{"id":3224,"date":"2019-11-19T13:58:01","date_gmt":"2019-11-19T18:58:01","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=3224"},"modified":"2019-12-29T19:35:35","modified_gmt":"2019-12-30T00:35:35","slug":"midterm-one-version-e-answer-key","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/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":"[latexpage]\r\n
    \r\n \t
  1. \\(\\phantom{1}\\)\r\n
      \r\n \t
    1. \u22129<\/li>\r\n \t
    2. 9<\/li>\r\n \t
    3. \u22129<\/li>\r\n \t
    4. 10<\/li>\r\n \t
    5. \u22123<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
    6. \\(\\begin{array}{rrrrrrlrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n2x&-&8&+&18&=&-12&+&4x&+&12 \\\\\r\n-2x&&&&&&&-&2x&& \\\\\r\n\\midrule\r\n&&&&\\dfrac{10}{2}&=&\\dfrac{2x}{2}&&&& \\\\ \\\\\r\n&&&&x&=&5&&&&\r\n\\end{array}\\)<\/li>\r\n \t
    7. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{1}{R}-\\dfrac{1}{r_1}=\\dfrac{1}{r_2}\\right)(Rr_1r_2) \\\\ \\)\r\n\\(\\begin{array}{rrrrlrr}\r\nr_1r_2&-&Rr_2&=&\\phantom{-}Rr_1&& \\\\\r\n-Rr_1&+&Rr_2&&-Rr_1&+&Rr_2 \\\\\r\n\\midrule\r\nr_1r_2&-&Rr_1&=&Rr_2&& \\\\\r\nr_1(r_2&-&R)&=&Rr_2&& \\\\ \\\\\r\n&&r_1&=&\\dfrac{Rr_2}{r_2-R}&&\r\n\\end{array}\\)<\/li>\r\n \t
    8. \\(\\phantom{1}\\)\r\n\\(\\left(\\dfrac{x}{12}-\\dfrac{x-4}{3}=\\dfrac{2}{3} \\right)(12) \\\\ \\)\r\n\\(\\begin{array}{rrcrrrl}\r\nx&-&4(x&-&4)&=&4(2) \\\\\r\nx&-&4x&+&16&=&8 \\\\\r\n&&&-&16&&-16 \\\\\r\n\\midrule\r\n&&&&\\dfrac{-3x}{-3}&=&\\dfrac{-8}{-3} \\\\ \\\\\r\n&&&&x&=&\\dfrac{8}{3}\r\n\\end{array}\\)<\/li>\r\n \t
    9. \\(y=-6\\)\r\n\"-4<\/li>\r\n \t
    10. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n\\dfrac{2}{5}&=&\\dfrac{y-1}{x--1}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrrrlrr}\r\n\\\\ \\\\ \\\\\r\n&&2(x&+&1)&=&\\phantom{-}5(y&-&1) \\\\\r\n&&2x&+&2&=&\\phantom{-}5y&-&5 \\\\\r\n&-&5y&+&5&&-5y&+&5 \\\\\r\n\\midrule\r\n2x&-&5y&+&7&=&0&& \\\\ \\\\\r\n&&&&y&=&\\dfrac{2}{5}x&+&\\dfrac{7}{5}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    11. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrl}\r\n&&\\textbf{1st slope:} \\\\ \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\nm&=&\\dfrac{5--1}{2-0} \\\\ \\\\\r\nm&=&\\dfrac{6}{2} \\\\ \\\\\r\nm&=&3\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\\r\n&&\\textbf{Now:} \\\\ \\\\\r\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\r\n3&=&\\dfrac{y--1}{x-0} \\\\ \\\\\r\n3x&=&y+1 \\\\ \\\\\r\n3x-y-1&=&0 \\\\ \\\\\r\n\\therefore 0&=&3x-y-1 \\\\\r\ny&=&3x-1\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
    12. \"Line<\/li>\r\n \t
    13. \\(\\begin{array}{rrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n-20&\\le &8x&-&4&\\le &28 \\\\\r\n+4&&&+&4&&+4 \\\\\r\n\\midrule\r\n\\dfrac{-16}{8}&\\le &&\\dfrac{8x}{8}&&\\le &\\dfrac{32}{8} \\\\ \\\\\r\n-2&\\le &&x&&\\le &4\r\n\\end{array}\\)\r\n\"-2<\/li>\r\n \t
    14. \\(\\phantom{1}\\)\r\n\\(\\left(-2\\le \\dfrac{2x+2}{6} \\le 2 \\right)(6) \\\\ \\)\r\n\\(\\begin{array}{rrrrrrr}\r\n-12&\\le &2x&+&2&\\le &12 \\\\\r\n-2&&&-&2&&-2 \\\\\r\n\\midrule\r\n\\dfrac{-14}{2}&\\le &&\\dfrac{2x}{2}&&\\le &\\dfrac{10}{2} \\\\ \\\\\r\n-7&\\le &&x&&\\le &5\r\n\\end{array}\\)\r\n\"-7<\/li>\r\n \t
    15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\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) \\\\ \\\\\r\n\\begin{array}{rrrrr}\r\n3x&-&4&<&-5 \\\\\r\n&+&4&&+4 \\\\\r\n\\midrule\r\n&&3x&<&-1 \\\\ \\\\\r\n&&x&<&-\\dfrac{1}{3}\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrrrr}\r\n5&<&3x&-&4 \\\\\r\n+4&&&+&4 \\\\\r\n\\midrule\r\n\\dfrac{9}{3}&<&\\dfrac{3x}{3}&& \\\\ \\\\\r\nx&>&3&&\r\n\\end{array}\r\n\\end{array}\\)\r\n\"x<\/li>\r\n \t
    16. \r\n\r\n\r\n\r\n\r\n
      \\(3x-2y<12\\)<\/caption>\r\n
      \\(x\\)<\/th>\r\n\\(y\\)<\/th>\r\n<\/tr>\r\n
      0<\/td>\r\n\u22126<\/td>\r\n<\/tr>\r\n
      4<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\"Line<\/li>\r\n \t
    17. \\(\\phantom{1}\\)\r\n\\(x, x+2, x+4 \\\\ \\)\r\n\\(\\begin{array}{rrcrrrcrrrl}\r\nx&+&2(x&+&2)&+&3(x&+&4)&=&\\phantom{-}94 \\\\\r\nx&+&2x&+&4&+&3x&+&12&=&\\phantom{-}94 \\\\\r\n&&&&&&6x&+&16&=&\\phantom{-}94 \\\\\r\n&&&&&&&-&16&&-16 \\\\\r\n\\midrule\r\n&&&&&&&&\\dfrac{6x}{6}&=&\\dfrac{78}{6} \\\\ \\\\\r\n&&&&&&&&x&=&13\r\n\\end{array}\\)\r\n\\(\\phantom{1}\\)\r\nnumbers are 13, 15, 17<\/li>\r\n \t
    18. \"\"\r\n\\(\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\\r\n3x+x&=&800\\text{ cm} \\\\\r\n4x&=&800\\text{ cm} \\\\\r\nx&=&\\dfrac{800\\text{ cm}}{4}\\text{ or }200\\text{ cm} \\\\ \\\\\r\n3x&=&600\\text{ cm}\r\n\\end{array}\\)<\/li>\r\n \t
    19. \\(\\begin{array}{ll}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\ny&=&\\dfrac{km}{n^2} \\\\ \\\\\r\n&&\\underline{\\text{1st}} \\\\\r\ny&=&12 \\\\\r\nk&=&\\text{find} \\\\\r\nm&=&3 \\\\\r\nn&=&4 \\\\ \\\\\r\n12&=&\\dfrac{k(3)}{(4)^2} \\\\ \\\\\r\nk&=&\\dfrac{12\\cdot (4)^2}{3} \\\\ \\\\\r\nk&=&64\r\n\\end{array}\r\n& \\hspace{0.25in}\r\n\\begin{array}{rrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&\\underline{\\text{2nd}} \\\\\r\ny&=&\\text{find} \\\\\r\nk&=&64 \\\\\r\nm&=&3 \\\\\r\nn&=&-3 \\\\ \\\\\r\ny&=&\\dfrac{(64)(3)}{(-3)^2} \\\\ \\\\\r\ny&=&\\dfrac{64}{3}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
        \n
      1. \"\phantom{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. \"\begin{array}{rrrrrrlrrrr}<\/li>\n
        7. \"\phantom{1}\"
          \n\"\left(\dfrac{1}{R}-\dfrac{1}{r_1}=\dfrac{1}{r_2}\right)(Rr_1r_2) \\\"
          \n\"\begin{array}{rrrrlrr}<\/li>\n
        8. \"\phantom{1}\"
          \n\"\left(\dfrac{x}{12}-\dfrac{x-4}{3}=\dfrac{2}{3} \right)(12) \\\"
          \n\"\begin{array}{rrcrrrl}<\/li>\n
        9. \"y=-6\"
          \n\"-4<\/li>\n
        10. \"\begin{array}{ll}<\/li>\n
        11. \"\begin{array}{ll}<\/li>\n
        12. \"Line<\/li>\n
        13. \"\begin{array}{rrrrrrr}
          \n\"-2<\/li>\n
        14. \"\phantom{1}\"
          \n\"\left(-2\le \dfrac{2x+2}{6} \le 2 \right)(6) \\\"
          \n\"\begin{array}{rrrrrrr}
          \n\"-7<\/li>\n
        15. \"\begin{array}{ll}
          \n\"x<\/li>\n
        16. \n\n\n\n\n\n
          \"3x-2y<12\"<\/caption>\n
          \"x\"<\/th>\n\"y\"<\/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. \"\phantom{1}\"
          \n\"x, x+2, x+4 \\\"
          \n\"\begin{array}{rrcrrrcrrrl}
          \n\"\phantom{1}\"
          \nnumbers are 13, 15, 17<\/li>\n
        18. \"\"
          \n\"\begin{array}{rrl}<\/li>\n
        19. \"\begin{array}{ll}<\/li>\n<\/ol>\n","protected":false},"author":14,"menu_order":36,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-3224","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/14"}],"version-history":[{"count":12,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3224\/revisions"}],"predecessor-version":[{"id":3741,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3224\/revisions\/3741"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/3224\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=3224"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=3224"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=3224"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=3224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}