{"id":1795,"date":"2021-12-02T19:39:28","date_gmt":"2021-12-03T00:39:28","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/mid-term-1-prep-answer-key\/"},"modified":"2023-09-01T12:34:02","modified_gmt":"2023-09-01T16:34:02","slug":"mid-term-1-prep-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/mid-term-1-prep-answer-key\/","title":{"raw":"Mid Term 1: Review Questions Answer Key","rendered":"Mid Term 1: Review Questions Answer Key"},"content":{"raw":"
    \r\n \t
  1. True<\/li>\r\n \t
  2. Undefined<\/li>\r\n \t
  3. 15<\/li>\r\n \t
  4. 16<\/li>\r\n \t
  5. 12<\/li>\r\n \t
  6. 19<\/li>\r\n \t
  7. True<\/li>\r\n \t
  8. \u221218<\/li>\r\n \t
  9. 18<\/li>\r\n \t
  10. \u221216<\/li>\r\n \t
  11. 16<\/li>\r\n \t
  12. \u221216<\/li>\r\n<\/ol>\r\n
      \r\n \t
    1. [latex]-(-6) - \\sqrt{(-6)^2-4(8)(-2)}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n6 - \\sqrt{36+64} \\\\\r\n6-10 \\\\\r\n-4\r\n\\end{array}[\/latex]<\/li>\r\n \t
    2. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrrrr}\r\n&3x&-&12&-&27&=&7&-&5x&-&30 \\\\\r\n+&5x&+&12&+&27&&&+&5x&+&12 \\\\\r\n&&&&&&&&&&+&7 \\\\\r\n&&&&&&&&&&+&27 \\\\\r\n\\hline\r\n&&&&&8x&=&16&&&& \\\\\r\n&&&&&x&=&2&&&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    3. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{l}\r\n\\left(\\dfrac{1}{R} = \\dfrac{1}{r_1}+\\dfrac{1}{r_2}\\right)(Rr_1r_2) \\\\ \\\\\r\nr_1r_2 = Rr_2 + Rr_1 \\\\ \\\\\r\nr_1r_2 = R(r_2 + r_1) \\\\ \\\\\r\nR=\\dfrac{r_1r_2}{r_2 + r_1}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    4. [latex]\\left(\\dfrac{x+3}{8} - \\dfrac{3}{4} = \\dfrac {x+6}{10}\\right)(40)[\/latex]\r\n[latex]\\begin{array}{rrrrrcrrrr}\r\n&5(x&+&3)&-&3(10)&=&4(x&+&6) \\\\\r\n&5x&+&15&-&30&=&4x&+&24 \\\\\r\n-&4x&-&15&+&30&&-4x&-&15 \\\\\r\n&&&&&&&&+&30 \\\\\r\n\\hline\r\n&&&&&x&=&39&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
    5. Need graph drawn. [latex]y=5[\/latex]<\/li>\r\n \t
    6. [latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\nm&=&\\dfrac {\\Delta y}{\\Delta x}\\\\ \\\\\r\n\\dfrac{2}{3}& =& \\dfrac{y-2}{x- -1}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}[t]{rrrrrrrcl}\r\n&&2(x&+&1)& =& 3(y&-&2) \\\\\r\n&&2x &+& 2& = &3y& -& 6 \\\\\r\n&&-3y& + &6 &&-3y &+ &6 \\\\\r\n\\hline\r\n2x&-&3y&+&8&=&0&& \\\\ \\\\\r\n&&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{8}{3}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    7. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&& \\text{1st slope} \\\\ \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\nm&=&\\dfrac{11--1}{2--2} \\\\ \\\\\r\nm&=&\\dfrac{12}{4} \\\\ \\\\\r\nm&=& 3 \\\\ \\\\\r\n&& \\text{2nd slope} \\\\ \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n3&=&\\dfrac{y--1}{x--2}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}[t]{rrrrrrrrr}\r\n&&3(x&+&2)&=&y&+&1 \\\\\r\n&&3x&+&6&=&y&+&1 \\\\\r\n&&-y&-&1&&-y&-&1 \\\\\r\n\\hline\r\n3x&-&y&+&5&=&0&& \\\\\r\n&&&&y&=&3x&+&5\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    8. [latex]\\phantom{a}[\/latex]\r\n\r\n[caption id=\"attachment_1789\" align=\"aligncenter\" width=\"300\"]\"Line Use slop intercept method.[\/caption]<\/li>\r\n \t
    9. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nd^2& =& \\Delta x^2 + \\Delta y^2\\\\\r\nd^2 &=& (15-7)^2 + (3 - -3)^2\\\\\r\nd^2& =& 8^2 + 6^2 \\\\\r\nd&=&10\r\n\\end{array}[\/latex]<\/li>\r\n \t
    10. [latex]x=\\dfrac{x_1+x_2}{2}=\\dfrac{7+15}{2}=11[\/latex]\r\n[latex]y=\\dfrac{y_1+y_2}{2}=\\dfrac{-3+3}{2}=0[\/latex]\r\n[latex](11,0)[\/latex]<\/li>\r\n \t
    11. True<\/li>\r\n \t
    12. True<\/li>\r\n \t
    13. [latex]\\{r, s, t\\}[\/latex]<\/li>\r\n \t
    14. True<\/li>\r\n \t
    15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrr}\r\n3x&-&6&-&36x&>&60 \\\\\r\n&+&6&&&&+6 \\\\\r\n\\hline\r\n&&&&-33x&>&66 \\\\\r\n&&&&x&<&-2\r\n\\end{array}[\/latex]\r\n\r\n[caption id=\"attachment_1790\" align=\"aligncenter\" width=\"300\"]\"- (\u2212\u221e, \u22122)[\/caption]<\/li>\r\n \t
    16. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrcrcr}\r\n-18& \\le& 4x& - &6& \\le& 2\\\\\r\n+6&&&+&6&&+6\\\\\r\n\\hline\r\n\\dfrac{-12}{4}&\\le&&\\dfrac{4x}{4}&&\\le&\\dfrac{8}{4}\\\\ \\\\\r\n-3&\\le&&x&&\\le&2\r\n\\end{array}[\/latex][caption id=\"attachment_1791\" align=\"aligncenter\" width=\"300\"]\"-3, [\u22123, 2][\/caption]<\/li>\r\n \t
    17. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrrrr}\r\n2x&-&1&<&-7 \\\\\r\n&+&1&&+1 \\\\\r\n\\hline\r\n&&\\dfrac{2x}{2}&<&\\dfrac{-6}{2} \\\\ \\\\\r\n&&x&<&-3\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}[t]{rrrrr}\r\n7&<&2x&-&1 \\\\\r\n+1&&&+&1 \\\\\r\n\\hline\r\n\\dfrac{8}{2}&<&\\dfrac{2x}{2}&& \\\\ \\\\\r\n4&<&x&&\r\n\\end{array}\r\n\\end{array}[\/latex]\r\n\r\n[caption id=\"attachment_1792\" align=\"aligncenter\" width=\"300\"]\"- (\u2212\u221e, \u22123) or (4, \u221e)[\/caption]<\/li>\r\n \t
    18. [latex]\\left| \\dfrac{3x - 4}{5} \\right| < 1[\/latex]\r\n[latex]\\left(-1 < \\dfrac{3x-4}{5}< 1 \\right)(5)[\/latex]\r\n[latex]\\begin{array}{rrrrrrr}\r\n-5&<&3x&-&4&<&5 \\\\\r\n+4&&&+&4&&+4 \\\\\r\n\\hline\r\n\\dfrac{-1}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{9}{3} \\\\ \\\\\r\n-\\dfrac{1}{3}&<&&x&&<&3\r\n\\end{array}[\/latex][caption id=\"attachment_1793\" align=\"alignnone\" width=\"300\"]\"-1\/3, [latex](-\\dfrac{1}{3}, 3)[\/latex][\/caption]<\/li>\r\n \t
    19. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&3x&-&2y&=&10&& \\\\\r\n+&-10&+&2y&&-10&+&2y \\\\\r\n\\hline\r\n&\\dfrac{3x}{2}&-&\\dfrac{10}{2}&=&\\dfrac{2y}{2}&& \\\\ \\\\\r\n&&&y&=&\\dfrac{3}{2}x&-&5\r\n\\end{array}[\/latex]\r\n\r\n[caption id=\"attachment_1794\" align=\"alignnone\" width=\"300\"]\"Line Slope intercept method. Check (0, 0): 3(0) \u2212 2(0) < 10. Shade the (0, 0) side.[\/caption]<\/li>\r\n \t
    20. \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
      [latex]y=|x-1|-2[\/latex]<\/caption>\r\n
      [latex]x[\/latex]<\/th>\r\n[latex]y[\/latex]<\/th>\r\n<\/tr>\r\n
      4<\/td>\r\n1<\/td>\r\n<\/tr>\r\n
      3<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
      2<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
      1<\/td>\r\n\u22122<\/td>\r\n<\/tr>\r\n
      0<\/td>\r\n\u22121<\/td>\r\n<\/tr>\r\n
      \u22121<\/td>\r\n0<\/td>\r\n<\/tr>\r\n
      \u22122<\/td>\r\n1<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t
    21. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&6L&+&2S&=&38 \\\\\r\n+&4L&-&2S&=&12 \\\\\r\n\\hline\r\n&&&10L&=&50 \\\\\r\n&&&L&=&5 \\\\ \\\\\r\n\\therefore &6(5)&+&2S&=&38 \\\\\r\n&30&+&2S&=&38 \\\\\r\n-&30&&&&-30 \\\\\r\n\\hline\r\n&&&2S&=&8 \\\\\r\n&&&S&=&4\r\n\\end{array}[\/latex]<\/li>\r\n \t
    22. Insert diagram.\r\n[latex]\\begin{array}{rrl}\r\n5x+x&=&36 \\\\\r\n6x&=&36 \\\\\r\nx&=&6 \\\\\r\n\\therefore 5x&=&30\r\n\\end{array}[\/latex]<\/li>\r\n \t
    23. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrl}\r\n&(d&+&q&=&14)(-10) \\\\\r\n&10d&+&25q&=&260 \\\\ \\\\\r\n&-10d&-&10q&=&-140 \\\\\r\n+&10d&+&25q&=&\\phantom{-}260 \\\\\r\n\\hline\r\n&&&\\dfrac{15q}{15}&=&\\dfrac{120}{15} \\\\ \\\\\r\n&&&q&=&8 \\\\ \\\\\r\n\\therefore &d&+&8&=&14 \\\\\r\n&&-&8&&-8 \\\\\r\n\\hline\r\n&&&d&=&6\r\n\\end{array}[\/latex]<\/li>\r\n \t
    24. [latex]x, x+2 [\/latex]\r\n[latex]\\begin{array}{rrrrrrrrr}\r\nx&+&x&+&2&=&x&-&10 \\\\\r\n&&2x&+&2&=&x&-&10 \\\\\r\n&&-x&-&2&&-x&-&2 \\\\\r\n\\hline\r\n&&&&x&=&-12&& \\\\\r\n\\end{array}[\/latex]\r\nnumbers are \u221212, \u221210<\/li>\r\n \t
    25. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n\\underline{\\text{1st}}&& \\\\\r\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\r\n\\underline{\\text{2nd}}&& \\\\\r\ny&=&12 \\\\\r\nk&=&\\text{find} \\\\\r\nm&=&3 \\\\\r\nn&=&4 \\\\\r\nd&=&8 \\\\ \\\\\r\n12&=&\\dfrac{k(3)(4)^2}{8} \\\\ \\\\\r\nk&=&\\dfrac{12(8)}{3\\cdot 16} \\\\ \\\\\r\nk&=& 2\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}[t]{rrl}\r\n\\underline{\\text{3rd}}&& \\\\\r\ny&=&\\text{find} \\\\\r\nk&=& 2 \\\\\r\nm&=&-3 \\\\\r\nn&=&3 \\\\\r\nd&=& 6 \\\\ \\\\\r\ny&=&\\dfrac{(2)(-3)(3)^2}{6} \\\\ \\\\\r\ny&=&-9\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n","rendered":"
        \n
      1. True<\/li>\n
      2. Undefined<\/li>\n
      3. 15<\/li>\n
      4. 16<\/li>\n
      5. 12<\/li>\n
      6. 19<\/li>\n
      7. True<\/li>\n
      8. \u221218<\/li>\n
      9. 18<\/li>\n
      10. \u221216<\/li>\n
      11. 16<\/li>\n
      12. \u221216<\/li>\n<\/ol>\n
          \n
        1. [latex]-(-6) - \\sqrt{(-6)^2-4(8)(-2)}[\/latex]
          \n[latex]\\begin{array}[t]{l} 6 - \\sqrt{36+64} \\\\ 6-10 \\\\ -4 \\end{array}[\/latex]<\/li>\n
        2. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrrrrrrr} &3x&-&12&-&27&=&7&-&5x&-&30 \\\\ +&5x&+&12&+&27&&&+&5x&+&12 \\\\ &&&&&&&&&&+&7 \\\\ &&&&&&&&&&+&27 \\\\ \\hline &&&&&8x&=&16&&&& \\\\ &&&&&x&=&2&&&& \\end{array}[\/latex]<\/li>\n
        3. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{l} \\left(\\dfrac{1}{R} = \\dfrac{1}{r_1}+\\dfrac{1}{r_2}\\right)(Rr_1r_2) \\\\ \\\\ r_1r_2 = Rr_2 + Rr_1 \\\\ \\\\ r_1r_2 = R(r_2 + r_1) \\\\ \\\\ R=\\dfrac{r_1r_2}{r_2 + r_1} \\end{array}[\/latex]<\/li>\n
        4. [latex]\\left(\\dfrac{x+3}{8} - \\dfrac{3}{4} = \\dfrac {x+6}{10}\\right)(40)[\/latex]
          \n[latex]\\begin{array}{rrrrrcrrrr} &5(x&+&3)&-&3(10)&=&4(x&+&6) \\\\ &5x&+&15&-&30&=&4x&+&24 \\\\ -&4x&-&15&+&30&&-4x&-&15 \\\\ &&&&&&&&+&30 \\\\ \\hline &&&&&x&=&39&& \\end{array}[\/latex]<\/li>\n
        5. Need graph drawn. [latex]y=5[\/latex]<\/li>\n
        6. [latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} m&=&\\dfrac {\\Delta y}{\\Delta x}\\\\ \\\\ \\dfrac{2}{3}& =& \\dfrac{y-2}{x- -1} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrrcl} &&2(x&+&1)& =& 3(y&-&2) \\\\ &&2x &+& 2& = &3y& -& 6 \\\\ &&-3y& + &6 &&-3y &+ &6 \\\\ \\hline 2x&-&3y&+&8&=&0&& \\\\ \\\\ &&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{8}{3} \\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{11--1}{2--2} \\\\ \\\\ m&=&\\dfrac{12}{4} \\\\ \\\\ m&=& 3 \\\\ \\\\ && \\text{2nd slope} \\\\ \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ 3&=&\\dfrac{y--1}{x--2} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrrrr} &&3(x&+&2)&=&y&+&1 \\\\ &&3x&+&6&=&y&+&1 \\\\ &&-y&-&1&&-y&-&1 \\\\ \\hline 3x&-&y&+&5&=&0&& \\\\ &&&&y&=&3x&+&5 \\end{array} \\end{array}[\/latex]<\/li>\n
        8. [latex]\\phantom{a}[\/latex]
          \n
          \"Line
          Use slop intercept method.<\/figcaption><\/figure>\n<\/li>\n
        9. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} d^2& =& \\Delta x^2 + \\Delta y^2\\\\ d^2 &=& (15-7)^2 + (3 - -3)^2\\\\ d^2& =& 8^2 + 6^2 \\\\ d&=&10 \\end{array}[\/latex]<\/li>\n
        10. [latex]x=\\dfrac{x_1+x_2}{2}=\\dfrac{7+15}{2}=11[\/latex]
          \n[latex]y=\\dfrac{y_1+y_2}{2}=\\dfrac{-3+3}{2}=0[\/latex]
          \n[latex](11,0)[\/latex]<\/li>\n
        11. True<\/li>\n
        12. True<\/li>\n
        13. [latex]\\{r, s, t\\}[\/latex]<\/li>\n
        14. True<\/li>\n
        15. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrr} 3x&-&6&-&36x&>&60 \\\\ &+&6&&&&+6 \\\\ \\hline &&&&-33x&>&66 \\\\ &&&&x&<&-2 \\end{array}[\/latex]\n\n\n\n
          \"-
          (\u2212\u221e, \u22122)<\/figcaption><\/figure>\n<\/li>\n
        16. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrcrcr} -18& \\le& 4x& - &6& \\le& 2\\\\ +6&&&+&6&&+6\\\\ \\hline \\dfrac{-12}{4}&\\le&&\\dfrac{4x}{4}&&\\le&\\dfrac{8}{4}\\\\ \\\\ -3&\\le&&x&&\\le&2 \\end{array}[\/latex]<\/p>\n
          \"-3,
          [\u22123, 2]<\/figcaption><\/figure>\n<\/li>\n
        17. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrr} 2x&-&1&<&-7 \\\\ &+&1&&+1 \\\\ \\hline &&\\dfrac{2x}{2}&<&\\dfrac{-6}{2} \\\\ \\\\ &&x&<&-3 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} 7&<&2x&-&1 \\\\ +1&&&+&1 \\\\ \\hline \\dfrac{8}{2}&<&\\dfrac{2x}{2}&& \\\\ \\\\ 4&<&x&& \\end{array} \\end{array}[\/latex]\n\n\n\n
          \"-
          (\u2212\u221e, \u22123) or (4, \u221e)<\/figcaption><\/figure>\n<\/li>\n
        18. [latex]\\left| \\dfrac{3x - 4}{5} \\right| < 1[\/latex]\n[latex]\\left(-1 < \\dfrac{3x-4}{5}< 1 \\right)(5)[\/latex]\n[latex]\\begin{array}{rrrrrrr} -5&<&3x&-&4&<&5 \\\\ +4&&&+&4&&+4 \\\\ \\hline \\dfrac{-1}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{9}{3} \\\\ \\\\ -\\dfrac{1}{3}&<&&x&&<&3 \\end{array}[\/latex]\n\n
          \"-1\/3,
          [latex](-\\dfrac{1}{3}, 3)[\/latex]<\/figcaption><\/figure>\n<\/li>\n
        19. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrrr} &3x&-&2y&=&10&& \\\\ +&-10&+&2y&&-10&+&2y \\\\ \\hline &\\dfrac{3x}{2}&-&\\dfrac{10}{2}&=&\\dfrac{2y}{2}&& \\\\ \\\\ &&&y&=&\\dfrac{3}{2}x&-&5 \\end{array}[\/latex]<\/p>\n
          \"Line
          Slope intercept method. Check (0, 0): 3(0) \u2212 2(0) < 10. Shade the (0, 0) side.<\/figcaption><\/figure>\n<\/li>\n
        20. \n\n\n\n\n\n\n\n\n\n\n
          [latex]y=|x-1|-2[\/latex]<\/caption>\n
          [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
          4<\/td>\n1<\/td>\n<\/tr>\n
          3<\/td>\n0<\/td>\n<\/tr>\n
          2<\/td>\n\u22121<\/td>\n<\/tr>\n
          1<\/td>\n\u22122<\/td>\n<\/tr>\n
          0<\/td>\n\u22121<\/td>\n<\/tr>\n
          \u22121<\/td>\n0<\/td>\n<\/tr>\n
          \u22122<\/td>\n1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n
        21. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrr} &6L&+&2S&=&38 \\\\ +&4L&-&2S&=&12 \\\\ \\hline &&&10L&=&50 \\\\ &&&L&=&5 \\\\ \\\\ \\therefore &6(5)&+&2S&=&38 \\\\ &30&+&2S&=&38 \\\\ -&30&&&&-30 \\\\ \\hline &&&2S&=&8 \\\\ &&&S&=&4 \\end{array}[\/latex]<\/li>\n
        22. Insert diagram.
          \n[latex]\\begin{array}{rrl} 5x+x&=&36 \\\\ 6x&=&36 \\\\ x&=&6 \\\\ \\therefore 5x&=&30 \\end{array}[\/latex]<\/li>\n
        23. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrl} &(d&+&q&=&14)(-10) \\\\ &10d&+&25q&=&260 \\\\ \\\\ &-10d&-&10q&=&-140 \\\\ +&10d&+&25q&=&\\phantom{-}260 \\\\ \\hline &&&\\dfrac{15q}{15}&=&\\dfrac{120}{15} \\\\ \\\\ &&&q&=&8 \\\\ \\\\ \\therefore &d&+&8&=&14 \\\\ &&-&8&&-8 \\\\ \\hline &&&d&=&6 \\end{array}[\/latex]<\/li>\n
        24. [latex]x, x+2[\/latex]
          \n[latex]\\begin{array}{rrrrrrrrr} x&+&x&+&2&=&x&-&10 \\\\ &&2x&+&2&=&x&-&10 \\\\ &&-x&-&2&&-x&-&2 \\\\ \\hline &&&&x&=&-12&& \\\\ \\end{array}[\/latex]
          \nnumbers are \u221212, \u221210<\/li>\n
        25. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} \\underline{\\text{1st}}&& \\\\ y&=&\\dfrac{kmn^2}{d} \\\\ \\\\ \\underline{\\text{2nd}}&& \\\\ y&=&12 \\\\ k&=&\\text{find} \\\\ m&=&3 \\\\ n&=&4 \\\\ d&=&8 \\\\ \\\\ 12&=&\\dfrac{k(3)(4)^2}{8} \\\\ \\\\ k&=&\\dfrac{12(8)}{3\\cdot 16} \\\\ \\\\ k&=& 2 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} \\underline{\\text{3rd}}&& \\\\ y&=&\\text{find} \\\\ k&=& 2 \\\\ m&=&-3 \\\\ n&=&3 \\\\ d&=& 6 \\\\ \\\\ y&=&\\dfrac{(2)(-3)(3)^2}{6} \\\\ \\\\ y&=&-9 \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n

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