{"id":3220,"date":"2019-11-19T13:55:53","date_gmt":"2019-11-19T18:55:53","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3220"},"modified":"2020-01-04T14:22:26","modified_gmt":"2020-01-04T19:22:26","slug":"midterm-one-version-d-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-one-version-d-answer-key\/","title":{"raw":"Midterm 1: Version D Answer Key","rendered":"Midterm 1: Version D Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\\r\n3(4)-\\sqrt{4^2-4(4)(1)} \\\\ \\\\\r\n12-\\sqrt{16-16} \\\\ \\\\\r\n12\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&-&8&+&8&=&-6&+&3x&+&9 \\\\\r\n&&&&2x&=&3x&+&3&& \\\\\r\n&&&&-3x&&-3x&&&& \\\\\r\n\\midrule\r\n&&&&-x&=&3&&&& \\\\\r\n&&&&x&=&-3&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{1}{R}=\\dfrac{1}{r_1}+\\dfrac{1}{r_2}\\right)(Rr_1r_2) \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\n&&r_1r_2&=&\\phantom{-}Rr_2&+&Rr_1 \\\\\r\n&&-Rr_2&&-Rr_2&& \\\\\r\n\\midrule\r\nr_1r_2&-&Rr_2&=&Rr_1&& \\\\\r\nr_2(r_1&-&R)&=&Rr_1&& \\\\ \\\\\r\n&&r_2&=&\\dfrac{Rr_1}{r_1-R}&&\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x}{15}-\\dfrac{x-3}{3}=\\dfrac{1}{3}\\right)(15) \\\\ \\)\r\n\\(\\begin{array}{rrcrrrr}\r\nx&-&5(x&-&3)&=&5 \\\\\r\nx&-&5x&+&15&=&5 \\\\\r\n&&&-&15&&-15 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-4x}{-4}&=&\\dfrac{-10}{-4} \\\\ \\\\\r\n&&&&x&=&\\dfrac{5}{2}\r\n\\end{array}\\)<\/li>\r\n \t
  5. \\(y=5\\)\r\n\"point<\/li>\r\n \t
  6. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n\\dfrac{2}{3}&=&\\dfrac{y-4}{x--2}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrlrr}\r\n\\\\ \\\\ \\\\\r\n&&2(x&+&2)&=&\\phantom{-}3(y&-&4) \\\\\r\n&&2x&+&4&=&\\phantom{-}3y&-&12 \\\\\r\n&-&3y&+&12&&-3y&+&12 \\\\\r\n\\midrule\r\n2x&-&3y&+&16&=&0&& \\\\ \\\\\r\n&&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{16}{3}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\textbf{1st slope:} \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\nm&=&\\dfrac{-9--7}{8-12} \\\\ \\\\\r\nm&=&\\dfrac{-2}{-4} \\\\ \\\\\r\nm&=&\\dfrac{1}{2} \\\\ \\\\\r\n&&\\textbf{Now:} \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n\\dfrac{1}{2}&=&\\dfrac{y--9}{x-8}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrrrr}\r\n&&x&-&8&=&2(y&+&9) \\\\\r\n&&x&-&8&=&2y&+&18 \\\\\r\n&-&2y&-&18&&-2y&-&18 \\\\\r\n\\midrule\r\nx&-&2y&-&26&=&0&&\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  8. \"Line<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-27&\\le &6x&-&9&\\le &3 \\\\\r\n+9&&&+&9&&+9 \\\\\r\n\\midrule\r\n\\dfrac{-18}{6}&\\le &&\\dfrac{6x}{6}&&\\le &\\dfrac{12}{6} \\\\ \\\\\r\n-3&\\le &&x&&\\le &2\r\n\\end{array}\\)\r\n\"-3<\/li>\r\n \t
  10. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\dfrac{2x+2}{6}=2& \\hspace{0.75in} \\dfrac{2x+2}{6}=-2 \\\\ \\\\\r\n\\begin{array}{rrrrl}\r\n2x&+&2&=&2\\cdot 6 \\\\\r\n2x&+&2&=&12 \\\\\r\n&-&2&&-2 \\\\\r\n\\midrule\r\n&&\\dfrac{2x}{2}&=&\\dfrac{10}{2} \\\\ \\\\\r\n&&x&=&5\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrl}\r\n2x&+&2&=&-2\\cdot 6 \\\\\r\n2x&+&2&=&-12 \\\\\r\n&-&2&&-2 \\\\\r\n\\midrule\r\n&&\\dfrac{2x}{2}&=&\\dfrac{-14}{2} \\\\ \\\\\r\n&&x&=&-7\r\n\\end{array}\r\n\\end{array}\\)\r\n\"x=5,<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&-&1&<&-6&\\hspace{0.25in}&6&<&2x&-&1 \\\\\r\n&+&1&&+1&&+1&&&+&1 \\\\\r\n\\midrule\r\n&&\\dfrac{2x}{2}&<&\\dfrac{-5}{2}&&\\dfrac{7}{2}&<&\\dfrac{2x}{2}&& \\\\ \\\\\r\n&&x&<&-\\dfrac{5}{2}&&x&>&\\dfrac{7}{2}&&\r\n\\end{array}\\)\r\nINSERT IMAGE<\/li>\r\n \t
  12. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(y=|2x|-1\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    3<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    2<\/td>\r\n3<\/td>\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\n1<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n3<\/td>\r\n<\/tr>\r\n
    \u22123<\/td>\r\n5<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"V<\/li>\r\n \t
  13. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\nA_1&=&A_2 \\\\\r\nA_3&=&2A_1-10^{\\circ} \\\\ \\\\\r\nA_1+A_2+A_3&=&180^{\\circ} \\\\\r\nA_1+A_1+2A_1-10^{\\circ}&=&180^{\\circ} \\\\\r\n+10^{\\circ}&&+10^{\\circ} \\\\\r\n\\midrule\r\n\\dfrac{4A_1}{4}&=&\\dfrac{190^{\\circ}}{4}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\nA_1&=&47.5^{\\circ} \\\\ \\\\\r\nA_2&=&47.5^{\\circ} \\\\ \\\\\r\nA_3&=&2A_1-10^{\\circ} \\\\\r\nA_3&=&2(47.5^{\\circ})-10^{\\circ} \\\\\r\nA_3&=&95^{\\circ}-10^{\\circ} \\\\\r\nA_3&=&85^{\\circ}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\phantom{1}\\)\r\n\\(x, x+2 \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrrr}\r\nx&+&x&+&2&=&x&-&20 \\\\\r\n&&2x&+&2&=&x&-&20 \\\\\r\n&&-x&-&2&&-x&-&2 \\\\\r\n\\midrule\r\n&&&&x&=&-22&&\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\nnumbers are \u221222, \u221220<\/li>\r\n \t
  15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\r\n&&\\textbf{1st data} \\\\\r\ny&=&16 \\\\\r\nk&=&\\text{find 1st} \\\\\r\nm&=&3 \\\\\r\nn&=&4 \\\\\r\nd&=&6 \\\\ \\\\\r\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\r\n16&=&\\dfrac{k(3)(4)^2}{6} \\\\ \\\\\r\nk&=&\\dfrac{16\\cdot 6}{3\\cdot (4)^2} \\\\ \\\\\r\nk&=&2\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n&&\\textbf{2nd data} \\\\\r\ny&=&\\text{find 2nd} \\\\\r\nk&=&2 \\\\\r\nm&=&-2 \\\\\r\nn&=&4 \\\\\r\nd&=&8 \\\\ \\\\\r\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\r\ny&=&\\dfrac{(2)(-2)(4)^2}{8} \\\\ \\\\\r\ny&=&-8\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>\r\n

    <\/h1>","rendered":"
      \n
    1. \"\begin{array}{l}<\/li>\n
    2. \"\begin{array}{rrrrrrrrrrr}<\/li>\n
    3. \"\phantom{1}\"
      \n\"\left(\dfrac{1}{R}=\dfrac{1}{r_1}+\dfrac{1}{r_2}\right)(Rr_1r_2) \\\"
      \n\"\begin{array}{rrrrlrr}<\/li>\n
    4. \"\phantom{1}\"
      \n\"\left(\dfrac{x}{15}-\dfrac{x-3}{3}=\dfrac{1}{3}\right)(15) \\\"
      \n\"\begin{array}{rrcrrrr}<\/li>\n
    5. \"y=5\"
      \n\"point<\/li>\n
    6. \"\begin{array}{ll}<\/li>\n
    7. \"\begin{array}{ll}<\/li>\n
    8. \"Line<\/li>\n
    9. \"\begin{array}{rrrrrrr}
      \n\"-3<\/li>\n
    10. \"\begin{array}{ll}
      \n\"x=5,<\/li>\n
    11. \"\begin{array}{rrrrrrrrrrr}
      \nINSERT IMAGE<\/li>\n
    12. \n\n\n\n\n\n\n\n\n\n\n
      \"y=|2x|-1\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      3<\/td>\n5<\/td>\n<\/tr>\n
      2<\/td>\n3<\/td>\n<\/tr>\n
      1<\/td>\n1<\/td>\n<\/tr>\n
      0<\/td>\n\u22121<\/td>\n<\/tr>\n
      \u22121<\/td>\n1<\/td>\n<\/tr>\n
      \u22122<\/td>\n3<\/td>\n<\/tr>\n
      \u22123<\/td>\n5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"V<\/li>\n

    13. \"\begin{array}{ll}<\/li>\n
    14. \"\phantom{1}\"
      \n\"x, x+2 \\\"
      \n\"\begin{array}{rrrrrrrrr}
      \n\"\phantom{1}\"
      \nnumbers are \u221222, \u221220<\/li>\n
    15. \"\begin{array}{ll}<\/li>\n<\/ol>\n

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