{"id":2044,"date":"2021-12-02T19:40:37","date_gmt":"2021-12-03T00:40:37","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/final-exam-version-b-answer-key\/"},"modified":"2022-11-02T10:39:20","modified_gmt":"2022-11-02T14:39:20","slug":"final-exam-version-b-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/final-exam-version-b-answer-key\/","title":{"raw":"Final Exam: Version B Answer Key","rendered":"Final Exam: Version B Answer Key"},"content":{"raw":"

Questions from Chapters 1 to 3<\/h1>\n
    \n \t
  1. [latex]-2(-3)-\\sqrt{(-3)^2-4(4)(-1)}[\/latex]\n[latex]6-\\sqrt{9+16}[\/latex]\n[latex]6-5\u00a0[\/latex]\n[latex]1[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrcllll}\n&18x&-&30&=&3[4&-&4x&-&7] \\\\\n&18x&-&30&=&3[-4x&-&3]&& \\\\\n&18x&-&30&=&-12x&-&\\phantom{1}9&& \\\\\n+&12x&+&30&&+12x&+&30&& \\\\\n\\hline\n&&&30x&=&21&&&& \\\\ \\\\\n&&&x&=&\\dfrac{21}{30}&=&\\dfrac{7}{10}&&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\left(\\dfrac{x+4}{2}-\\dfrac{1}{3}=\\dfrac{x+2}{6}\\right)(6)[\/latex]\n[latex]\\begin{array}[t]{rrcrcrrrr}\n(x&+&4)(3)&-&1(2)&=&x&+&2 \\\\\n3x&+&12&-&2&=&x&+&2 \\\\\n-x&-&10&&&&-x&-&10 \\\\\n\\hline\n&&&&\\dfrac{2x}{2}&=&\\dfrac{-8}{2}&& \\\\ \\\\\n&&&&x&=&-4&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\n&&&&m&=&\\dfrac{\\Delta y}{\\Delta x}&& \\\\ \\\\\n&&&&\\dfrac{2}{3}&=&\\dfrac{y-4}{x-1}&& \\\\ \\\\\n&&2(x&-&1)&=&3(y&-&4) \\\\\n&&2x&-&2&=&3y&-&12 \\\\\n&&-3y&+&12&&-3y&+&12 \\\\\n\\hline\n2x&-&3y&+&10&=&0&& \\\\ \\\\\n&&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{10}{3} \\\\\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]\\hspace{0.1in} d^2=\\Delta x^2+\\Delta y^2[\/latex]\n<\/span>[latex]\\begin{array}[t]{rrl}\n&=&(4--4)^2+(4--2)^2 \\\\\n&=&8^2+6^2 \\\\\n&=&64+36 \\\\\n&=&100 \\\\ \\\\\nd&=&10\n\\end{array}[\/latex]<\/li>\n \t
  6. \n\n\n\n\n\n
    [latex]3x-2y=6[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    2<\/td>\n0<\/td>\n<\/tr>\n
    0<\/td>\n\u22123<\/td>\n<\/tr>\n
    \u22122<\/td>\n\u22126<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Line<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr}\n3&\\le &6x&+&3&<&9 \\\\\n-3&&&-&3&&-3 \\\\\n\\hline\n\\dfrac{0}{6}&\\le &&\\dfrac{6x}{6}&&<&\\dfrac{6}{6} \\\\ \\\\\n0&\\le &&x&&<&1\\\\\n\\end{array}\\\\\n(0,1)[\/latex]\n\"0,1\"<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\left(\\dfrac{3x+1}{4}=2\\right)^4 & \\hspace{0.25in} \\left(\\dfrac{3x+1}{4}=-2\\right)^4 \\\\\n\\begin{array}[t]{rrrrr}\n3x&+&1&=&8 \\\\\n&-&1&&-1 \\\\\n\\hline\n&&3x&=&7 \\\\ \\\\\n&&x&=&\\dfrac{7}{3}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\n3x&+&1&=&-8 \\\\\n&-&1&&-1 \\\\\n\\hline\n&&3x&=&-9 \\\\\n&&x&=&-3\n\\end{array}\n\\end{array}[\/latex]\n\"x=-3,<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\hspace{0.75in} w_{\\text{m}}=kw_e \\\\\n\\begin{array}[t]{rrl}\n&&\\text{1st data} \\\\ \\\\\nw_{\\text{m}}&=&38\\text{ lb} \\\\\nk&=&\\text{find 1st} \\\\\nw_{\\text{e}}&=&95\\text{ lb} \\\\ \\\\\nw_{\\text{m}}&=&kw_{\\text{e}} \\\\\n38&=&k(95) \\\\ \\\\\nk&=&\\dfrac{38}{95} \\\\ \\\\\nk&=&0.4\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n&&\\text{2nd data} \\\\ \\\\\nw_{\\text{m}}&=&\\text{find} \\\\\nk&=&0.4 \\\\\nw_{\\text{e}}&=&240\\text{ lb} \\\\ \\\\\nw_{\\text{m}}&=&kw_{\\text{e}} \\\\\nw_{\\text{m}}&=&(0.4)(240) \\\\\nw_{\\text{m}}&=&96\\text{ lb}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]x, x+2[\/latex]\n<\/span>[latex]\\begin{array}[t]{rrrrrrrrrrr}\nx&+&x&+&2&=&x&+&2&-&20 \\\\\n&&2x&+&2&=&x&-&18&& \\\\\n&&-x&-&2&&-x&-&2&& \\\\\n\\hline\n&&&&x&=&-20&&&&\\\\\n\\end{array}\\\\ \\text{numbers are }-20, -18[\/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]{rrrrrl}\n&(4x&-&3y&=&13)(5) \\\\\n&(6x&+&5y&=&-9)(3) \\\\ \\\\\n&20x&-&15y&=&\\phantom{-}65 \\\\\n+&18x&+&15y&=&-27 \\\\\n\\hline\n&&&38x&=&38 \\\\\n&&&x&=&1 \\\\ \\\\\n&4(1)&-&3y&=&13 \\\\\n&-4&&&&-4 \\\\\n\\hline\n&&&-3y&=&9 \\\\\n&&&y&=&-3\\\\\n\\end{array}\\\\(1,-3)[\/latex]<\/li>\n \t
    2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrl}\n&&&&x&=&-1-y \\\\ \\\\\n\\therefore 3(-1&-&y)&-&4y&=&-5 \\\\\n-3&-&3y&-&4y&=&-5 \\\\\n+3&&&&&&+3 \\\\\n\\hline\n&&&&-7y&=&-2 \\\\\n&&&&y&=&\\dfrac{2}{7} \\\\ \\\\\n&&x&+&y&=&-1 \\\\\n&&x&+&\\dfrac{2}{7}&=&-1 \\\\ \\\\\n&&&-&\\dfrac{2}{7}&&-\\dfrac{2}{7} \\\\\n\\hline\n&&&&x&=&-\\dfrac{9}{7}\n\\end{array}[\/latex]<\/li>\n \t
    3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrl}\n&&&(x&-&4z&=&0)(-1) \\\\ \\\\\n&x&+&2y&&&=&0 \\\\\n+&-x&&&+&4z&=&0 \\\\\n\\hline\n&&&(2y&+&4z&=&0)(\\div 2) \\\\\n&&&y&+&2z&=&0 \\\\ \\\\\n&&&y&+&2z&=&0 \\\\\n&&+&y&-&2z&=&0 \\\\\n\\hline\n&&&&&2y&=&0 \\\\\n&&&&&y&=&0 \\\\ \\\\\n&&&\\cancel{y}0&-&2z&=&0 \\\\\n&&&&&z&=&0 \\\\ \\\\\n&&&x&+&\\cancel{2y}0&=&0 \\\\\n&&&&&x&=&0\\\\\n\\end{array}\\\\ (0,0,0)[\/latex]<\/li>\n \t
    4. [latex]28-\\{5\\cancel{x^0}1-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+5\\cancel{x^0}1[\/latex]\n[latex]28-\\{5-1\\}+5[\/latex]\n[latex]28-4+5[\/latex]\n[latex]29[\/latex]<\/li>\n \t
    5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&x^2&-&3x&+&8\\phantom{x}&& \\\\\n\\times&&&x&-&4\\phantom{x}&& \\\\\n\\hline\n&x^3&-&3x^2&+&8x&& \\\\\n+&&-&4x^2&+&12x&-&32 \\\\\n\\hline\n&x^3&-&7x^2&+&20x&-&32 \\\\\n\\end{array}[\/latex]<\/li>\n \t
    6. [latex](x^{3n-6-3n})^{-1}[\/latex]\n[latex](x^{-6})^{-1}[\/latex]\n[latex]x^6[\/latex]<\/li>\n \t
    7. [latex]5y(5y^2-3y+1)[\/latex]<\/li>\n \t
    8. [latex]x^3+(2y)^3[\/latex]\n[latex](x+2y)(x^2-2xy+4y^2)[\/latex]<\/li>\n \t
    9. \n\n\n\n\n\n\n
      Solution<\/th>\nAmount<\/th>\nStrength<\/th>\nEquation<\/th>\n<\/tr>\n
      Soda<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
      Juice<\/th>\n2<\/td>\n35<\/td>\n2 (35)<\/td>\n<\/tr>\n
      Diluted<\/th>\n[latex]x+2[\/latex]<\/td>\n8<\/td>\n[latex](x+2)8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[latex]\\begin{array}[t]{rrrrrl}\n&2(35)&=&8(x&+&2) \\\\\n&70&=&8x&+&16 \\\\\n-&16&&&-&16 \\\\\n\\hline\n&54&=&8x&& \\\\ \\\\\n&x&=&\\dfrac{54}{8}&\\text{ or }&6\\dfrac{3}{4}\\text{ litres} \\\\\n\\end{array}[\/latex]<\/li>\n \t
    10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(d&+&q&=&14)(-10) \\\\\n&10d&+&25q&=&185 \\\\ \\\\\n&-10d&-&10q&=&-140 \\\\\n+&10d&+&25q&=&\\phantom{-}185 \\\\\n\\hline\n&&&\\dfrac{15q}{15}&=&\\dfrac{45}{15} \\\\ \\\\\n&&&q&=&3 \\\\ \\\\\n&\\therefore d&+&3&=&14 \\\\\n&&&d&=&11\n\\end{array}[\/latex]<\/li>\n<\/ol>\n

      Questions from Chapters 7 to 10<\/h1>\n
        \n \t
      1. [latex]\\dfrac{\\cancel{9}\\cancel{s^2}}{7t^3}\\cdot \\dfrac{15\\cancel{t}}{\\cancel{13}\\cancel{s^2}}\\cdot \\dfrac{\\cancel{26}2s}{\\cancel{9}\\cancel{t}}\\Rightarrow \\dfrac{15\\cdot 2\\cdot 5}{7t^3}\\Rightarrow \\dfrac{30s}{7t^3}[\/latex]<\/li>\n \t
      2. [latex]\\dfrac{(a-1)2a}{(a-1)(a-6)(a+6)}-\\dfrac{5(a+6)}{(a-6)(a-1)(a+6)} \\Rightarrow \\dfrac{2a^2-2a-5a-30}{(a-1)(a-6)(a+6)}[\/latex]\n[latex]\\Rightarrow \\dfrac{2a^2-7a-30}{(a-1)(a-6)(a+6)}\\Rightarrow \\dfrac{2a^2-12a+5a-30}{(a-1)(a-6)(a+6)}[\/latex]\n[latex]\\Rightarrow \\dfrac{2a(a-6)+5(a-6)}{(a-1)(a-6)(a+6)}\\Rightarrow \\dfrac{\\cancel{(a-6)}(2a+5)}{(a-1)\\cancel{(a-6)}(a+6)}\\Rightarrow \\dfrac{2a+5}{(a-1)(a+6)}[\/latex]<\/li>\n \t
      3. [latex]\\dfrac{\\left(1-\\dfrac{8}{x}\\right)x^2}{\\left(\\dfrac{3}{x}-\\dfrac{24}{x^2}\\right)x^2}\\Rightarrow \\dfrac{x^2-8x}{3x-24}\\Rightarrow \\dfrac{x\\cancel{(x-8)}}{3\\cancel{(x-8)}}\\Rightarrow \\dfrac{x}{3}[\/latex]<\/li>\n \t
      4. [latex]\\sqrt{x^4\\cdot x\\cdot y^6\\cdot y}+2xy\\sqrt{16\\cdot x\\cdot y^2\\cdot y}-\\sqrt{x\\cdot y^2\\cdot y}[\/latex]\n[latex]x^2y^3\\sqrt{xy}+2xy\\cdot 4y\\sqrt{xy}-y\\sqrt{xy}[\/latex]\n[latex](x^2y^3+8xy^2-y)\\sqrt{xy}[\/latex]<\/li>\n \t
      5. [latex]\\dfrac{2+x}{1-\\sqrt{7}}\\cdot \\dfrac{1+\\sqrt{7}}{1+\\sqrt{7}}\\Rightarrow \\dfrac{2+2\\sqrt{7}+x+x\\sqrt{7}}{1-7}\\Rightarrow \\dfrac{2+x+2\\sqrt{7}+x\\sqrt{7}}{-6}[\/latex]<\/li>\n \t
      6. [latex]\\left(\\dfrac{a^6b^3}{\\cancel{c^0}1d^{-9}}\\right)^{\\frac{2}{3}}\\Rightarrow \\dfrac{a^{6\\cdot \\frac{2}{3}}b^{3\\cdot \\frac{2}{3}}}{d^{-9\\cdot \\frac{2}{3}}}\\Rightarrow \\dfrac{a^4b^2}{d^{-6}}\\Rightarrow a^4b^2d^6[\/latex]<\/li>\n \t
      7. [latex]\\begin{array}{rrl}\\\\\n(x-5)(x+3)&=&0 \\\\\nx&=&5, -3\n\\end{array}[\/latex]<\/li>\n \t
      8. [latex]\\left(\\dfrac{2x-1}{3x}=\\dfrac{x-3}{x}\\right)(3x)[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&2x&-&1&=&(x&-&3)(3) \\\\ \\\\\n&2x&-&1&=&3x&-&9\\phantom{)(3)} \\\\\n+&-3x&+&1&&-3x&+&1\\phantom{)(3)} \\\\\n\\hline\n&&&-x&=&-8&& \\\\\n&&&x&=&8&&\n\\end{array}[\/latex]<\/li>\n \t
      9. [latex]A=L\\cdot W [\/latex]\n[latex]L=5+2W[\/latex]\n[latex]\\begin{array}[t]{rrl}\\\\\n75&=&W(5+2W) \\\\\n75&=&5W+2W^2 \\\\ \\\\\n0&=&2W^2+5W-75 \\\\\n0&=&2W^2-10W+15W-75 \\\\\n0&=&2W(W-5)+15(W-5) \\\\\n0&=&(W-5)(2W+15) \\\\\nW&=&5, \\cancel{-\\dfrac{15}{2}} \\\\ \\\\\nL&=&5+2(5) \\\\\nL&=&15\n\\end{array}[\/latex]<\/li>\n \t
      10. [latex]x, x+2, x+4[\/latex]\n[latex]\\begin{array}{rrcrrrrrrrr}\n&&x(x&+&2)&=&8(x&+&4)&-&25 \\\\\nx^2&+&2x&&&=&8x&+&32&-&25 \\\\\n&-&8x&-&32&&-8x&-&32&+&25 \\\\\n&&&+&25&&&&&& \\\\\n\\hline\nx^2&-&6x&-&7&=&0&&&& \\\\\n(x&-&7)(x&+&1)&=&0&&&& \\\\\n&&&&x&=&7,&-1&&& \\\\\n\\end{array}[\/latex]\n[latex]\\text{numbers are }7,9,11\\text{ or }-1,1,3[\/latex]<\/li>\n<\/ol>","rendered":"

        Questions from Chapters 1 to 3<\/h1>\n
          \n
        1. [latex]-2(-3)-\\sqrt{(-3)^2-4(4)(-1)}[\/latex]
          \n[latex]6-\\sqrt{9+16}[\/latex]
          \n[latex]6-5\u00a0[\/latex]
          \n[latex]1[\/latex]<\/li>\n
        2. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrcllll} &18x&-&30&=&3[4&-&4x&-&7] \\\\ &18x&-&30&=&3[-4x&-&3]&& \\\\ &18x&-&30&=&-12x&-&\\phantom{1}9&& \\\\ +&12x&+&30&&+12x&+&30&& \\\\ \\hline &&&30x&=&21&&&& \\\\ \\\\ &&&x&=&\\dfrac{21}{30}&=&\\dfrac{7}{10}&& \\end{array}[\/latex]<\/li>\n
        3. [latex]\\left(\\dfrac{x+4}{2}-\\dfrac{1}{3}=\\dfrac{x+2}{6}\\right)(6)[\/latex]
          \n[latex]\\begin{array}[t]{rrcrcrrrr} (x&+&4)(3)&-&1(2)&=&x&+&2 \\\\ 3x&+&12&-&2&=&x&+&2 \\\\ -x&-&10&&&&-x&-&10 \\\\ \\hline &&&&\\dfrac{2x}{2}&=&\\dfrac{-8}{2}&& \\\\ \\\\ &&&&x&=&-4&& \\end{array}[\/latex]<\/li>\n
        4. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrrrr} &&&&m&=&\\dfrac{\\Delta y}{\\Delta x}&& \\\\ \\\\ &&&&\\dfrac{2}{3}&=&\\dfrac{y-4}{x-1}&& \\\\ \\\\ &&2(x&-&1)&=&3(y&-&4) \\\\ &&2x&-&2&=&3y&-&12 \\\\ &&-3y&+&12&&-3y&+&12 \\\\ \\hline 2x&-&3y&+&10&=&0&& \\\\ \\\\ &&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{10}{3} \\\\ \\end{array}[\/latex]<\/li>\n
        5. [latex]\\hspace{0.1in} d^2=\\Delta x^2+\\Delta y^2[\/latex]
          \n<\/span>[latex]\\begin{array}[t]{rrl} &=&(4--4)^2+(4--2)^2 \\\\ &=&8^2+6^2 \\\\ &=&64+36 \\\\ &=&100 \\\\ \\\\ d&=&10 \\end{array}[\/latex]<\/li>\n
        6. \n\n\n\n\n\n\n
          [latex]3x-2y=6[\/latex]<\/caption>\n
          [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
          2<\/td>\n0<\/td>\n<\/tr>\n
          0<\/td>\n\u22123<\/td>\n<\/tr>\n
          \u22122<\/td>\n\u22126<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          \"Line<\/li>\n

        7. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrcrrr} 3&\\le &6x&+&3&<&9 \\\\ -3&&&-&3&&-3 \\\\ \\hline \\dfrac{0}{6}&\\le &&\\dfrac{6x}{6}&&<&\\dfrac{6}{6} \\\\ \\\\ 0&\\le &&x&&<&1\\\\ \\end{array}\\\\ (0,1)[\/latex]\n\"0,1\"<\/li>\n
        8. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\left(\\dfrac{3x+1}{4}=2\\right)^4 & \\hspace{0.25in} \\left(\\dfrac{3x+1}{4}=-2\\right)^4 \\\\ \\begin{array}[t]{rrrrr} 3x&+&1&=&8 \\\\ &-&1&&-1 \\\\ \\hline &&3x&=&7 \\\\ \\\\ &&x&=&\\dfrac{7}{3} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} 3x&+&1&=&-8 \\\\ &-&1&&-1 \\\\ \\hline &&3x&=&-9 \\\\ &&x&=&-3 \\end{array} \\end{array}[\/latex]
          \n\"x=-3,<\/li>\n
        9. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\hspace{0.75in} w_{\\text{m}}=kw_e \\\\ \\begin{array}[t]{rrl} &&\\text{1st data} \\\\ \\\\ w_{\\text{m}}&=&38\\text{ lb} \\\\ k&=&\\text{find 1st} \\\\ w_{\\text{e}}&=&95\\text{ lb} \\\\ \\\\ w_{\\text{m}}&=&kw_{\\text{e}} \\\\ 38&=&k(95) \\\\ \\\\ k&=&\\dfrac{38}{95} \\\\ \\\\ k&=&0.4 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} &&\\text{2nd data} \\\\ \\\\ w_{\\text{m}}&=&\\text{find} \\\\ k&=&0.4 \\\\ w_{\\text{e}}&=&240\\text{ lb} \\\\ \\\\ w_{\\text{m}}&=&kw_{\\text{e}} \\\\ w_{\\text{m}}&=&(0.4)(240) \\\\ w_{\\text{m}}&=&96\\text{ lb} \\end{array} \\end{array}[\/latex]<\/li>\n
        10. [latex]x, x+2[\/latex]
          \n<\/span>[latex]\\begin{array}[t]{rrrrrrrrrrr} x&+&x&+&2&=&x&+&2&-&20 \\\\ &&2x&+&2&=&x&-&18&& \\\\ &&-x&-&2&&-x&-&2&& \\\\ \\hline &&&&x&=&-20&&&&\\\\ \\end{array}\\\\ \\text{numbers are }-20, -18[\/latex]<\/li>\n<\/ol>\n

          Questions from Chapters 4 to 6<\/h1>\n
            \n
          1. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &(4x&-&3y&=&13)(5) \\\\ &(6x&+&5y&=&-9)(3) \\\\ \\\\ &20x&-&15y&=&\\phantom{-}65 \\\\ +&18x&+&15y&=&-27 \\\\ \\hline &&&38x&=&38 \\\\ &&&x&=&1 \\\\ \\\\ &4(1)&-&3y&=&13 \\\\ &-4&&&&-4 \\\\ \\hline &&&-3y&=&9 \\\\ &&&y&=&-3\\\\ \\end{array}\\\\(1,-3)[\/latex]<\/li>\n
          2. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrrl} &&&&x&=&-1-y \\\\ \\\\ \\therefore 3(-1&-&y)&-&4y&=&-5 \\\\ -3&-&3y&-&4y&=&-5 \\\\ +3&&&&&&+3 \\\\ \\hline &&&&-7y&=&-2 \\\\ &&&&y&=&\\dfrac{2}{7} \\\\ \\\\ &&x&+&y&=&-1 \\\\ &&x&+&\\dfrac{2}{7}&=&-1 \\\\ \\\\ &&&-&\\dfrac{2}{7}&&-\\dfrac{2}{7} \\\\ \\hline &&&&x&=&-\\dfrac{9}{7} \\end{array}[\/latex]<\/li>\n
          3. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrrrl} &&&(x&-&4z&=&0)(-1) \\\\ \\\\ &x&+&2y&&&=&0 \\\\ +&-x&&&+&4z&=&0 \\\\ \\hline &&&(2y&+&4z&=&0)(\\div 2) \\\\ &&&y&+&2z&=&0 \\\\ \\\\ &&&y&+&2z&=&0 \\\\ &&+&y&-&2z&=&0 \\\\ \\hline &&&&&2y&=&0 \\\\ &&&&&y&=&0 \\\\ \\\\ &&&\\cancel{y}0&-&2z&=&0 \\\\ &&&&&z&=&0 \\\\ \\\\ &&&x&+&\\cancel{2y}0&=&0 \\\\ &&&&&x&=&0\\\\ \\end{array}\\\\ (0,0,0)[\/latex]<\/li>\n
          4. [latex]28-\\{5\\cancel{x^0}1-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+5\\cancel{x^0}1[\/latex]
            \n[latex]28-\\{5-1\\}+5[\/latex]
            \n[latex]28-4+5[\/latex]
            \n[latex]29[\/latex]<\/li>\n
          5. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrrrr} &x^2&-&3x&+&8\\phantom{x}&& \\\\ \\times&&&x&-&4\\phantom{x}&& \\\\ \\hline &x^3&-&3x^2&+&8x&& \\\\ +&&-&4x^2&+&12x&-&32 \\\\ \\hline &x^3&-&7x^2&+&20x&-&32 \\\\ \\end{array}[\/latex]<\/li>\n
          6. [latex](x^{3n-6-3n})^{-1}[\/latex]
            \n[latex](x^{-6})^{-1}[\/latex]
            \n[latex]x^6[\/latex]<\/li>\n
          7. [latex]5y(5y^2-3y+1)[\/latex]<\/li>\n
          8. [latex]x^3+(2y)^3[\/latex]
            \n[latex](x+2y)(x^2-2xy+4y^2)[\/latex]<\/li>\n
          9. \n\n\n\n\n\n\n
            Solution<\/th>\nAmount<\/th>\nStrength<\/th>\nEquation<\/th>\n<\/tr>\n
            Soda<\/th>\n[latex]x[\/latex]<\/td>\n0<\/td>\n0<\/td>\n<\/tr>\n
            Juice<\/th>\n2<\/td>\n35<\/td>\n2 (35)<\/td>\n<\/tr>\n
            Diluted<\/th>\n[latex]x+2[\/latex]<\/td>\n8<\/td>\n[latex](x+2)8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            [latex]\\begin{array}[t]{rrrrrl} &2(35)&=&8(x&+&2) \\\\ &70&=&8x&+&16 \\\\ -&16&&&-&16 \\\\ \\hline &54&=&8x&& \\\\ \\\\ &x&=&\\dfrac{54}{8}&\\text{ or }&6\\dfrac{3}{4}\\text{ litres} \\\\ \\end{array}[\/latex]<\/li>\n

          10. [latex]\\phantom{a}[\/latex]
            \n[latex]\\begin{array}[t]{rrrrrl} &(d&+&q&=&14)(-10) \\\\ &10d&+&25q&=&185 \\\\ \\\\ &-10d&-&10q&=&-140 \\\\ +&10d&+&25q&=&\\phantom{-}185 \\\\ \\hline &&&\\dfrac{15q}{15}&=&\\dfrac{45}{15} \\\\ \\\\ &&&q&=&3 \\\\ \\\\ &\\therefore d&+&3&=&14 \\\\ &&&d&=&11 \\end{array}[\/latex]<\/li>\n<\/ol>\n

            Questions from Chapters 7 to 10<\/h1>\n
              \n
            1. [latex]\\dfrac{\\cancel{9}\\cancel{s^2}}{7t^3}\\cdot \\dfrac{15\\cancel{t}}{\\cancel{13}\\cancel{s^2}}\\cdot \\dfrac{\\cancel{26}2s}{\\cancel{9}\\cancel{t}}\\Rightarrow \\dfrac{15\\cdot 2\\cdot 5}{7t^3}\\Rightarrow \\dfrac{30s}{7t^3}[\/latex]<\/li>\n
            2. [latex]\\dfrac{(a-1)2a}{(a-1)(a-6)(a+6)}-\\dfrac{5(a+6)}{(a-6)(a-1)(a+6)} \\Rightarrow \\dfrac{2a^2-2a-5a-30}{(a-1)(a-6)(a+6)}[\/latex]
              \n[latex]\\Rightarrow \\dfrac{2a^2-7a-30}{(a-1)(a-6)(a+6)}\\Rightarrow \\dfrac{2a^2-12a+5a-30}{(a-1)(a-6)(a+6)}[\/latex]
              \n[latex]\\Rightarrow \\dfrac{2a(a-6)+5(a-6)}{(a-1)(a-6)(a+6)}\\Rightarrow \\dfrac{\\cancel{(a-6)}(2a+5)}{(a-1)\\cancel{(a-6)}(a+6)}\\Rightarrow \\dfrac{2a+5}{(a-1)(a+6)}[\/latex]<\/li>\n
            3. [latex]\\dfrac{\\left(1-\\dfrac{8}{x}\\right)x^2}{\\left(\\dfrac{3}{x}-\\dfrac{24}{x^2}\\right)x^2}\\Rightarrow \\dfrac{x^2-8x}{3x-24}\\Rightarrow \\dfrac{x\\cancel{(x-8)}}{3\\cancel{(x-8)}}\\Rightarrow \\dfrac{x}{3}[\/latex]<\/li>\n
            4. [latex]\\sqrt{x^4\\cdot x\\cdot y^6\\cdot y}+2xy\\sqrt{16\\cdot x\\cdot y^2\\cdot y}-\\sqrt{x\\cdot y^2\\cdot y}[\/latex]
              \n[latex]x^2y^3\\sqrt{xy}+2xy\\cdot 4y\\sqrt{xy}-y\\sqrt{xy}[\/latex]
              \n[latex](x^2y^3+8xy^2-y)\\sqrt{xy}[\/latex]<\/li>\n
            5. [latex]\\dfrac{2+x}{1-\\sqrt{7}}\\cdot \\dfrac{1+\\sqrt{7}}{1+\\sqrt{7}}\\Rightarrow \\dfrac{2+2\\sqrt{7}+x+x\\sqrt{7}}{1-7}\\Rightarrow \\dfrac{2+x+2\\sqrt{7}+x\\sqrt{7}}{-6}[\/latex]<\/li>\n
            6. [latex]\\left(\\dfrac{a^6b^3}{\\cancel{c^0}1d^{-9}}\\right)^{\\frac{2}{3}}\\Rightarrow \\dfrac{a^{6\\cdot \\frac{2}{3}}b^{3\\cdot \\frac{2}{3}}}{d^{-9\\cdot \\frac{2}{3}}}\\Rightarrow \\dfrac{a^4b^2}{d^{-6}}\\Rightarrow a^4b^2d^6[\/latex]<\/li>\n
            7. [latex]\\begin{array}{rrl}\\\\ (x-5)(x+3)&=&0 \\\\ x&=&5, -3 \\end{array}[\/latex]<\/li>\n
            8. [latex]\\left(\\dfrac{2x-1}{3x}=\\dfrac{x-3}{x}\\right)(3x)[\/latex]
              \n[latex]\\begin{array}[t]{rrrrrrrr} &2x&-&1&=&(x&-&3)(3) \\\\ \\\\ &2x&-&1&=&3x&-&9\\phantom{)(3)} \\\\ +&-3x&+&1&&-3x&+&1\\phantom{)(3)} \\\\ \\hline &&&-x&=&-8&& \\\\ &&&x&=&8&& \\end{array}[\/latex]<\/li>\n
            9. [latex]A=L\\cdot W[\/latex]
              \n[latex]L=5+2W[\/latex]
              \n[latex]\\begin{array}[t]{rrl}\\\\ 75&=&W(5+2W) \\\\ 75&=&5W+2W^2 \\\\ \\\\ 0&=&2W^2+5W-75 \\\\ 0&=&2W^2-10W+15W-75 \\\\ 0&=&2W(W-5)+15(W-5) \\\\ 0&=&(W-5)(2W+15) \\\\ W&=&5, \\cancel{-\\dfrac{15}{2}} \\\\ \\\\ L&=&5+2(5) \\\\ L&=&15 \\end{array}[\/latex]<\/li>\n
            10. [latex]x, x+2, x+4[\/latex]
              \n[latex]\\begin{array}{rrcrrrrrrrr} &&x(x&+&2)&=&8(x&+&4)&-&25 \\\\ x^2&+&2x&&&=&8x&+&32&-&25 \\\\ &-&8x&-&32&&-8x&-&32&+&25 \\\\ &&&+&25&&&&&& \\\\ \\hline x^2&-&6x&-&7&=&0&&&& \\\\ (x&-&7)(x&+&1)&=&0&&&& \\\\ &&&&x&=&7,&-1&&& \\\\ \\end{array}[\/latex]
              \n[latex]\\text{numbers are }7,9,11\\text{ or }-1,1,3[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":117,"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-2044","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\/2044","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\/2044\/revisions"}],"predecessor-version":[{"id":2045,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2044\/revisions\/2045"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/2044\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=2044"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=2044"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=2044"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=2044"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}