessor-version":[{"id":3745,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3256\/revisions\/3745"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3256\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3256"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3256"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3256"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}