{"id":1826,"date":"2021-12-02T19:39:36","date_gmt":"2021-12-03T00:39:36","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-d-answer-key\/"},"modified":"2022-11-02T10:37:47","modified_gmt":"2022-11-02T14:37:47","slug":"midterm-one-version-d-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-d-answer-key\/","title":{"raw":"Midterm 1: Version D Answer Key","rendered":"Midterm 1: Version D Answer Key"},"content":{"raw":"
    \n \t
  1. [latex]3(4)-\\sqrt{4^2-4(4)(1)}[\/latex]\n<\/span>[latex]\\begin{array}[t]{l}\\\\\n12-\\sqrt{16-16} \\\\ \\\\\n12\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\n2x&-&8&+&8&=&-6&+&3x&+&9 \\\\\n&&&&2x&=&3x&+&3&& \\\\\n&&&&-3x&&-3x&&&& \\\\\n\\hline\n&&&&-x&=&3&&&& \\\\\n&&&&x&=&-3&&&&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\left(\\dfrac{1}{R}=\\dfrac{1}{r_1}+\\dfrac{1}{r_2}\\right)(Rr_1r_2)[\/latex]\n[latex]\\begin{array}[t]{rrrrlrr}\n&&r_1r_2&=&\\phantom{-}Rr_2&+&Rr_1 \\\\\n&&-Rr_2&&-Rr_2&& \\\\\n\\hline\nr_1r_2&-&Rr_2&=&Rr_1&& \\\\\nr_2(r_1&-&R)&=&Rr_1&& \\\\ \\\\\n&&r_2&=&\\dfrac{Rr_1}{r_1-R}&&\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\left(\\dfrac{x}{15}-\\dfrac{x-3}{3}=\\dfrac{1}{3}\\right)(15)[\/latex]\n[latex]\\begin{array}[t]{rrcrrrr}\nx&-&5(x&-&3)&=&5 \\\\\nx&-&5x&+&15&=&5 \\\\\n&&&-&15&&-15 \\\\\n\\hline\n&&&&\\dfrac{-4x}{-4}&=&\\dfrac{-10}{-4} \\\\ \\\\\n&&&&x&=&\\dfrac{5}{2}\n\\end{array}[\/latex]<\/li>\n \t
  5. [latex]y=5[\/latex]\n\"point<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\n\\dfrac{2}{3}&=&\\dfrac{y-4}{x--2}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrrrlrr}\n&&2(x&+&2)&=&\\phantom{-}3(y&-&4) \\\\\n&&2x&+&4&=&\\phantom{-}3y&-&12 \\\\\n&-&3y&+&12&&-3y&+&12 \\\\\n\\hline\n2x&-&3y&+&16&=&0&& \\\\ \\\\\n&&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{16}{3}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  7. [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{-9--7}{8-12} \\\\ \\\\\nm&=&\\dfrac{-2}{-4} \\\\ \\\\\nm&=&\\dfrac{1}{2} \\\\ \\\\\n&&\\textbf{Now:} \\\\\nm&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\n\\dfrac{1}{2}&=&\\dfrac{y--9}{x-8}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrrrrrr}\n&&x&-&8&=&2(y&+&9) \\\\\n&&x&-&8&=&2y&+&18 \\\\\n&-&2y&-&18&&-2y&-&18 \\\\\n\\hline\nx&-&2y&-&26&=&0&&\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n\"Line<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrr}\n-27&\\le &6x&-&9&\\le &3 \\\\\n+9&&&+&9&&+9 \\\\\n\\hline\n\\dfrac{-18}{6}&\\le &&\\dfrac{6x}{6}&&\\le &\\dfrac{12}{6} \\\\ \\\\\n-3&\\le &&x&&\\le &2\n\\end{array}[\/latex]\n\"-3<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\dfrac{2x+2}{6}=2& \\hspace{0.75in} \\dfrac{2x+2}{6}=-2 \\\\ \\\\\n\\begin{array}[t]{rrrrl}\n2x&+&2&=&2\\cdot 6 \\\\\n2x&+&2&=&12 \\\\\n&-&2&&-2 \\\\\n\\hline\n&&\\dfrac{2x}{2}&=&\\dfrac{10}{2} \\\\ \\\\\n&&x&=&5\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrl}\n2x&+&2&=&-2\\cdot 6 \\\\\n2x&+&2&=&-12 \\\\\n&-&2&&-2 \\\\\n\\hline\n&&\\dfrac{2x}{2}&=&\\dfrac{-14}{2} \\\\ \\\\\n&&x&=&-7\n\\end{array}\n\\end{array}[\/latex]\n\"x=5,<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\n2x&-&1&<&-6&\\hspace{0.25in}&6&<&2x&-&1 \\\\\n&+&1&&+1&&+1&&&+&1 \\\\\n\\hline\n&&\\dfrac{2x}{2}&<&\\dfrac{-5}{2}&&\\dfrac{7}{2}&<&\\dfrac{2x}{2}&& \\\\ \\\\\n&&x&<&-\\dfrac{5}{2}&&x&>&\\dfrac{7}{2}&&\n\\end{array}[\/latex]<\/li>\n \t
  12. \n\n\n\n\n\n\n\n\n\n
    [latex]y=|2x|-1[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    3<\/td>\n5<\/td>\n<\/tr>\n
    2<\/td>\n3<\/td>\n<\/tr>\n
    1<\/td>\n1<\/td>\n<\/tr>\n
    0<\/td>\n\u22121<\/td>\n<\/tr>\n
    \u22121<\/td>\n1<\/td>\n<\/tr>\n
    \u22122<\/td>\n3<\/td>\n<\/tr>\n
    \u22123<\/td>\n5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"V<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\nA_1&=&A_2 \\\\\nA_3&=&2A_1-10^{\\circ} \\\\ \\\\\nA_1+A_2+A_3&=&180^{\\circ} \\\\\nA_1+A_1+2A_1-10^{\\circ}&=&180^{\\circ} \\\\\n+10^{\\circ}&&+10^{\\circ} \\\\\n\\hline\n\\dfrac{4A_1}{4}&=&\\dfrac{190^{\\circ}}{4}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\nA_1&=&47.5^{\\circ} \\\\ \\\\\nA_2&=&47.5^{\\circ} \\\\ \\\\\nA_3&=&2A_1-10^{\\circ} \\\\\nA_3&=&2(47.5^{\\circ})-10^{\\circ} \\\\\nA_3&=&95^{\\circ}-10^{\\circ} \\\\\nA_3&=&85^{\\circ}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]x, x+2 [\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrr}\nx&+&x&+&2&=&x&-&20 \\\\\n&&2x&+&2&=&x&-&20 \\\\\n&&-x&-&2&&-x&-&2 \\\\\n\\hline\n&&&&x&=&-22&&\\\\\n\\end{array}[\/latex]\nnumbers are \u221222, \u221220<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\n&&\\textbf{1st data} \\\\\ny&=&16 \\\\\nk&=&\\text{find 1st} \\\\\nm&=&3 \\\\\nn&=&4 \\\\\nd&=&6 \\\\ \\\\\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\n16&=&\\dfrac{k(3)(4)^2}{6} \\\\ \\\\\nk&=&\\dfrac{16\\cdot 6}{3\\cdot (4)^2} \\\\ \\\\\nk&=&2\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\\\\ \\\\\n&&\\textbf{2nd data} \\\\\ny&=&\\text{find 2nd} \\\\\nk&=&2 \\\\\nm&=&-2 \\\\\nn&=&4 \\\\\nd&=&8 \\\\ \\\\\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\ny&=&\\dfrac{(2)(-2)(4)^2}{8} \\\\ \\\\\ny&=&-8\n\\end{array}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]3(4)-\\sqrt{4^2-4(4)(1)}[\/latex]
      \n<\/span>[latex]\\begin{array}[t]{l}\\\\ 12-\\sqrt{16-16} \\\\ \\\\ 12 \\end{array}[\/latex]<\/li>\n
    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrr} 2x&-&8&+&8&=&-6&+&3x&+&9 \\\\ &&&&2x&=&3x&+&3&& \\\\ &&&&-3x&&-3x&&&& \\\\ \\hline &&&&-x&=&3&&&& \\\\ &&&&x&=&-3&&&& \\end{array}[\/latex]<\/li>\n
    3. [latex]\\left(\\dfrac{1}{R}=\\dfrac{1}{r_1}+\\dfrac{1}{r_2}\\right)(Rr_1r_2)[\/latex]
      \n[latex]\\begin{array}[t]{rrrrlrr} &&r_1r_2&=&\\phantom{-}Rr_2&+&Rr_1 \\\\ &&-Rr_2&&-Rr_2&& \\\\ \\hline r_1r_2&-&Rr_2&=&Rr_1&& \\\\ r_2(r_1&-&R)&=&Rr_1&& \\\\ \\\\ &&r_2&=&\\dfrac{Rr_1}{r_1-R}&& \\end{array}[\/latex]<\/li>\n
    4. [latex]\\left(\\dfrac{x}{15}-\\dfrac{x-3}{3}=\\dfrac{1}{3}\\right)(15)[\/latex]
      \n[latex]\\begin{array}[t]{rrcrrrr} x&-&5(x&-&3)&=&5 \\\\ x&-&5x&+&15&=&5 \\\\ &&&-&15&&-15 \\\\ \\hline &&&&\\dfrac{-4x}{-4}&=&\\dfrac{-10}{-4} \\\\ \\\\ &&&&x&=&\\dfrac{5}{2} \\end{array}[\/latex]<\/li>\n
    5. [latex]y=5[\/latex]
      \n\"point<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ \\dfrac{2}{3}&=&\\dfrac{y-4}{x--2} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrlrr} &&2(x&+&2)&=&\\phantom{-}3(y&-&4) \\\\ &&2x&+&4&=&\\phantom{-}3y&-&12 \\\\ &-&3y&+&12&&-3y&+&12 \\\\ \\hline 2x&-&3y&+&16&=&0&& \\\\ \\\\ &&&&y&=&\\dfrac{2}{3}x&+&\\dfrac{16}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
    7. [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{-9--7}{8-12} \\\\ \\\\ m&=&\\dfrac{-2}{-4} \\\\ \\\\ m&=&\\dfrac{1}{2} \\\\ \\\\ &&\\textbf{Now:} \\\\ m&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ \\dfrac{1}{2}&=&\\dfrac{y--9}{x-8} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrrrr} &&x&-&8&=&2(y&+&9) \\\\ &&x&-&8&=&2y&+&18 \\\\ &-&2y&-&18&&-2y&-&18 \\\\ \\hline x&-&2y&-&26&=&0&& \\end{array} \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n\"Line<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrr} -27&\\le &6x&-&9&\\le &3 \\\\ +9&&&+&9&&+9 \\\\ \\hline \\dfrac{-18}{6}&\\le &&\\dfrac{6x}{6}&&\\le &\\dfrac{12}{6} \\\\ \\\\ -3&\\le &&x&&\\le &2 \\end{array}[\/latex]
      \n\"-3<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\dfrac{2x+2}{6}=2& \\hspace{0.75in} \\dfrac{2x+2}{6}=-2 \\\\ \\\\ \\begin{array}[t]{rrrrl} 2x&+&2&=&2\\cdot 6 \\\\ 2x&+&2&=&12 \\\\ &-&2&&-2 \\\\ \\hline &&\\dfrac{2x}{2}&=&\\dfrac{10}{2} \\\\ \\\\ &&x&=&5 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrl} 2x&+&2&=&-2\\cdot 6 \\\\ 2x&+&2&=&-12 \\\\ &-&2&&-2 \\\\ \\hline &&\\dfrac{2x}{2}&=&\\dfrac{-14}{2} \\\\ \\\\ &&x&=&-7 \\end{array} \\end{array}[\/latex]
      \n\"x=5,<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrr} 2x&-&1&<&-6&\\hspace{0.25in}&6&<&2x&-&1 \\\\ &+&1&&+1&&+1&&&+&1 \\\\ \\hline &&\\dfrac{2x}{2}&<&\\dfrac{-5}{2}&&\\dfrac{7}{2}&<&\\dfrac{2x}{2}&& \\\\ \\\\ &&x&<&-\\dfrac{5}{2}&&x&>&\\dfrac{7}{2}&& \\end{array}[\/latex]<\/li>\n
    12. \n\n\n\n\n\n\n\n\n\n\n
      [latex]y=|2x|-1[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      3<\/td>\n5<\/td>\n<\/tr>\n
      2<\/td>\n3<\/td>\n<\/tr>\n
      1<\/td>\n1<\/td>\n<\/tr>\n
      0<\/td>\n\u22121<\/td>\n<\/tr>\n
      \u22121<\/td>\n1<\/td>\n<\/tr>\n
      \u22122<\/td>\n3<\/td>\n<\/tr>\n
      \u22123<\/td>\n5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"V<\/li>\n

    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} A_1&=&A_2 \\\\ A_3&=&2A_1-10^{\\circ} \\\\ \\\\ A_1+A_2+A_3&=&180^{\\circ} \\\\ A_1+A_1+2A_1-10^{\\circ}&=&180^{\\circ} \\\\ +10^{\\circ}&&+10^{\\circ} \\\\ \\hline \\dfrac{4A_1}{4}&=&\\dfrac{190^{\\circ}}{4} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} A_1&=&47.5^{\\circ} \\\\ \\\\ A_2&=&47.5^{\\circ} \\\\ \\\\ A_3&=&2A_1-10^{\\circ} \\\\ A_3&=&2(47.5^{\\circ})-10^{\\circ} \\\\ A_3&=&95^{\\circ}-10^{\\circ} \\\\ A_3&=&85^{\\circ} \\end{array} \\end{array}[\/latex]<\/li>\n
    14. [latex]x, x+2[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrr} x&+&x&+&2&=&x&-&20 \\\\ &&2x&+&2&=&x&-&20 \\\\ &&-x&-&2&&-x&-&2 \\\\ \\hline &&&&x&=&-22&&\\\\ \\end{array}[\/latex]
      \nnumbers are \u221222, \u221220<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} y&=&\\dfrac{kmn^2}{d} \\\\ \\\\ &&\\textbf{1st data} \\\\ y&=&16 \\\\ k&=&\\text{find 1st} \\\\ m&=&3 \\\\ n&=&4 \\\\ d&=&6 \\\\ \\\\ y&=&\\dfrac{kmn^2}{d} \\\\ \\\\ 16&=&\\dfrac{k(3)(4)^2}{6} \\\\ \\\\ k&=&\\dfrac{16\\cdot 6}{3\\cdot (4)^2} \\\\ \\\\ k&=&2 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl}\\\\ \\\\ &&\\textbf{2nd data} \\\\ y&=&\\text{find 2nd} \\\\ k&=&2 \\\\ m&=&-2 \\\\ n&=&4 \\\\ d&=&8 \\\\ \\\\ y&=&\\dfrac{kmn^2}{d} \\\\ \\\\ y&=&\\dfrac{(2)(-2)(4)^2}{8} \\\\ \\\\ y&=&-8 \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":40,"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-1826","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\/1826","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\/1826\/revisions"}],"predecessor-version":[{"id":1827,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1826\/revisions\/1827"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1826\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1826"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1826"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1826"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}