{"id":2039,"date":"2021-12-02T19:40:35","date_gmt":"2021-12-03T00:40:35","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/final-exam-prep-answer-key\/"},"modified":"2022-11-02T10:39:18","modified_gmt":"2022-11-02T14:39:18","slug":"final-exam-prep-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/final-exam-prep-answer-key\/","title":{"raw":"Final Exam: Version A Answer Key","rendered":"Final Exam: Version A Answer Key"},"content":{"raw":"

Questions from Chapters 1 to 3<\/h1>\n
    \n \t
  1. [latex]-(6)-\\sqrt{6^2-4(4)(2)}[\/latex]\n[latex]\\begin{array}[t]{l}\\\\\n-6-\\sqrt{36-32} \\\\ \\\\\n-6-\\sqrt{4} \\\\ \\\\\n-6-2=-8\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\n6x&+&24&=&35&-&5x&-&8&+&12x \\\\\n6x&+&24&=&27&+&7x&&&& \\\\\n-7x&-&24&&-24&-&7x&&&& \\\\\n\\hline\n&&-x&=&3&&&&&& \\\\\n&&\\therefore x&=&-3&&&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\left(\\dfrac{x+4}{2}-\\dfrac{1}{2}=\\dfrac{x+2}{4}\\right)(4) [\/latex]\n[latex]\\begin{array}[t]{crrrcrrrl}\n2(x&+&4)&-&1(2)&=&x&+&2 \\\\\n2x&+&8&-&2&=&x&+&2 \\\\\n-x&-&8&+&2&&-x&-&8+2 \\\\\n\\hline\n&&&&x&=&-4&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]x=-2[\/latex]<\/li>\n \t
  5. [latex]\\quad d^2=\\Delta x^2+\\Delta y^2[\/latex]\n[latex]\\begin{array}[t]{l}\n&=&(2--4)^2+(6--2)^2 \\\\\n&=&6^2+8^2 \\\\\n&=&36+64 \\\\\n&=&100 \\\\ \\\\\n\\therefore d&=&\\sqrt{100}=10\n\\end{array}[\/latex]<\/li>\n \t
  6. \n\n\n\n\n\n
    [latex]2x-3y=6[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n\u22122<\/td>\n<\/tr>\n
    3<\/td>\n0<\/td>\n<\/tr>\n
    6<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Line<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nx&-&2x&+&10&\\le &18&+&3x \\\\\n&&-x&+&10&\\le &18&+&3x \\\\\n+&&-3x&-&10&&-10&-&3x \\\\\n\\hline\n&&&&\\dfrac{-4x}{-4}&\\le &\\dfrac{8}{-4}&& \\\\ \\\\\n&&&&x&\\ge &-2&& \\\\\n\\end{array}[\/latex]\n[latex][-2, \\infty)[\/latex]\n\"x or equal to -2\" width=\"300\" height=\"69\"><\/li>\n \t
  8. [latex]\\left(-1 < \\dfrac{3x-2}{7}<1 \\right)(7)[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr}\n-7&<&3x&-&2&<&7 \\\\\n+2&&&+&2&&+2 \\\\\n\\hline\n\\dfrac{-5}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{9}{3} \\\\ \\\\\n-\\dfrac{5}{3}&<&&x&&<&3\n\\end{array}[\/latex]\n[latex]\\phantom{1}[\/latex]\n[latex]\\left(-\\dfrac{5}{3}, 3\\right)[\/latex]\n\"-5<\/li>\n \t
  9. [latex]t=\\dfrac{k}{r}[\/latex]\n<\/span>[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n&&\\text{1st data} \\\\ \\\\\nt&=&45\\text{ min} \\\\\nk&=&\\text{find 1st} \\\\\nr&=&600\\text{ kL\/min} \\\\ \\\\\nt&=&\\dfrac{k}{r} \\\\ \\\\\n45&=&\\dfrac{k}{600} \\\\ \\\\\nk&=&45(600) \\\\\nk&=&27000\\text{ kL}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n&&\\text{2nd data} \\\\ \\\\\nt&=&\\text{find} \\\\\nk&=&27000 \\\\\nr&=&1000\\text{ kL\/min} \\\\ \\\\\nt&=&\\dfrac{k}{r} \\\\ \\\\\nt&=&\\dfrac{27000}{1000} \\\\ \\\\\nt&=&27\\text{ min}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]x, x+2[\/latex]\n[latex] \\begin{array}[t]{rrrrrrrrr}\nx&+&x&+&2&=&4(x)&-&12 \\\\\n&&2x&+&2&=&4x&-&12 \\\\\n&-&2x&+&12&&-2x&+&12 \\\\\n\\hline\n&&&&\\dfrac{14}{2}&=&\\dfrac{2x}{2}&& \\\\ \\\\\n&&&&x&=&7&&\n\\end{array}\\\\ \\text{numbers are }7,9[\/latex]<\/li>\n<\/ol>\n

    Questions from Chapters 4 to 6<\/h1>\n
      \n \t
    1. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&2x&+&5y&=&-18 \\\\\n+&-2x&+&y&=&6 \\\\\n\\hline\n&&&\\dfrac{6y}{6}&=&\\dfrac{-12}{6} \\\\ \\\\\n&&&y&=&-2 \\\\ \\\\\n&\\therefore y&-&6&=&2x \\\\\n&-2&-&6&=&2x \\\\\n&&&2x&=&-8 \\\\\n&&&x&=&-4\n\\end{array}[\/latex]\nAnswer: [latex](-4, -2)[\/latex]<\/li>\n \t
    2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrl}\n&(8x&+&7y&=&51)(-2) \\\\\n&(5x&+&2y&=&20)(7) \\\\ \\\\\n&-16x&-&14y&=&-102 \\\\\n+&35x&+&14y&=&\\phantom{-}140 \\\\\n\\hline\n&&&\\dfrac{19x}{19}&=&\\dfrac{38}{19} \\\\ \\\\\n&&&x&=&2 \\\\ \\\\\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\n\\therefore 5x&+&2y&=&20 \\\\\n5(2)&+&2y&=&20 \\\\\n10&+&2y&=&20 \\\\\n-10&&&&-10 \\\\\n\\hline\n&&2y&=&10 \\\\\n&&y&=&5\n\\end{array}\n\\end{array}[\/latex]\nAnswer: [latex](2, 5)[\/latex]<\/li>\n \t
    3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrrl}\n&-2x&-&2y&-&12z&=&-10 \\\\\n+&2x&&&-&3z&=&\\phantom{-}4 \\\\\n\\hline\n&&&(-2y&-&15z&=&-6)(3) \\\\\n&&&(3y&+&4z&=&\\phantom{-}9)(2) \\\\ \\\\\n&&&-6y&-&45z&=&-18 \\\\\n&&+&6y&+&8z&=&\\phantom{-}18 \\\\\n\\hline\n&&&&&-37z&=&0 \\\\\n&&&&&z&=&0 \\\\ \\\\\n\\end{array}\n&\\hspace{0.25in}\n\\begin{array}[t]{rrrrl}\n2x&-&\\cancel{3z}0&=&4 \\\\\n&&x&=&\\dfrac{4}{2}\\text{ or }2 \\\\ \\\\\n3y&+&\\cancel{4z}0&=&9 \\\\\n&&y&=&\\dfrac{9}{3}\\text{ or }3\n\\end{array}\n\\end{array}[\/latex]\nAnswer [latex](2, 3, 0)[\/latex]<\/li>\n \t
    4. [latex]24+\\{-3x-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+3x[\/latex]\n[latex]24-3x-1+3x[\/latex]\n[latex]23[\/latex]<\/li>\n \t
    5. [latex]2ab^3(a^2-16)\\Rightarrow 2a^3b^3-32ab^3[\/latex]<\/li>\n \t
    6. [latex](x^{1--2}y^{-3-4})^{-1}[\/latex]\n[latex](x^3y^{-7})^{-1}[\/latex]\n[latex]x^{-3}y^7\u00a0[\/latex]\n[latex]\\dfrac{y^7}{x^3}[\/latex]<\/li>\n \t
    7. [latex]3x^2+3x+8x+8[\/latex]\n[latex]3x(x+1)+8(x+1)[\/latex]\n[latex](x+1)(3x+8)[\/latex]<\/li>\n \t
    8. [latex](4x)^3-y^3\\Rightarrow (4x-y)(16x^2+4xy+y^2)[\/latex]<\/li>\n \t
    9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrl}\n&(A&+&B&=&\\phantom{191.}50)(-370) \\\\\n&(3.95A&+&3.70B&=&191.25)(100) \\\\ \\\\\n&-370A&-&370B&=&-18500 \\\\\n+&395A&+&370B&=&\\phantom{-}19125 \\\\\n\\hline\n&&&25A&=&625 \\\\ \\\\\n&&&A&=&\\dfrac{625}{25}\\text{ or }25 \\\\ \\\\\n&A&+&B&=&50 \\\\\n&25&+&B&=&50 \\\\\n&&&B&=&25 \\\\\n\\end{array}[\/latex]<\/li>\n \t
    10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(d&+&q&=&16)(-10) \\\\\n&10d&+&25q&=&235 \\\\ \\\\\n&-10d&-&10q&=&-160 \\\\\n+&10d&+&25q&=&\\phantom{-}235 \\\\\n\\hline\n&&&\\dfrac{15q}{15}&=&\\dfrac{75}{15} \\\\ \\\\\n&&&q&=&5 \\\\\n&&&\\therefore d&=&16-5=11 \\\\\n\\end{array}[\/latex]<\/li>\n<\/ol>\n

      Questions from Chapters 7 to 10<\/h1>\n
        \n \t
      1. [latex]\\dfrac{\\cancel{15}3s^{\\cancel{3}2}}{\\cancel{3t^2}1}\\cdot \\dfrac{\\cancel{17}1\\cancel{s^3}}{\\cancel{5}1\\cancel{t}}\\cdot \\dfrac{\\cancel{3t^3}}{\\cancel{34}2\\cancel{s^4}}\\Rightarrow \\dfrac{3s^2}{2}[\/latex]<\/li>\n \t
      2. [latex]\\text{LCD}=(x+2)(x-2)[\/latex]\n[latex]\\begin{array}[t]{l}\n\\dfrac{2x(x-2)-4x(x+2)+20}{(x+2)(x-2)} \\\\ \\\\\n\\dfrac{2x^2-4x-4x^2-8x+20}{(x+2)(x-2)} \\\\ \\\\\n\\dfrac{-2x^2-12x+20}{(x+2)(x-2)} \\\\ \\\\\n\\dfrac{-2(x^2+6x-10)}{(x+2)(x-2)}\n\\end{array}[\/latex]<\/li>\n \t
      3. [latex]\\dfrac{\\left(\\dfrac{x^2}{y^2}-9\\right)y^3}{\\left(\\dfrac{x+3y}{y^3}\\right)y^3}\\Rightarrow \\dfrac{x^2y-9y^3}{x+3y}\\Rightarrow \\dfrac{y(x^2-9y^2)}{x+3y}\\Rightarrow \\dfrac{y(x-3y)\\cancel{(x+3y)}}{\\cancel{(x+3y)}}[\/latex]\n[latex]\\Rightarrow y(x-3y)[\/latex]<\/li>\n \t
      4. [latex]3\\cdot 5\\sqrt{x}-2\\sqrt{36\\cdot 2x}-\\sqrt{16\\cdot x^2\\cdot x}[\/latex]\n[latex]15\\sqrt{x}-2\\cdot 6\\sqrt{2x}-4x\\sqrt{x}[\/latex]\n[latex]15\\sqrt{x}-12\\sqrt{2x}-4x\\sqrt{x}[\/latex]<\/li>\n \t
      5. [latex]\\dfrac{\\sqrt{m^6\\cancel{n}}}{\\sqrt{3\\cancel{n}}}\\Rightarrow \\dfrac{m^3}{\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{m^3\\sqrt{3}}{3}[\/latex]<\/li>\n \t
      6. [latex]\\left(\\dfrac{\\cancel{a^0}1b^4}{c^8d^{-12}}\\right)^{\\frac{1}{4}}\\Rightarrow \\dfrac{b^{4\\cdot \\frac{1}{4}}}{c^{8\\cdot \\frac{1}{4}}d^{-12\\cdot \\frac{1}{4}}}\\Rightarrow \\dfrac{b}{c^2d^{-3}}\\Rightarrow \\dfrac{bd^3}{c^2}[\/latex]<\/li>\n \t
      7. [latex](x-5)(x+1)=0[\/latex]\n[latex]x=5,-1[\/latex]<\/li>\n \t
      8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrcrl}\n&&&(x&-&3)^2&=&(x)^2 \\\\ \\\\\n&x^2&-&6x&+&9&=&\\phantom{-}x^2 \\\\\n-&x^2&&&&&&-x^2 \\\\\n\\hline\n&&&-6x&+&9&=&0 \\\\ \\\\\n&&&&&\\dfrac{-6x}{-6}&=&\\dfrac{-9}{-6} \\\\ \\\\\n&&&&&x&=&\\dfrac{3}{2}\n\\end{array}[\/latex]<\/li>\n \t
      9. [latex]A\\quad =\\dfrac{1}{2}bh[\/latex]\n<\/span>[latex]\\begin{array}[t]{rrl}\n20&=&\\dfrac{1}{2}(h+6)h \\\\ \\\\\n40&=&h^2+6h \\\\ \\\\\n0&=&h^2+6h-40 \\\\\n0&=&h^2+10h-4h-40 \\\\\n0&=&h(h+10)-4(h+10) \\\\\n0&=&(h-4)(h+10) \\\\ \\\\\nh&=&4, \\cancel{-10} \\\\\nb&=&4+6=10\n\\end{array}[\/latex]<\/li>\n \t
      10. [latex]x, x+2, x+4[\/latex]\n[latex]\\begin{array}[t]{rrrrcrrrlrrrr}\n&&&&x(x&+&2)&=&\\phantom{-}8&+&6(x&+&4) \\\\\nx^2&+&2x&&&&&=&\\phantom{-}8&+&6x&+&24 \\\\\n&-&6x&-&8&-&24&&-8&-&6x&-&24 \\\\\n\\hline\n&&x^2&-&4x&-&32&=&0&&&& \\\\ \\\\\nx^2&+&4x&-&8x&-&32&=&0&&&& \\\\\nx(x&+&4)&-&8(x&+&4)&=&0&&&& \\\\\n&&(x&+&4)(x&-&8)&=&0&&&& \\\\\n&&&&&&x&=&-4,8&&&&\\\\\n\\end{array}\\\\ \\therefore \\text{ numbers are }-4,-2,0 \\text{ or } 8,10,12[\/latex]<\/li>\n<\/ol>","rendered":"

        Questions from Chapters 1 to 3<\/h1>\n
          \n
        1. [latex]-(6)-\\sqrt{6^2-4(4)(2)}[\/latex]
          \n[latex]\\begin{array}[t]{l}\\\\ -6-\\sqrt{36-32} \\\\ \\\\ -6-\\sqrt{4} \\\\ \\\\ -6-2=-8 \\end{array}[\/latex]<\/li>\n
        2. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrrrrrr} 6x&+&24&=&35&-&5x&-&8&+&12x \\\\ 6x&+&24&=&27&+&7x&&&& \\\\ -7x&-&24&&-24&-&7x&&&& \\\\ \\hline &&-x&=&3&&&&&& \\\\ &&\\therefore x&=&-3&&&&&& \\\\ \\end{array}[\/latex]<\/li>\n
        3. [latex]\\left(\\dfrac{x+4}{2}-\\dfrac{1}{2}=\\dfrac{x+2}{4}\\right)(4)[\/latex]
          \n[latex]\\begin{array}[t]{crrrcrrrl} 2(x&+&4)&-&1(2)&=&x&+&2 \\\\ 2x&+&8&-&2&=&x&+&2 \\\\ -x&-&8&+&2&&-x&-&8+2 \\\\ \\hline &&&&x&=&-4&& \\end{array}[\/latex]<\/li>\n
        4. [latex]x=-2[\/latex]<\/li>\n
        5. [latex]\\quad d^2=\\Delta x^2+\\Delta y^2[\/latex]
          \n[latex]\\begin{array}[t]{l} &=&(2--4)^2+(6--2)^2 \\\\ &=&6^2+8^2 \\\\ &=&36+64 \\\\ &=&100 \\\\ \\\\ \\therefore d&=&\\sqrt{100}=10 \\end{array}[\/latex]<\/li>\n
        6. \n\n\n\n\n\n\n
          [latex]2x-3y=6[\/latex]<\/caption>\n
          [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
          0<\/td>\n\u22122<\/td>\n<\/tr>\n
          3<\/td>\n0<\/td>\n<\/tr>\n
          6<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          \"Line<\/li>\n

        7. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrrrr} x&-&2x&+&10&\\le &18&+&3x \\\\ &&-x&+&10&\\le &18&+&3x \\\\ +&&-3x&-&10&&-10&-&3x \\\\ \\hline &&&&\\dfrac{-4x}{-4}&\\le &\\dfrac{8}{-4}&& \\\\ \\\\ &&&&x&\\ge &-2&& \\\\ \\end{array}[\/latex]
          \n[latex][-2, \\infty)[\/latex]
          \n\"image\" or equal to -2″ width=”300″ height=”69″><\/li>\n
        8. [latex]\\left(-1 < \\dfrac{3x-2}{7}<1 \\right)(7)[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr} -7&<&3x&-&2&<&7 \\\\ +2&&&+&2&&+2 \\\\ \\hline \\dfrac{-5}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{9}{3} \\\\ \\\\ -\\dfrac{5}{3}&<&&x&&<&3 \\end{array}[\/latex]\n[latex]\\phantom{1}[\/latex]\n[latex]\\left(-\\dfrac{5}{3}, 3\\right)[\/latex]\n\"-5<\/li>\n
        9. [latex]t=\\dfrac{k}{r}[\/latex]
          \n<\/span>[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\text{1st data} \\\\ \\\\ t&=&45\\text{ min} \\\\ k&=&\\text{find 1st} \\\\ r&=&600\\text{ kL\/min} \\\\ \\\\ t&=&\\dfrac{k}{r} \\\\ \\\\ 45&=&\\dfrac{k}{600} \\\\ \\\\ k&=&45(600) \\\\ k&=&27000\\text{ kL} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} &&\\text{2nd data} \\\\ \\\\ t&=&\\text{find} \\\\ k&=&27000 \\\\ r&=&1000\\text{ kL\/min} \\\\ \\\\ t&=&\\dfrac{k}{r} \\\\ \\\\ t&=&\\dfrac{27000}{1000} \\\\ \\\\ t&=&27\\text{ min} \\end{array} \\end{array}[\/latex]<\/li>\n
        10. [latex]x, x+2[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrrrr} x&+&x&+&2&=&4(x)&-&12 \\\\ &&2x&+&2&=&4x&-&12 \\\\ &-&2x&+&12&&-2x&+&12 \\\\ \\hline &&&&\\dfrac{14}{2}&=&\\dfrac{2x}{2}&& \\\\ \\\\ &&&&x&=&7&& \\end{array}\\\\ \\text{numbers are }7,9[\/latex]<\/li>\n<\/ol>\n

          Questions from Chapters 4 to 6<\/h1>\n
            \n
          1. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrr} &2x&+&5y&=&-18 \\\\ +&-2x&+&y&=&6 \\\\ \\hline &&&\\dfrac{6y}{6}&=&\\dfrac{-12}{6} \\\\ \\\\ &&&y&=&-2 \\\\ \\\\ &\\therefore y&-&6&=&2x \\\\ &-2&-&6&=&2x \\\\ &&&2x&=&-8 \\\\ &&&x&=&-4 \\end{array}[\/latex]
            \nAnswer: [latex](-4, -2)[\/latex]<\/li>\n
          2. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrl} &(8x&+&7y&=&51)(-2) \\\\ &(5x&+&2y&=&20)(7) \\\\ \\\\ &-16x&-&14y&=&-102 \\\\ +&35x&+&14y&=&\\phantom{-}140 \\\\ \\hline &&&\\dfrac{19x}{19}&=&\\dfrac{38}{19} \\\\ \\\\ &&&x&=&2 \\\\ \\\\ \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} \\therefore 5x&+&2y&=&20 \\\\ 5(2)&+&2y&=&20 \\\\ 10&+&2y&=&20 \\\\ -10&&&&-10 \\\\ \\hline &&2y&=&10 \\\\ &&y&=&5 \\end{array} \\end{array}[\/latex]
            \nAnswer: [latex](2, 5)[\/latex]<\/li>\n
          3. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrrl} &-2x&-&2y&-&12z&=&-10 \\\\ +&2x&&&-&3z&=&\\phantom{-}4 \\\\ \\hline &&&(-2y&-&15z&=&-6)(3) \\\\ &&&(3y&+&4z&=&\\phantom{-}9)(2) \\\\ \\\\ &&&-6y&-&45z&=&-18 \\\\ &&+&6y&+&8z&=&\\phantom{-}18 \\\\ \\hline &&&&&-37z&=&0 \\\\ &&&&&z&=&0 \\\\ \\\\ \\end{array} &\\hspace{0.25in} \\begin{array}[t]{rrrrl} 2x&-&\\cancel{3z}0&=&4 \\\\ &&x&=&\\dfrac{4}{2}\\text{ or }2 \\\\ \\\\ 3y&+&\\cancel{4z}0&=&9 \\\\ &&y&=&\\dfrac{9}{3}\\text{ or }3 \\end{array} \\end{array}[\/latex]
            \nAnswer [latex](2, 3, 0)[\/latex]<\/li>\n
          4. [latex]24+\\{-3x-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+3x[\/latex]
            \n[latex]24-3x-1+3x[\/latex]
            \n[latex]23[\/latex]<\/li>\n
          5. [latex]2ab^3(a^2-16)\\Rightarrow 2a^3b^3-32ab^3[\/latex]<\/li>\n
          6. [latex](x^{1--2}y^{-3-4})^{-1}[\/latex]
            \n[latex](x^3y^{-7})^{-1}[\/latex]
            \n[latex]x^{-3}y^7\u00a0[\/latex]
            \n[latex]\\dfrac{y^7}{x^3}[\/latex]<\/li>\n
          7. [latex]3x^2+3x+8x+8[\/latex]
            \n[latex]3x(x+1)+8(x+1)[\/latex]
            \n[latex](x+1)(3x+8)[\/latex]<\/li>\n
          8. [latex](4x)^3-y^3\\Rightarrow (4x-y)(16x^2+4xy+y^2)[\/latex]<\/li>\n
          9. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrcrl} &(A&+&B&=&\\phantom{191.}50)(-370) \\\\ &(3.95A&+&3.70B&=&191.25)(100) \\\\ \\\\ &-370A&-&370B&=&-18500 \\\\ +&395A&+&370B&=&\\phantom{-}19125 \\\\ \\hline &&&25A&=&625 \\\\ \\\\ &&&A&=&\\dfrac{625}{25}\\text{ or }25 \\\\ \\\\ &A&+&B&=&50 \\\\ &25&+&B&=&50 \\\\ &&&B&=&25 \\\\ \\end{array}[\/latex]<\/li>\n
          10. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &(d&+&q&=&16)(-10) \\\\ &10d&+&25q&=&235 \\\\ \\\\ &-10d&-&10q&=&-160 \\\\ +&10d&+&25q&=&\\phantom{-}235 \\\\ \\hline &&&\\dfrac{15q}{15}&=&\\dfrac{75}{15} \\\\ \\\\ &&&q&=&5 \\\\ &&&\\therefore d&=&16-5=11 \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n

            Questions from Chapters 7 to 10<\/h1>\n
              \n
            1. [latex]\\dfrac{\\cancel{15}3s^{\\cancel{3}2}}{\\cancel{3t^2}1}\\cdot \\dfrac{\\cancel{17}1\\cancel{s^3}}{\\cancel{5}1\\cancel{t}}\\cdot \\dfrac{\\cancel{3t^3}}{\\cancel{34}2\\cancel{s^4}}\\Rightarrow \\dfrac{3s^2}{2}[\/latex]<\/li>\n
            2. [latex]\\text{LCD}=(x+2)(x-2)[\/latex]
              \n[latex]\\begin{array}[t]{l} \\dfrac{2x(x-2)-4x(x+2)+20}{(x+2)(x-2)} \\\\ \\\\ \\dfrac{2x^2-4x-4x^2-8x+20}{(x+2)(x-2)} \\\\ \\\\ \\dfrac{-2x^2-12x+20}{(x+2)(x-2)} \\\\ \\\\ \\dfrac{-2(x^2+6x-10)}{(x+2)(x-2)} \\end{array}[\/latex]<\/li>\n
            3. [latex]\\dfrac{\\left(\\dfrac{x^2}{y^2}-9\\right)y^3}{\\left(\\dfrac{x+3y}{y^3}\\right)y^3}\\Rightarrow \\dfrac{x^2y-9y^3}{x+3y}\\Rightarrow \\dfrac{y(x^2-9y^2)}{x+3y}\\Rightarrow \\dfrac{y(x-3y)\\cancel{(x+3y)}}{\\cancel{(x+3y)}}[\/latex]
              \n[latex]\\Rightarrow y(x-3y)[\/latex]<\/li>\n
            4. [latex]3\\cdot 5\\sqrt{x}-2\\sqrt{36\\cdot 2x}-\\sqrt{16\\cdot x^2\\cdot x}[\/latex]
              \n[latex]15\\sqrt{x}-2\\cdot 6\\sqrt{2x}-4x\\sqrt{x}[\/latex]
              \n[latex]15\\sqrt{x}-12\\sqrt{2x}-4x\\sqrt{x}[\/latex]<\/li>\n
            5. [latex]\\dfrac{\\sqrt{m^6\\cancel{n}}}{\\sqrt{3\\cancel{n}}}\\Rightarrow \\dfrac{m^3}{\\sqrt{3}}\\cdot \\dfrac{\\sqrt{3}}{\\sqrt{3}}\\Rightarrow \\dfrac{m^3\\sqrt{3}}{3}[\/latex]<\/li>\n
            6. [latex]\\left(\\dfrac{\\cancel{a^0}1b^4}{c^8d^{-12}}\\right)^{\\frac{1}{4}}\\Rightarrow \\dfrac{b^{4\\cdot \\frac{1}{4}}}{c^{8\\cdot \\frac{1}{4}}d^{-12\\cdot \\frac{1}{4}}}\\Rightarrow \\dfrac{b}{c^2d^{-3}}\\Rightarrow \\dfrac{bd^3}{c^2}[\/latex]<\/li>\n
            7. [latex](x-5)(x+1)=0[\/latex]
              \n[latex]x=5,-1[\/latex]<\/li>\n
            8. [latex]\\phantom{a}[\/latex]
              \n[latex]\\begin{array}[t]{rrrrrcrl} &&&(x&-&3)^2&=&(x)^2 \\\\ \\\\ &x^2&-&6x&+&9&=&\\phantom{-}x^2 \\\\ -&x^2&&&&&&-x^2 \\\\ \\hline &&&-6x&+&9&=&0 \\\\ \\\\ &&&&&\\dfrac{-6x}{-6}&=&\\dfrac{-9}{-6} \\\\ \\\\ &&&&&x&=&\\dfrac{3}{2} \\end{array}[\/latex]<\/li>\n
            9. [latex]A\\quad =\\dfrac{1}{2}bh[\/latex]
              \n<\/span>[latex]\\begin{array}[t]{rrl} 20&=&\\dfrac{1}{2}(h+6)h \\\\ \\\\ 40&=&h^2+6h \\\\ \\\\ 0&=&h^2+6h-40 \\\\ 0&=&h^2+10h-4h-40 \\\\ 0&=&h(h+10)-4(h+10) \\\\ 0&=&(h-4)(h+10) \\\\ \\\\ h&=&4, \\cancel{-10} \\\\ b&=&4+6=10 \\end{array}[\/latex]<\/li>\n
            10. [latex]x, x+2, x+4[\/latex]
              \n[latex]\\begin{array}[t]{rrrrcrrrlrrrr} &&&&x(x&+&2)&=&\\phantom{-}8&+&6(x&+&4) \\\\ x^2&+&2x&&&&&=&\\phantom{-}8&+&6x&+&24 \\\\ &-&6x&-&8&-&24&&-8&-&6x&-&24 \\\\ \\hline &&x^2&-&4x&-&32&=&0&&&& \\\\ \\\\ x^2&+&4x&-&8x&-&32&=&0&&&& \\\\ x(x&+&4)&-&8(x&+&4)&=&0&&&& \\\\ &&(x&+&4)(x&-&8)&=&0&&&& \\\\ &&&&&&x&=&-4,8&&&&\\\\ \\end{array}\\\\ \\therefore \\text{ numbers are }-4,-2,0 \\text{ or } 8,10,12[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":116,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-2039","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2039","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2039\/revisions"}],"predecessor-version":[{"id":2040,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2039\/revisions\/2040"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2039\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2039"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2039"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2039"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}