{"id":3259,"date":"2019-11-19T14:29:27","date_gmt":"2019-11-19T19:29:27","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3259"},"modified":"2019-12-29T19:45:35","modified_gmt":"2019-12-30T00:45:35","slug":"midterm-two-version-d-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-two-version-d-answer-key\/","title":{"raw":"Midterm 2: Version D Answer Key","rendered":"Midterm 2: Version D Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \r\n\r\n\r\n\r\n\r\n
    \\(x-2y=-6\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
    \u22126<\/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=6\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    0<\/td>\r\n6<\/td>\r\n<\/tr>\r\n
    6<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Graph<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(3x&-&2y&=&0)(5) \\\\\r\n&(2x&+&5y&=&0)(2) \\\\ \\\\\r\n&15x&-&10y&=&0 \\\\\r\n+&4x&+&10y&=&0 \\\\\r\n\\midrule\r\n&&&19x&=&0 \\\\\r\n&&&x&=&0 \\\\ \\\\\r\n&\\therefore \\cancel{2x}0&+&5y&=&0 \\\\\r\n&&&5y&=&0 \\\\\r\n&&&y&=&0\r\n\\end{array}\\)\r\n\\((0,0)\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrrr}\r\n\\\\ \\\\\r\n&2x&-&3y&=&8 \\\\\r\n+&-2x&+&3y&=&4 \\\\\r\n\\midrule\r\n&&&0&=&12 \\\\\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\n\u2234 No solution. Parallel lines.<\/li>\r\n \t
  4. \\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(2x&+&y&-&3z&=&-7)(2) \\\\ \\\\\r\n&4x&+&2y&-&6z&=&-14 \\\\\r\n+&&-&2y&+&3z&=&\\phantom{-1}9 \\\\\r\n\\midrule\r\n&&&4x&-&3z&=&-5 \\\\ \\\\\r\n&&&(3x&+&z&=&6)(3) \\\\ \\\\\r\n&&&4x&-&3z&=&-5 \\\\\r\n+&&&9x&+&3z&=&18 \\\\\r\n\\midrule\r\n&&&&&13x&=&13 \\\\\r\n&&&&&x&=&1\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n3x&+&z&=&6 \\\\\r\n3(1)&+&z&=&6 \\\\\r\n-3&&&&-3 \\\\\r\n\\midrule\r\n&&z&=&3 \\\\ \\\\\r\n-2y&+&3z&=&9 \\\\\r\n-2y&+&3(3)&=&9 \\\\\r\n&&-9&&-9 \\\\\r\n\\midrule\r\n&&-2y&=&0 \\\\\r\n&&y&=&0\r\n\\end{array}\r\n\\end{array}\\)\r\n\\((1,0,3)\\)<\/li>\r\n \t
  5. \\(36-\\cancel{\\{-2x-\\left[6x-3(5-2x)\\right]\\}^0}1+3x^2\\)\r\n\\(36-1+3x^2\\)\r\n\\(35+3x^2\\)<\/li>\r\n \t
  6. \\(3a^2(a^2-4a+4)\\)\r\n\\(3a^4-12a^3+12a^2\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&+&2x&-&4&&&& \\\\\r\n\\times &x^2&+&2x&-&4&&&& \\\\\r\n\\midrule\r\n&x^4&+&2x^3&-&4x^2&&&& \\\\\r\n&&&2x^3&+&4x^2&-&8x&& \\\\\r\n+&&&&-&4x^2&-&8x&+&16 \\\\\r\n\\midrule\r\n&x^4&+&4x^3&-&4x^2&-&16x&+&16\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\(\\polylongdiv{x^4+4x^3+4x^2+10x+20}{x+2}\\)<\/li>\r\n \t
  9. \\(x^2-3x+6x-18\\)\r\n\\(x(x-3)+6(x-3)\\)\r\n\\((x-3)(x+6)\\)<\/li>\r\n \t
  10. \\(3x^2+xy+24xy+8y^2\\)\r\n\\(x(3x+y)+8y(3x+y)\\)\r\n\\((3x+y)(x+8y)\\)<\/li>\r\n \t
  11. \\((5x)^3-y^3\\)\r\n\\((5x-y)(25x^2+5xy+y^2)\\)<\/li>\r\n \t
  12. \\((9y^2-4x^2)(9y^2+4x^2)\\)\r\n\\((3y-2x)(3y+2x)(9y^2+4x^2)\\)<\/li>\r\n \t
  13. \\(\\phantom{1}\\)\r\n\\(B+G=18\\Rightarrow G=18-B \\\\ \\)\r\n\\(\\begin{array}{rrrcrrrr}\r\n&G&-&4&=&4(B&-&4) \\\\\r\n&18-B&-&4&=&4B&-&16 \\\\\r\n+&16+B&&&&+B&+&16 \\\\\r\n\\midrule\r\n&&&30&=&5B&& \\\\ \\\\\r\n&&&B&=&\\dfrac{30}{5}&=&6 \\\\ \\\\\r\n&&&\\therefore G&=&18&-&B \\\\\r\n&&&\\phantom{\\therefore}G&=&18&-&6 \\\\\r\n&&&\\phantom{\\therefore}G&=&12&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&(D&+&Q&=&20)(-10) \\\\\r\n&10D&+&25Q&=&350 \\\\ \\\\\r\n&-10D&-&10Q&=&-200 \\\\\r\n+&10D&+&25Q&=&\\phantom{-}350 \\\\\r\n\\midrule\r\n&&&15Q&=&150 \\\\ \\\\\r\n&&&Q&=&\\dfrac{150}{15}\\text{ or }10 \\\\ \\\\\r\n\\therefore &D&+&Q&=&\\phantom{-}20 \\\\\r\n&D&+&10&=&\\phantom{-}20 \\\\\r\n&&-&10&&-10 \\\\\r\n\\midrule\r\n&&&D&=&10\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\phantom{1}\\)\r\n\\(A+B=60\\Rightarrow B=60-A \\\\ \\)\r\n\\(\\begin{array}{llclrll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&3.80A&+&3.55B&=&\\phantom{-}218.50 \\\\\r\n3.80A&+&3.55(60&-&A)&=&\\phantom{-}218.50 \\\\\r\n3.80A&+&213&-&3.55A&=&\\phantom{-}218.50 \\\\\r\n&-&213&&&=&-213 \\\\\r\n\\midrule\r\n&&&&0.25A&=&5.50 \\\\ \\\\\r\n&&&&A&=&\\dfrac{5.50}{0.25}\\text{ or 22 kg} \\\\ \\\\\r\n&&&&B&=&60-A \\\\\r\n&&&&B&=&60-22 \\\\\r\n&&&&B&=&38\\text{ kg}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

    <\/h1>","rendered":"
      \n
    1. \n\n\n\n\n\n
      \"x-2y=-6\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n3<\/td>\n<\/tr>\n
      \u22126<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
      \"x+y=6\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      0<\/td>\n6<\/td>\n<\/tr>\n
      6<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. \"\begin{array}{rrrrrl}
      \n\"(0,0)\"<\/li>\n
    3. \"\begin{array}{rrrrrr}
      \n\"\phantom{1}\"
      \n\u2234 No solution. Parallel lines.<\/li>\n
    4. \"\begin{array}{ll}
      \n\"(1,0,3)\"<\/li>\n
    5. \"36-\cancel{\{-2x-\left[6x-3(5-2x)\right]\}^0}1+3x^2\"
      \n\"36-1+3x^2\"
      \n\"35+3x^2\"<\/li>\n
    6. \"3a^2(a^2-4a+4)\"
      \n\"3a^4-12a^3+12a^2\"<\/li>\n
    7. \"\begin{array}{rrrrrlrrrr}<\/li>\n
    8. \"\polylongdiv{x^4+4x^3+4x^2+10x+20}{x+2}\"<\/li>\n
    9. \"x^2-3x+6x-18\"
      \n\"x(x-3)+6(x-3)\"
      \n\"(x-3)(x+6)\"<\/li>\n
    10. \"3x^2+xy+24xy+8y^2\"
      \n\"x(3x+y)+8y(3x+y)\"
      \n\"(3x+y)(x+8y)\"<\/li>\n
    11. \"(5x)^3-y^3\"
      \n\"(5x-y)(25x^2+5xy+y^2)\"<\/li>\n
    12. \"(9y^2-4x^2)(9y^2+4x^2)\"
      \n\"(3y-2x)(3y+2x)(9y^2+4x^2)\"<\/li>\n
    13. \"\phantom{1}\"
      \n\"B+G=18\Rightarrow G=18-B \\\"
      \n\"\begin{array}{rrrcrrrr}<\/li>\n
    14. \"\begin{array}{rrrrrl}<\/li>\n
    15. \"\phantom{1}\"
      \n\"A+B=60\Rightarrow B=60-A \\\"
      \n\"\begin{array}{llclrll}<\/li>\n<\/ol>\n

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