{"id":3213,"date":"2019-11-19T13:50:05","date_gmt":"2019-11-19T18:50:05","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3213"},"modified":"2019-12-29T19:24:24","modified_gmt":"2019-12-30T00:24:24","slug":"midterm-one-version-b-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/midterm-one-version-b-answer-key\/","title":{"raw":"Midterm 1: Version B Answer Key","rendered":"Midterm 1: Version B Answer Key"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n-6-\\sqrt{6^2-4(5)(1)} \\\\ \\\\\r\n-6-\\sqrt{36-20} \\\\ \\\\\r\n-6-\\sqrt{16} \\\\ \\\\\r\n-6-4 \\\\ \\\\\r\n-10\r\n\\end{array}\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&15x&-&18&=&4[-6&+&3x] \\\\\r\n&15x&-&18&=&-24&+&12x \\\\\r\n-&12x&+&18&&+18&-&12x \\\\\r\n\\midrule\r\n&&&\\dfrac{3x}{3}&=&\\dfrac{-6}{3} && \\\\ \\\\\r\n&&&x&=&-2 &&\r\n\\end{array}\\)<\/li>\r\n \t
  3. \\(\\begin{array}{l}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\left(A=\\dfrac{h}{B\\cdot b}\\right)(b) \\\\ \\\\\r\n\\left(Ab=\\dfrac{h}{B}\\right)\\div A \\\\ \\\\\r\n\\phantom{A}b=\\dfrac{h}{BA}\r\n\\end{array}\\)<\/li>\r\n \t
  4. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x+3}{5}-\\dfrac{x}{2}=\\dfrac{5-3x}{10}\\right)(10) \\\\ \\)\r\n\\(\\begin{array}{rrcrcrrrr}\r\n2(x&+&3)&-&5(x)&=&5&-&3x \\\\\r\n2x&+&6&-&5x&=&5&-&3x \\\\\r\n&-&3x&+&6&=&5&-&3x \\\\\r\n&+&3x&-&6&&-6&+&3x \\\\\r\n\\midrule\r\n&&&&0&=&-1&&\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\nNo solution<\/li>\r\n \t
  5. \\(y=4\\)\r\n\"-3,<\/li>\r\n \t
  6. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\text{slope}&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n\\dfrac{1}{3}&=&\\dfrac{y-4}{x--1}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrlrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&1(x&+&1)&=&3(y&-&4) \\\\\r\n&&x&+&1&=&3y&-&12 \\\\\r\n&&&-&1&&&-&1 \\\\\r\n\\midrule\r\n&&&&x&=&3y&-&13 \\\\ \\\\\r\nx&-&3y&+&13&=&0&& \\\\ \\\\\r\n&&&&y&=&\\dfrac{1}{3}x&+&\\dfrac{13}{3}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  7. \\(\\phantom{1}\\)\r\n\\(\\text{1st slope }\\dots\\text{ } m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{5-4}{-3-0}\\Rightarrow -\\dfrac{1}{3} \\\\ \\)\r\n\\(\\text{now }\\dots\\text{ } m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow -\\dfrac{1}{3}\\Rightarrow \\dfrac{y-4}{x-0} \\\\ \\)\r\n\\(\\begin{array}{rrl}\r\n-1(x)&=&3(y-4) \\\\\r\n-x&=&3y-12 \\\\ \\\\\r\nx+3y-12&=&0 \\\\\r\ny&=&-\\dfrac{1}{3}x+4 \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  8. \"Line<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\\r\n6x&-&12&+&8x&>&15&-&20x&+&7 \\\\\r\n&+&12&+&20x&&&+&20x&+&15 \\\\\r\n&&&+&6x&&&&&+&12 \\\\\r\n\\midrule\r\n&&&&34x&>&34&&&& \\\\\r\n&&&&x&>&1&&&&\r\n\\end{array}\\)\r\n\"x<\/li>\r\n \t
  10. \\(\\begin{array}{rrrcrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-3&\\le &2x&+&3&<&9 \\\\\r\n-3&&&-&3&&-3 \\\\\r\n\\midrule\r\n\\dfrac{-6}{2}&\\le &&\\dfrac{2x}{2}&&<&\\dfrac{6}{2} \\\\ \\\\\r\n-3&\\le &&x&&<&3\r\n\\end{array}\\)\r\n\"-3<\/li>\r\n \t
  11. \\(\\phantom{1}\\)\r\n\\(\\left(-2<\\dfrac{3x+2}{5}<2\\right)(5) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-10&<&3x&+&2&<&10 \\\\\r\n-2&&&-&2&&-2 \\\\\r\n\\midrule\r\n\\dfrac{-12}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{8}{3} \\\\ \\\\\r\n-4&<&&x&&<&\\dfrac{8}{3}\r\n\\end{array}\\)\r\n\"-4<\/li>\r\n \t
  12. \r\n\r\n\r\n\r\n\r\n\r\n\r\n
    \\(5x+2y=10\\)<\/caption>\r\n
    \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
    2<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
    0<\/td>\r\n5<\/td>\r\n<\/tr>\r\n
    \u22122<\/td>\r\n10<\/td>\r\n<\/tr>\r\n
    4<\/td>\r\n\u22125<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
  13. \\(\\phantom{1}\\)\r\n\\(x, x+2 \\\\ \\)\r\n\\(\\begin{array}{rrrrrrrrr}\r\nx&+&(x&+&2)&=&5x&-&16 \\\\\r\n&&2x&+&2&=&5x&-&16 \\\\\r\n&+&-5x&-&2&&-5x&-&2 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-3x}{-3}&=&\\dfrac{-18}{-3}&& \\\\ \\\\\r\n&&&&x&=&6&& \\\\\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\nnumbers are 6, 8<\/li>\r\n \t
  14. \\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n4x+x&=&40\\text{ cm} \\\\\r\n5x&=&40\\text{ cm} \\\\\r\nx&=&\\dfrac{40\\text{ cm}}{5}\\text{ or }8\\text{ cm} \\\\ \\\\\r\n\\therefore 4x&=&4(8)\\text{ or }32\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\underline{\\text{1st}} \\\\ \\\\\r\nP&=&\\dfrac{kT}{V} \\\\ \\\\\r\n&&\\underline{\\text{2nd}} \\\\ \\\\\r\n&&\\textbf{1st data} \\\\\r\nP&=&100 \\\\\r\nk&=&\\text{find 1st} \\\\\r\nT&=&200 \\\\\r\nV&=&500 \\\\ \\\\\r\nP&=&\\dfrac{kT}{V} \\\\ \\\\\r\n100&=&\\dfrac{k(200)}{500} \\\\ \\\\\r\nk&=&\\dfrac{\\cancel{100}(500)}{\\cancel{200}2} \\\\ \\\\\r\nk&=&250\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\textbf{2nd data} \\\\\r\nP&=&\\text{find 2nd} \\\\\r\nk&=&250 \\\\\r\nT&=&100 \\\\\r\nV&=&500 \\\\ \\\\\r\nP&=&\\dfrac{kT}{V} \\\\ \\\\\r\nP&=&\\dfrac{(250)(100)}{500} \\\\ \\\\\r\nP&=&50\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}{rrrrrrrr}<\/li>\n
    3. \"\begin{array}{l}<\/li>\n
    4. \"\phantom{1}\"
      \n\"\left(\dfrac{x+3}{5}-\dfrac{x}{2}=\dfrac{5-3x}{10}\right)(10) \\\"
      \n\"\begin{array}{rrcrcrrrr}
      \n\"\phantom{1}\"
      \nNo solution<\/li>\n
    5. \"y=4\"
      \n\"-3,<\/li>\n
    6. \"\begin{array}{ll}<\/li>\n
    7. \"\phantom{1}\"
      \n\"\text{1st slope }\dots\text{ } m=\dfrac{\Delta y}{\Delta x}\Rightarrow \dfrac{5-4}{-3-0}\Rightarrow -\dfrac{1}{3} \\\"
      \n\"\text{now }\dots\text{ } m=\dfrac{\Delta y}{\Delta x}\Rightarrow -\dfrac{1}{3}\Rightarrow \dfrac{y-4}{x-0} \\\"
      \n\"\begin{array}{rrl}<\/li>\n
    8. \"Line<\/li>\n
    9. \"\begin{array}{rrrrrrrrrrr}
      \n\"x<\/li>\n
    10. \"\begin{array}{rrrcrrr}
      \n\"-3<\/li>\n
    11. \"\phantom{1}\"
      \n\"\left(-2<\dfrac{3x+2}{5}<2\right)(5) \\\"
      \n\"\begin{array}{rrrrrrr}
      \n\"-4<\/li>\n
    12. \n\n\n\n\n\n\n\n
      \"5x+2y=10\"<\/caption>\n
      \"x\"<\/th>\n\"y\"<\/th>\n<\/tr>\n
      2<\/td>\n0<\/td>\n<\/tr>\n
      0<\/td>\n5<\/td>\n<\/tr>\n
      \u22122<\/td>\n10<\/td>\n<\/tr>\n
      4<\/td>\n\u22125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n

    13. \"\phantom{1}\"
      \n\"x, x+2 \\\"
      \n\"\begin{array}{rrrrrrrrr}
      \n\"\phantom{1}\"
      \nnumbers are 6, 8<\/li>\n
    14. \"\begin{array}{rrl}<\/li>\n
    15. \"\begin{array}{ll}<\/li>\n<\/ol>\n

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