{"id":1835,"date":"2021-12-02T19:39:38","date_gmt":"2021-12-03T00:39:38","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-e-answer-key\/"},"modified":"2022-11-02T10:37:49","modified_gmt":"2022-11-02T14:37:49","slug":"midterm-one-version-e-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-e-answer-key\/","title":{"raw":"Midterm 1: Version E Answer Key","rendered":"Midterm 1: Version E Answer Key"},"content":{"raw":"
    \n \t
  1. \n
      \n \t
    1. \u22129<\/li>\n \t
    2. 9<\/li>\n \t
    3. \u22129<\/li>\n \t
    4. 10<\/li>\n \t
    5. \u22123<\/li>\n<\/ol>\n<\/li>\n \t
    6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrlrrrr}\n2x&-&8&+&18&=&-12&+&4x&+&12 \\\\\n-2x&&&&&&&-&2x&& \\\\\n\\hline\n&&&&\\dfrac{10}{2}&=&\\dfrac{2x}{2}&&&& \\\\ \\\\\n&&&&x&=&5&&&&\n\\end{array}[\/latex]<\/li>\n \t
    7. [latex]\\left(\\dfrac{1}{R}-\\dfrac{1}{r_1}=\\dfrac{1}{r_2}\\right)(Rr_1r_2) [\/latex]\n[latex]\\begin{array}{rrrrlrr}\nr_1r_2&-&Rr_2&=&\\phantom{-}Rr_1&& \\\\\n-Rr_1&+&Rr_2&&-Rr_1&+&Rr_2 \\\\\n\\hline\nr_1r_2&-&Rr_1&=&Rr_2&& \\\\\nr_1(r_2&-&R)&=&Rr_2&& \\\\ \\\\\n&&r_1&=&\\dfrac{Rr_2}{r_2-R}&&\n\\end{array}[\/latex]<\/li>\n \t
    8. [latex]\\left(\\dfrac{x}{12}-\\dfrac{x-4}{3}=\\dfrac{2}{3} \\right)(12)[\/latex]\n[latex]\\begin{array}{rrcrrrl}\nx&-&4(x&-&4)&=&4(2) \\\\\nx&-&4x&+&16&=&8 \\\\\n&&&-&16&&-16 \\\\\n\\hline\n&&&&\\dfrac{-3x}{-3}&=&\\dfrac{-8}{-3} \\\\ \\\\\n&&&&x&=&\\dfrac{8}{3}\n\\end{array}[\/latex]<\/li>\n \t
    9. [latex]y=-6[\/latex]\n\"-4<\/li>\n \t
    10. [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-1}{x--1}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrrrlrr}\n&&2(x&+&1)&=&\\phantom{-}5(y&-&1) \\\\\n&&2x&+&2&=&\\phantom{-}5y&-&5 \\\\\n&-&5y&+&5&&-5y&+&5 \\\\\n\\hline\n2x&-&5y&+&7&=&0&& \\\\ \\\\\n&&&&y&=&\\dfrac{2}{5}x&+&\\dfrac{7}{5}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
    11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n&&\\textbf{1st slope:} \\\\ \\\\\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\nm&=&\\dfrac{5--1}{2-0} \\\\ \\\\\nm&=&\\dfrac{6}{2} \\\\ \\\\\nm&=&3\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n&&\\textbf{Now:} \\\\ \\\\\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\n3&=&\\dfrac{y--1}{x-0} \\\\ \\\\\n3x&=&y+1 \\\\ \\\\\n3x-y-1&=&0 \\\\ \\\\\n\\therefore 0&=&3x-y-1 \\\\\ny&=&3x-1\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
    12. [latex]\\phantom{a}[\/latex]\n\"Line<\/li>\n \t
    13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n-20&\\le &8x&-&4&\\le &28 \\\\\n+4&&&+&4&&+4 \\\\\n\\hline\n\\dfrac{-16}{8}&\\le &&\\dfrac{8x}{8}&&\\le &\\dfrac{32}{8} \\\\ \\\\\n-2&\\le &&x&&\\le &4\n\\end{array}[\/latex]\n\"-2<\/li>\n \t
    14. [latex]\\left(-2\\le \\dfrac{2x+2}{6} \\le 2 \\right)(6) [\/latex]\n[latex]\\begin{array}{rrrrrrr}\n-12&\\le &2x&+&2&\\le &12 \\\\\n-2&&&-&2&&-2 \\\\\n\\hline\n\\dfrac{-14}{2}&\\le &&\\dfrac{2x}{2}&&\\le &\\dfrac{10}{2} \\\\ \\\\\n-7&\\le &&x&&\\le &5\n\\end{array}[\/latex]\n\"-7<\/li>\n \t
    15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\left(\\dfrac{3x-4}{5} < -1 \\right)(5) \\hspace{0.25in}& \\text{or} \\hspace{0.25in} \\left(1 < \\dfrac{3x-4}{5}\\right)(5) \\\\ \\\\\n\\begin{array}[t]{rrrrr}\n3x&-&4&<&-5 \\\\\n&+&4&&+4 \\\\\n\\hline\n&&3x&<&-1 \\\\ \\\\\n&&x&<&-\\dfrac{1}{3}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\n5&<&3x&-&4 \\\\\n+4&&&+&4 \\\\\n\\hline\n\\dfrac{9}{3}&<&\\dfrac{3x}{3}&& \\\\ \\\\\nx&>&3&&\n\\end{array}\n\\end{array}[\/latex]\n\"x -1 over 3, x < 3\" width=\"300\" height=\"71\"><\/li>\n \t
    16. \n\n\n\n\n
      [latex]3x-2y<12[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n\u22126<\/td>\n<\/tr>\n
      4<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Line<\/li>\n \t
    17. [latex]x, x+2, x+4[\/latex]\n[latex]\\begin{array}[t]{rrcrrrcrrrl}\nx&+&2(x&+&2)&+&3(x&+&4)&=&\\phantom{-}94 \\\\\nx&+&2x&+&4&+&3x&+&12&=&\\phantom{-}94 \\\\\n&&&&&&6x&+&16&=&\\phantom{-}94 \\\\\n&&&&&&&-&16&&-16 \\\\\n\\hline\n&&&&&&&&\\dfrac{6x}{6}&=&\\dfrac{78}{6} \\\\ \\\\\n&&&&&&&&x&=&13\\\\\n\\end{array}[\/latex]\nnumbers are 13, 15, 17<\/li>\n \t
    18. \"\"\n[latex]\\begin{array}[t]{rrl}\n3x+x&=&800\\text{ cm} \\\\\n4x&=&800\\text{ cm} \\\\\nx&=&\\dfrac{800\\text{ cm}}{4}\\text{ or }200\\text{ cm} \\\\ \\\\\n3x&=&600\\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
    19. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ny&=&\\dfrac{km}{n^2} \\\\ \\\\\n&&\\underline{\\text{1st}} \\\\\ny&=&12 \\\\\nk&=&\\text{find} \\\\\nm&=&3 \\\\\nn&=&4 \\\\ \\\\\n12&=&\\dfrac{k(3)}{(4)^2} \\\\ \\\\\nk&=&\\dfrac{12\\cdot (4)^2}{3} \\\\ \\\\\nk&=&64\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n&&\\underline{\\text{2nd}} \\\\\ny&=&\\text{find} \\\\\nk&=&64 \\\\\nm&=&3 \\\\\nn&=&-3 \\\\ \\\\\ny&=&\\dfrac{(64)(3)}{(-3)^2} \\\\ \\\\\ny&=&\\dfrac{64}{3}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
        \n
      1. \n
          \n
        1. \u22129<\/li>\n
        2. 9<\/li>\n
        3. \u22129<\/li>\n
        4. 10<\/li>\n
        5. \u22123<\/li>\n<\/ol>\n<\/li>\n
        6. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrlrrrr} 2x&-&8&+&18&=&-12&+&4x&+&12 \\\\ -2x&&&&&&&-&2x&& \\\\ \\hline &&&&\\dfrac{10}{2}&=&\\dfrac{2x}{2}&&&& \\\\ \\\\ &&&&x&=&5&&&& \\end{array}[\/latex]<\/li>\n
        7. [latex]\\left(\\dfrac{1}{R}-\\dfrac{1}{r_1}=\\dfrac{1}{r_2}\\right)(Rr_1r_2)[\/latex]
          \n[latex]\\begin{array}{rrrrlrr} r_1r_2&-&Rr_2&=&\\phantom{-}Rr_1&& \\\\ -Rr_1&+&Rr_2&&-Rr_1&+&Rr_2 \\\\ \\hline r_1r_2&-&Rr_1&=&Rr_2&& \\\\ r_1(r_2&-&R)&=&Rr_2&& \\\\ \\\\ &&r_1&=&\\dfrac{Rr_2}{r_2-R}&& \\end{array}[\/latex]<\/li>\n
        8. [latex]\\left(\\dfrac{x}{12}-\\dfrac{x-4}{3}=\\dfrac{2}{3} \\right)(12)[\/latex]
          \n[latex]\\begin{array}{rrcrrrl} x&-&4(x&-&4)&=&4(2) \\\\ x&-&4x&+&16&=&8 \\\\ &&&-&16&&-16 \\\\ \\hline &&&&\\dfrac{-3x}{-3}&=&\\dfrac{-8}{-3} \\\\ \\\\ &&&&x&=&\\dfrac{8}{3} \\end{array}[\/latex]<\/li>\n
        9. [latex]y=-6[\/latex]
          \n\"-4<\/li>\n
        10. [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-1}{x--1} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrlrr} &&2(x&+&1)&=&\\phantom{-}5(y&-&1) \\\\ &&2x&+&2&=&\\phantom{-}5y&-&5 \\\\ &-&5y&+&5&&-5y&+&5 \\\\ \\hline 2x&-&5y&+&7&=&0&& \\\\ \\\\ &&&&y&=&\\dfrac{2}{5}x&+&\\dfrac{7}{5} \\end{array} \\end{array}[\/latex]<\/li>\n
        11. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st slope:} \\\\ \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ m&=&\\dfrac{5--1}{2-0} \\\\ \\\\ m&=&\\dfrac{6}{2} \\\\ \\\\ m&=&3 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} &&\\textbf{Now:} \\\\ \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ 3&=&\\dfrac{y--1}{x-0} \\\\ \\\\ 3x&=&y+1 \\\\ \\\\ 3x-y-1&=&0 \\\\ \\\\ \\therefore 0&=&3x-y-1 \\\\ y&=&3x-1 \\end{array} \\end{array}[\/latex]<\/li>\n
        12. [latex]\\phantom{a}[\/latex]
          \n\"Line<\/li>\n
        13. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrrrrrr} -20&\\le &8x&-&4&\\le &28 \\\\ +4&&&+&4&&+4 \\\\ \\hline \\dfrac{-16}{8}&\\le &&\\dfrac{8x}{8}&&\\le &\\dfrac{32}{8} \\\\ \\\\ -2&\\le &&x&&\\le &4 \\end{array}[\/latex]
          \n\"-2<\/li>\n
        14. [latex]\\left(-2\\le \\dfrac{2x+2}{6} \\le 2 \\right)(6)[\/latex]
          \n[latex]\\begin{array}{rrrrrrr} -12&\\le &2x&+&2&\\le &12 \\\\ -2&&&-&2&&-2 \\\\ \\hline \\dfrac{-14}{2}&\\le &&\\dfrac{2x}{2}&&\\le &\\dfrac{10}{2} \\\\ \\\\ -7&\\le &&x&&\\le &5 \\end{array}[\/latex]
          \n\"-7<\/li>\n
        15. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\left(\\dfrac{3x-4}{5} < -1 \\right)(5) \\hspace{0.25in}& \\text{or} \\hspace{0.25in} \\left(1 < \\dfrac{3x-4}{5}\\right)(5) \\\\ \\\\ \\begin{array}[t]{rrrrr} 3x&-&4&<&-5 \\\\ &+&4&&+4 \\\\ \\hline &&3x&<&-1 \\\\ \\\\ &&x&<&-\\dfrac{1}{3} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} 5&<&3x&-&4 \\\\ +4&&&+&4 \\\\ \\hline \\dfrac{9}{3}&<&\\dfrac{3x}{3}&& \\\\ \\\\ x&>&3&& \\end{array} \\end{array}[\/latex]
          \n\"image\" -1 over 3, x < 3\" width=\"300\" height=\"71\"><\/li>\n
        16. \n\n\n\n\n\n
          [latex]3x-2y<12[\/latex]<\/caption>\n
          [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
          0<\/td>\n\u22126<\/td>\n<\/tr>\n
          4<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          \"Line<\/li>\n

        17. [latex]x, x+2, x+4[\/latex]
          \n[latex]\\begin{array}[t]{rrcrrrcrrrl} x&+&2(x&+&2)&+&3(x&+&4)&=&\\phantom{-}94 \\\\ x&+&2x&+&4&+&3x&+&12&=&\\phantom{-}94 \\\\ &&&&&&6x&+&16&=&\\phantom{-}94 \\\\ &&&&&&&-&16&&-16 \\\\ \\hline &&&&&&&&\\dfrac{6x}{6}&=&\\dfrac{78}{6} \\\\ \\\\ &&&&&&&&x&=&13\\\\ \\end{array}[\/latex]
          \nnumbers are 13, 15, 17<\/li>\n
        18. \"\"
          \n[latex]\\begin{array}[t]{rrl} 3x+x&=&800\\text{ cm} \\\\ 4x&=&800\\text{ cm} \\\\ x&=&\\dfrac{800\\text{ cm}}{4}\\text{ or }200\\text{ cm} \\\\ \\\\ 3x&=&600\\text{ cm} \\end{array}[\/latex]<\/li>\n
        19. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} y&=&\\dfrac{km}{n^2} \\\\ \\\\ &&\\underline{\\text{1st}} \\\\ y&=&12 \\\\ k&=&\\text{find} \\\\ m&=&3 \\\\ n&=&4 \\\\ \\\\ 12&=&\\dfrac{k(3)}{(4)^2} \\\\ \\\\ k&=&\\dfrac{12\\cdot (4)^2}{3} \\\\ \\\\ k&=&64 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} &&\\underline{\\text{2nd}} \\\\ y&=&\\text{find} \\\\ k&=&64 \\\\ m&=&3 \\\\ n&=&-3 \\\\ \\\\ y&=&\\dfrac{(64)(3)}{(-3)^2} \\\\ \\\\ y&=&\\dfrac{64}{3} \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":41,"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-1835","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\/1835","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\/1835\/revisions"}],"predecessor-version":[{"id":1836,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1835\/revisions\/1836"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1835\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1835"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1835"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1835"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1835"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}