{"id":1803,"date":"2021-12-02T19:39:30","date_gmt":"2021-12-03T00:39:30","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-a-answer-key\/"},"modified":"2022-11-02T10:37:41","modified_gmt":"2022-11-02T14:37:41","slug":"midterm-one-version-a-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-a-answer-key\/","title":{"raw":"Midterm 1: Version A Answer Key","rendered":"Midterm 1: Version A Answer Key"},"content":{"raw":"
    \n \t
  1. [latex]-(-3)-\\sqrt{(-3)^2-4(4)(-1)}[\/latex]\n[latex]\\begin{array}[t]{l}\\\\\n3-\\sqrt{9+16} \\\\ \\\\\n3-\\sqrt{25} \\\\ \\\\\n3-5 \\\\ \\\\\n-2\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrrr}\n&2x&-&10&-&85&=&3&-&9x&-&54 \\\\\n+&9x&+&10&+&85&&&+&9x&+&3 \\\\\n&&&&&&&&&&+&85 \\\\\n&&&&&&&&&&+&10 \\\\\n\\hline\n&&&&&\\dfrac{11x}{11}&=&\\dfrac{44}{11}&&&& \\\\ \\\\\n&&&&&x&=&4&&&&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\nA(B-b)&=&h \\\\ \\\\\nB-b&=&\\dfrac{h}{A} \\\\ \\\\\n-b&=&\\dfrac{h}{A}-B\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\left(\\dfrac{x+1}{4}-\\dfrac{5}{8}=\\dfrac{x-1}{8}\\right)(8)[\/latex]\n[latex]\\begin{array}{rrrrrrrrr}\n2(x&+&1)&-&5&=&x&-&1 \\\\\n2x&+&2&-&5&=&x&-&1 \\\\\n-x&-&2&+&5&&-x&+&5 \\\\\n&&&&&&&-&2 \\\\\n\\hline\n&&&&x&=&2&&\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]x=-2[\/latex]\n\"Line<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\n\\dfrac{2}{5}&=&\\dfrac{y--2}{x--1}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrrrrrl}\n&&2(x&+&1)&=&5(y&+&2) \\\\\n&&2x&+&2&=&5y&+&10 \\\\\n&&-5y&-&10&&-5y&-&10 \\\\\n\\hline\n2x&-&5y&-&8&=&0&& \\\\\n&&&&0&=&2x&-&5y-8 \\\\ \\\\\n&&&&y&=&\\dfrac{2}{5}x&-&\\dfrac{8}{5}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n\\text{1st slope} && \\\\\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\nm&=&\\dfrac{4-0}{6--2} \\\\ \\\\\nm&=&\\dfrac{4}{8}\\text{ or }\\dfrac{1}{2}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n\\text{Now:} && \\\\\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\n\\dfrac{1}{2}&=&\\dfrac{y-0}{x--2} \\\\ \\\\\n1(x+2) &=&2(y-0) \\\\\nx+2&=&2y \\\\ \\\\\n\\therefore y&=&\\dfrac{1}{2}+1 \\\\ \\\\\n\\text{or }x-2y+2&=&0\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n\"Line<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n6x&-&5&-&30x&>&67 \\\\\n&+&5&&&&+5 \\\\\n\\hline\n&&&&\\dfrac{-24x}{-24}&>&\\dfrac{72}{-24} \\\\ \\\\\n&&&&x&<&-3\n\\end{array}[\/latex]\n\"x<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr}\n-10&\\le &4x&-&2&\\le &14 \\\\\n+2&&&+&2&&+2 \\\\\n\\hline\n\\dfrac{-8}{4}&\\le &&\\dfrac{4x}{4}&&\\le &\\dfrac{16}{4} \\\\ \\\\\n-2&\\le &&x&&\\le &4\n\\end{array}[\/latex]\n\"x<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n\\dfrac{3x+2}{5}&=& 2 \\\\ \\\\\n3x+2&=&10 \\\\\n-2&&-2 \\\\\n\\hline\n\\dfrac{3x}{3}&=&\\dfrac{8}{3} \\\\ \\\\\nx&=&\\dfrac{8}{3}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n\\dfrac{3x+2}{5}&=& -2 \\\\ \\\\\n3x+2 &=&-10 \\\\\n-2&&-2 \\\\\n\\hline\n\\dfrac{3x}{3}&=&\\dfrac{-12}{3} \\\\ \\\\\nx&=&-4\n\\end{array}\n\\end{array}[\/latex]\n\"x<\/li>\n \t
  12. \n\n\n\n\n\n\n
    [latex]5x+2y<15[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n7.5<\/td>\n<\/tr>\n
    3<\/td>\n0<\/td>\n<\/tr>\n
    1<\/td>\n5<\/td>\n<\/tr>\n
    5<\/td>\n\u22125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Line<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(5L&+&3S&=&47)(2) \\\\\n&(4L&-&2S&=&20)(3) \\\\ \\\\\n&10L&+&6S&=&94 \\\\\n+&12L&-&6S&=&60 \\\\\n\\hline\n&&&\\dfrac{22L}{22}&=&\\dfrac{154}{22} \\\\ \\\\\n&&&L&=&7 \\\\ \\\\\n\\therefore &4L&-&2S&=&\\phantom{-}20 \\\\\n&4(7)&-&2S&=&\\phantom{-}20 \\\\\n&28&-&2S&=&\\phantom{-}20 \\\\\n-&28&&&&-28 \\\\\n\\hline\n&&&\\dfrac{-2S}{-2}&=&\\dfrac{-8}{-2} \\\\ \\\\\n&&&S&=&4\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n36\\text{ cm}&=&5x+x \\\\\n36\\text{ cm}&=&6x \\\\ \\\\\nx&=&\\dfrac{36\\text{ cm}}{6} \\\\ \\\\\nx&=&6\\text{ cm} \\\\\n5x&=&5(6)=30 \\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n\\underline{\\text{1st}}&& \\\\\ny&=&\\dfrac{kmn}{d^2} \\\\ \\\\\n\\underline{\\text{2nd}}&& \\\\\ny&=&3 \\\\\nk&=&\\text{find} \\\\\nm&=&2 \\\\\nn&=&8 \\\\\nd&=&4 \\\\ \\\\\ny&=&\\dfrac{kmn}{d^2} \\\\ \\\\\n3&=&\\dfrac{k(2)(8)}{(4)^2} \\\\ \\\\\nk&=&\\dfrac{3\\cdot (4)^2}{2\\cdot 8} \\\\ \\\\\nk&=& 3\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n\\underline{\\text{3rd}}&& \\\\\ny&=&\\text{find} \\\\\nk&=&3 \\\\\nm&=&15 \\\\\nn&=&10 \\\\\nd&=& 5 \\\\ \\\\\ny&=&\\dfrac{kmn}{d^2} \\\\ \\\\\ny&=&\\dfrac{(3)(15)(10)}{(5)^2} \\\\ \\\\\ny&=&18\n\\end{array}\n\\end{array}[\/latex]<\/li>\n<\/ol>\n","rendered":"
      \n
    1. [latex]-(-3)-\\sqrt{(-3)^2-4(4)(-1)}[\/latex]
      \n[latex]\\begin{array}[t]{l}\\\\ 3-\\sqrt{9+16} \\\\ \\\\ 3-\\sqrt{25} \\\\ \\\\ 3-5 \\\\ \\\\ -2 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrrr} &2x&-&10&-&85&=&3&-&9x&-&54 \\\\ +&9x&+&10&+&85&&&+&9x&+&3 \\\\ &&&&&&&&&&+&85 \\\\ &&&&&&&&&&+&10 \\\\ \\hline &&&&&\\dfrac{11x}{11}&=&\\dfrac{44}{11}&&&& \\\\ \\\\ &&&&&x&=&4&&&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} A(B-b)&=&h \\\\ \\\\ B-b&=&\\dfrac{h}{A} \\\\ \\\\ -b&=&\\dfrac{h}{A}-B \\end{array}[\/latex]<\/li>\n
    4. [latex]\\left(\\dfrac{x+1}{4}-\\dfrac{5}{8}=\\dfrac{x-1}{8}\\right)(8)[\/latex]
      \n[latex]\\begin{array}{rrrrrrrrr} 2(x&+&1)&-&5&=&x&-&1 \\\\ 2x&+&2&-&5&=&x&-&1 \\\\ -x&-&2&+&5&&-x&+&5 \\\\ &&&&&&&-&2 \\\\ \\hline &&&&x&=&2&& \\end{array}[\/latex]<\/li>\n
    5. [latex]x=-2[\/latex]
      \n\"Line<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ \\dfrac{2}{5}&=&\\dfrac{y--2}{x--1} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrrrl} &&2(x&+&1)&=&5(y&+&2) \\\\ &&2x&+&2&=&5y&+&10 \\\\ &&-5y&-&10&&-5y&-&10 \\\\ \\hline 2x&-&5y&-&8&=&0&& \\\\ &&&&0&=&2x&-&5y-8 \\\\ \\\\ &&&&y&=&\\dfrac{2}{5}x&-&\\dfrac{8}{5} \\end{array} \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} \\text{1st slope} && \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ m&=&\\dfrac{4-0}{6--2} \\\\ \\\\ m&=&\\dfrac{4}{8}\\text{ or }\\dfrac{1}{2} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} \\text{Now:} && \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ \\dfrac{1}{2}&=&\\dfrac{y-0}{x--2} \\\\ \\\\ 1(x+2) &=&2(y-0) \\\\ x+2&=&2y \\\\ \\\\ \\therefore y&=&\\dfrac{1}{2}+1 \\\\ \\\\ \\text{or }x-2y+2&=&0 \\end{array} \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n\"Line<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} 6x&-&5&-&30x&>&67 \\\\ &+&5&&&&+5 \\\\ \\hline &&&&\\dfrac{-24x}{-24}&>&\\dfrac{72}{-24} \\\\ \\\\ &&&&x&<&-3 \\end{array}[\/latex]\n\"x<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrcrrr} -10&\\le &4x&-&2&\\le &14 \\\\ +2&&&+&2&&+2 \\\\ \\hline \\dfrac{-8}{4}&\\le &&\\dfrac{4x}{4}&&\\le &\\dfrac{16}{4} \\\\ \\\\ -2&\\le &&x&&\\le &4 \\end{array}[\/latex]
      \n\"x<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} \\dfrac{3x+2}{5}&=& 2 \\\\ \\\\ 3x+2&=&10 \\\\ -2&&-2 \\\\ \\hline \\dfrac{3x}{3}&=&\\dfrac{8}{3} \\\\ \\\\ x&=&\\dfrac{8}{3} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} \\dfrac{3x+2}{5}&=& -2 \\\\ \\\\ 3x+2 &=&-10 \\\\ -2&&-2 \\\\ \\hline \\dfrac{3x}{3}&=&\\dfrac{-12}{3} \\\\ \\\\ x&=&-4 \\end{array} \\end{array}[\/latex]
      \n\"x<\/li>\n
    12. \n\n\n\n\n\n\n\n
      [latex]5x+2y<15[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n7.5<\/td>\n<\/tr>\n
      3<\/td>\n0<\/td>\n<\/tr>\n
      1<\/td>\n5<\/td>\n<\/tr>\n
      5<\/td>\n\u22125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Line<\/li>\n

    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(5L&+&3S&=&47)(2) \\\\ &(4L&-&2S&=&20)(3) \\\\ \\\\ &10L&+&6S&=&94 \\\\ +&12L&-&6S&=&60 \\\\ \\hline &&&\\dfrac{22L}{22}&=&\\dfrac{154}{22} \\\\ \\\\ &&&L&=&7 \\\\ \\\\ \\therefore &4L&-&2S&=&\\phantom{-}20 \\\\ &4(7)&-&2S&=&\\phantom{-}20 \\\\ &28&-&2S&=&\\phantom{-}20 \\\\ -&28&&&&-28 \\\\ \\hline &&&\\dfrac{-2S}{-2}&=&\\dfrac{-8}{-2} \\\\ \\\\ &&&S&=&4 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrl} 36\\text{ cm}&=&5x+x \\\\ 36\\text{ cm}&=&6x \\\\ \\\\ x&=&\\dfrac{36\\text{ cm}}{6} \\\\ \\\\ x&=&6\\text{ cm} \\\\ 5x&=&5(6)=30 \\text{ cm} \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} \\underline{\\text{1st}}&& \\\\ y&=&\\dfrac{kmn}{d^2} \\\\ \\\\ \\underline{\\text{2nd}}&& \\\\ y&=&3 \\\\ k&=&\\text{find} \\\\ m&=&2 \\\\ n&=&8 \\\\ d&=&4 \\\\ \\\\ y&=&\\dfrac{kmn}{d^2} \\\\ \\\\ 3&=&\\dfrac{k(2)(8)}{(4)^2} \\\\ \\\\ k&=&\\dfrac{3\\cdot (4)^2}{2\\cdot 8} \\\\ \\\\ k&=& 3 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} \\underline{\\text{3rd}}&& \\\\ y&=&\\text{find} \\\\ k&=&3 \\\\ m&=&15 \\\\ n&=&10 \\\\ d&=& 5 \\\\ \\\\ y&=&\\dfrac{kmn}{d^2} \\\\ \\\\ y&=&\\dfrac{(3)(15)(10)}{(5)^2} \\\\ \\\\ y&=&18 \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n

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