{"id":3254,"date":"2019-11-19T14:28:45","date_gmt":"2019-11-19T19:28:45","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3254"},"modified":"2019-12-29T19:44:29","modified_gmt":"2019-12-30T00:44:29","slug":"midterm-two-version-b-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-two-version-b-answer-key\/","title":{"raw":"Midterm 2: Version B Answer Key","rendered":"Midterm 2: Version B Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \r\n\r\n\r\n\r\n\r\n\r\n
    \\(x+y=5\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    5<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    3<\/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-y=1\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    1<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
    \u22121<\/td>\r\n\u22123<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Graph<\/li>\r\n \t
  2. \\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n4(4y&+&2)&+&3y&=&8 \\\\\r\n16y&+&8&+&3y&=&8 \\\\\r\n&-&8&&&&-8 \\\\\r\n\\midrule\r\n&&&&19y&=&0 \\\\\r\n&&&&y&=&0\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\\r\nx&=&4y&+&2 \\\\\r\nx&=&\\cancel{4y}0&+&2 \\\\\r\nx&=&2&&\r\n\\end{array}\r\n\\end{array}\\)\r\n\\((2,0)\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&5x&-&3y&=&2 \\\\\r\n&(3x&+&y&=&4)(3) \\\\ \\\\\r\n&5x&-&3y&=&\\phantom{1}2 \\\\\r\n+&9x&+&3y&=&12 \\\\\r\n\\midrule\r\n&&&14x&=&14 \\\\\r\n&&&x&=&1 \\\\ \\\\\r\n&\\therefore 3(1)&+&y&=&4 \\\\\r\n&3&+&y&=&4 \\\\\r\n&&&y&=&1\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&(x&-&2z&=&-7)(-1) \\\\ \\\\\r\n&x&+&y&+&z&=&3 \\\\\r\n+&-x&&&+&2z&=&7 \\\\\r\n\\midrule\r\n&&&y&+&3z&=&10 \\\\\r\n&&&(-2y&+&4z&=&20)(\\div 2) \\\\\r\n&&&&&\\Downarrow&& \\\\\r\n&&&y&+&3z&=&10 \\\\\r\n&&+&-y&+&2z&=&10 \\\\\r\n\\midrule\r\n&&&&&5z&=&20 \\\\\r\n&&&&&z&=&4 \\\\\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx&-&2z&=&-7 \\\\\r\nx&-&2(4)&=&-7 \\\\\r\nx&-&8&=&-7 \\\\\r\n&+&8&&+8 \\\\\r\n\\midrule\r\n&&x&=&1 \\\\ \\\\\r\ny&+&3z&=&10 \\\\\r\ny&+&3(4)&=&10 \\\\\r\ny&+&12&=&10 \\\\\r\n&-&12&&-12 \\\\\r\n\\midrule\r\n&&y&=&-2 \\\\\r\n\\end{array}\r\n\\end{array}\\)\r\n\\((1,-2,4)\\)<\/li>\r\n \t
  5. \\(5-3\\left[4x-2\\cancel{(6x-5)^0}1-(7-2x)\\right]\\)\r\n\\(5-3\\left[4x-2(1)-(7-2x)\\right]\\)\r\n\\(5-3\\left[6x-9\\right]\\)\r\n\\(5-18x+27\\Rightarrow -18x+32\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrrlrl}\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\\times&&&&&3a^2 \\\\\r\n\\midrule\r\n&3a^4&+&18a^3&+&27a^2\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrrlrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&x^2&+&x&+&5\\phantom{x^2}&&&& \\\\\r\n\\times&x^2&+&x&-&5\\phantom{x^2}&&&& \\\\\r\n\\midrule\r\n&x^4&+&x^3&+&5x^2&&&& \\\\\r\n&&&x^3&+&x^2&+&5x&& \\\\\r\n+&&&&&-5x^2&-&5x&-&25 \\\\\r\n\\midrule\r\n&x^4&+&2x^3&+&x^2&-&25&&\r\n\\end{array}\\)<\/li>\r\n \t
  8. \\((x^{4n-3n}x^{-6})^{-1}\\)\r\n\\((x^nx^{-6})^{-1}\\)\r\n\\(x^{-n}x^6\\text{ or }\\dfrac{x^6}{x^n}\\)<\/li>\r\n \t
  9. \\(2a(7xy-3z)-1(7xy-3z)\\)\r\n\\((7xy-3z)(2a-1)\\)<\/li>\r\n \t
  10. \\(a^2-3ab+5ab-15b^2\\)\r\n\\(a(a-3b)+5b(a-3b)\\)\r\n\\((a-3b)(a+5b)\\)<\/li>\r\n \t
  11. \\(2x^2(x+4)-1(x+4)\\)\r\n\\((x+4)(2x^2-1)\\)<\/li>\r\n \t
  12. \\((3x)^3+(2y)^3\\)\r\n\\((3x+2y)(9x^2-6xy+4y^2)\\)<\/li>\r\n \t
  13. \\(\\phantom{1}\\)\r\n\\(F+D=38\\Rightarrow F=38-D \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n(F&+&6)&=&4(D&+&6) \\\\\r\n38-D&+&6\\phantom{)}&=&4D&+&24 \\\\\r\n-24+D&&&&+D&-&24 \\\\\r\n\\midrule\r\n&&20&=&5D&& \\\\ \\\\\r\n&&D&=&\\dfrac{20}{5}&=&4 \\\\ \\\\\r\n&&\\therefore F&=&38&-&D \\\\\r\n&&F&=&38&-&4 \\\\\r\n&&F&=&34&&\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\phantom{1}\\)\r\n\\(A+B=90\\Rightarrow B=90-A \\\\ \\)\r\n\\(\\begin{array}{rrrrrrl}\r\n3A&+&5(90&-&A)&=&\\phantom{-}370 \\\\\r\n3A&+&450&-&5A&=&\\phantom{-}370 \\\\\r\n&-&450&&&&-450 \\\\\r\n\\midrule\r\n&&&&-2A&=&-80 \\\\ \\\\\r\n&&&&A&=&\\dfrac{-80}{-2}\\text{ or }40\\text{ kg} \\\\ \\\\\r\n&&&&\\therefore B&=&90-A \\\\\r\n&&&&B&=&90-40 \\\\\r\n&&&&B&=&50\\text{ kg}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n10x&+&25(40)&=&15(x&+&40) \\\\ \\\\\r\n10x&+&1000&=&15x&+&600 \\\\\r\n-10x&-&600&&-10x&-&600 \\\\\r\n\\midrule\r\n&&400&=&5x&& \\\\ \\\\\r\n&&x&=&\\dfrac{400}{5}&=&80\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

    <\/h1>","rendered":"
      \n
    1. \n\n\n\n\n\n\n
      \"x+y=5\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      5<\/td>\n0<\/td>\n<\/tr>\n
      0<\/td>\n5<\/td>\n<\/tr>\n
      3<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
      \"2x-y=1\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      1<\/td>\n1<\/td>\n<\/tr>\n
      0<\/td>\n\u22121<\/td>\n<\/tr>\n
      \u22121<\/td>\n\u22123<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. \"\begin{array}{ll}
      \n\"(2,0)\"<\/li>\n
    3. \"\begin{array}{rrrrrl}<\/li>\n
    4. \"\begin{array}{ll}
      \n\"(1,-2,4)\"<\/li>\n
    5. \"5-3\left[4x-2\cancel{(6x-5)^0}1-(7-2x)\right]\"
      \n\"5-3\left[4x-2(1)-(7-2x)\right]\"
      \n\"5-3\left[6x-9\right]\"
      \n\"5-18x+27\Rightarrow -18x+32\"<\/li>\n
    6. \"\begin{array}{rrrlrl}<\/li>\n
    7. \"\begin{array}{rrrlrrrrrr}<\/li>\n
    8. \"(x^{4n-3n}x^{-6})^{-1}\"
      \n\"(x^nx^{-6})^{-1}\"
      \n\"x^{-n}x^6\text{ or }\dfrac{x^6}{x^n}\"<\/li>\n
    9. \"2a(7xy-3z)-1(7xy-3z)\"
      \n\"(7xy-3z)(2a-1)\"<\/li>\n
    10. \"a^2-3ab+5ab-15b^2\"
      \n\"a(a-3b)+5b(a-3b)\"
      \n\"(a-3b)(a+5b)\"<\/li>\n
    11. \"2x^2(x+4)-1(x+4)\"
      \n\"(x+4)(2x^2-1)\"<\/li>\n
    12. \"(3x)^3+(2y)^3\"
      \n\"(3x+2y)(9x^2-6xy+4y^2)\"<\/li>\n
    13. \"\phantom{1}\"
      \n\"F+D=38\Rightarrow F=38-D \\\"
      \n\"\begin{array}{rrrrrrr}<\/li>\n
    14. \"\phantom{1}\"
      \n\"A+B=90\Rightarrow B=90-A \\\"
      \n\"\begin{array}{rrrrrrl}<\/li>\n
    15. \"\begin{array}{rrrrrrr}<\/li>\n<\/ol>\n

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