{"id":1921,"date":"2021-12-02T19:40:00","date_gmt":"2021-12-03T00:40:00","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-a-answer-key\/"},"modified":"2022-11-02T10:38:26","modified_gmt":"2022-11-02T14:38:26","slug":"midterm-two-version-a-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-a-answer-key\/","title":{"raw":"Midterm 2: Version A Answer Key","rendered":"Midterm 2: Version A Answer Key"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n
    [latex]x+2y=-5[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n[latex]-\\dfrac{5}{2}[\/latex]<\/td>\n<\/tr>\n
    \u22125<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n
    [latex]x-y=-2[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n2<\/td>\n<\/tr>\n
    \u22122<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Bar<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrl}\n&(4x&-&3y&=&13)(2) \\\\\n&(5x&-&2y&=&\\phantom{1}4)(-3) \\\\ \\\\\n&8x&-&6y&=&\\phantom{-}26 \\\\\n+&-15x&+&6y&=&-12 \\\\\n\\hline\n&&&-7x&=&\\phantom{-}14 \\\\ \\\\\n&&&x&=&\\dfrac{14}{-7}\\text{ or }-2\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrcrl}\\\\\n5x&-&2y&=&\\phantom{+1}4 \\\\\n5(-2)&-&2y&=&\\phantom{+1}4 \\\\\n-10&-&2y&=&\\phantom{+1}4 \\\\\n+10&&&&+10 \\\\\n\\hline\n&&-2y&=&\\phantom{+}14 \\\\ \\\\\n&&y&=&\\dfrac{14}{-2}\\text{ or }-7\n\\end{array}\n\\end{array}[\/latex]\n[latex](-2,-7)[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&x&-&2y&=&-5 \\\\\n&(2x&+&y&=&\\phantom{-}5)(2) \\\\ \\\\\n&x&-&2y&=&-5 \\\\\n+&4x&+&2y&=&10 \\\\\n\\hline\n&&&5x&=&5 \\\\\n&&&x&=&1 \\\\ \\\\\n\\therefore &2(1)&+&y&=&\\phantom{-}5 \\\\\n&-2&&&&-2 \\\\\n\\hline\n&&&y&=&\\phantom{-}3\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrrl}\n&(x&+&y&+&2z&=&0)(-2) \\\\ \\\\\n&-2x&-&2y&-&4z&=&0 \\\\\n+&2x&&&+&z&=&1 \\\\\n\\hline\n&&&-2y&-&3z&=&1 \\\\ \\\\\n&&&(-2y&-&3z&=&1)(3) \\\\\n&&&(3y&+&4z&=&0)(2) \\\\ \\\\\n&&&-6y&-&9z&=&3 \\\\\n&&+&6y&+&8z&=&0 \\\\\n\\hline\n&&&&&-z&=&3 \\\\\n&&&&&z&=&-3 \\\\\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrcrl}\n3y&+&4z&=&0 \\\\\n3y&+&4(-3)&=&0 \\\\\n3y&-&12&=&0 \\\\\n&&3y&=&12 \\\\\n&&y&=&4 \\\\ \\\\\n2x&+&z&=&1 \\\\\n2x&+&(-3)&=&1 \\\\\n&&2x&=&4 \\\\\n&&x&=&2 \\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex](2,4,-3)[\/latex]<\/li>\n \t
  5. [latex]28-\\{5x-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+5x^2[\/latex]\n[latex]28-\\{5x-1\\}+5x^2[\/latex]\n[latex]28-5x+1+5x^2[\/latex]\n[latex]5x^2-5x+29[\/latex]<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrl}\n&a&-&3&& \\\\\n\\times &a&-&3&& \\\\\n\\hline\n&a^2&-&3a&& \\\\\n+&&-&3a&+&9 \\\\\n\\hline\n&a^2&-&6a&+&9 \\\\ \\\\\n&a^2&-&6a&+&9 \\\\\n\\times&&&&&4a^2 \\\\\n\\hline\n&4a^4&-&24a^3&+&36a^2 \\\\\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrlrrrr}\n&x^2&+&2x&+&3&&&& \\\\\n\\times&x^2&+&2x&+&3&&&& \\\\\n\\hline\n&x^4&+&2x^3&+&3x^2&&&& \\\\\n&&&2x^3&+&4x^2&+&6x&& \\\\\n+&&&&&3x^2&+&6x&+&9 \\\\\n\\hline\n&x^4&+&4x^3&+&10x^2&+&12x&+&9\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n\"\"<\/li>\n \t
  9. [latex]a(2b+3c)-2(2b+3c)[\/latex]\n[latex](2b+3c)(a-2)[\/latex]<\/li>\n \t
  10. [latex]a^2-5ab+3ab-15b^2[\/latex]\n[latex]a(a-5b)+3b(a-5b)[\/latex]\n[latex](a-5b)(a+3b)[\/latex]<\/li>\n \t
  11. [latex]x^2(x+1)-9(x+1)[\/latex]\n[latex](x^2-9)(x+1)[\/latex]\n[latex](x+3)(x-3)(x+1)[\/latex]<\/li>\n \t
  12. [latex](x)^3-(4y)^3[\/latex]\n[latex](x-4y)(x^2+4xy+16y^2)[\/latex]<\/li>\n \t
  13. [latex]B+S=35\\Rightarrow B=35-S [\/latex]\n[latex]\\begin{array}{ll}\n\\begin{array}{rrrrrrrr}\n&B&-&10&=&2(S&-&10) \\\\\n&35-S&-&10&=&2S&-&20 \\\\\n&25&-&S&=&2S&-&20 \\\\\n+&20&+&S&&S&+&20 \\\\\n\\hline\n&&&45&=&3S&&\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}{rrl}\nS&=&\\dfrac{45}{3}\\text{ or }15 \\\\ \\\\\n\\therefore B&=&35-S \\\\\nB&=&35-15 \\\\\nB&=&20 \\\\\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]D+Q=20\\Rightarrow Q=20-D[\/latex]\n[latex]\\begin{array}{ll}\n\\begin{array}{rrlrr}\n10D&+&25Q&=&275 \\\\\n10D&+&25(20-D)&=&275 \\\\\n10D&+&500-25D&=&275 \\\\\n&-&500&&-500 \\\\\n\\hline\n&&\\phantom{500}-15D&=&-225\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}{rrl}\nD&=&\\dfrac{-225}{-15}\\text{ or }15 \\\\ \\\\\n\\therefore Q&=&20-D \\\\\nQ&=&20-15 \\\\\nQ&=&5 \\\\\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]A+B=50\\Rightarrow A=50-B[\/latex]\n[latex]\\begin{array}{rrrrrrl}\n(3.95A&+&3.70(50&-&A)&=&191.25)(100) \\\\ \\\\\n395A&+&370(50&-&A)&=&19125 \\\\\n395A&+&18500&-&370A&=&19125 \\\\\n&-&18500&&&&-18500 \\\\\n\\hline\n&&&&25A&=&625 \\\\ \\\\\n&&&&A&=&\\dfrac{625}{25}\\text{ or 25 kg} \\\\ \\\\\n&&&&B&=&50-25 \\\\\n&&&&B&=&25 \\text{ kg} \\\\\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n
      [latex]x+2y=-5[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n[latex]-\\dfrac{5}{2}[\/latex]<\/td>\n<\/tr>\n
      \u22125<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
      [latex]x-y=-2[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n2<\/td>\n<\/tr>\n
      \u22122<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Bar<\/li>\n

    2. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrl} &(4x&-&3y&=&13)(2) \\\\ &(5x&-&2y&=&\\phantom{1}4)(-3) \\\\ \\\\ &8x&-&6y&=&\\phantom{-}26 \\\\ +&-15x&+&6y&=&-12 \\\\ \\hline &&&-7x&=&\\phantom{-}14 \\\\ \\\\ &&&x&=&\\dfrac{14}{-7}\\text{ or }-2 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrcrl}\\\\ 5x&-&2y&=&\\phantom{+1}4 \\\\ 5(-2)&-&2y&=&\\phantom{+1}4 \\\\ -10&-&2y&=&\\phantom{+1}4 \\\\ +10&&&&+10 \\\\ \\hline &&-2y&=&\\phantom{+}14 \\\\ \\\\ &&y&=&\\dfrac{14}{-2}\\text{ or }-7 \\end{array} \\end{array}[\/latex]
      \n[latex](-2,-7)[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &x&-&2y&=&-5 \\\\ &(2x&+&y&=&\\phantom{-}5)(2) \\\\ \\\\ &x&-&2y&=&-5 \\\\ +&4x&+&2y&=&10 \\\\ \\hline &&&5x&=&5 \\\\ &&&x&=&1 \\\\ \\\\ \\therefore &2(1)&+&y&=&\\phantom{-}5 \\\\ &-2&&&&-2 \\\\ \\hline &&&y&=&\\phantom{-}3 \\end{array}[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrrl} &(x&+&y&+&2z&=&0)(-2) \\\\ \\\\ &-2x&-&2y&-&4z&=&0 \\\\ +&2x&&&+&z&=&1 \\\\ \\hline &&&-2y&-&3z&=&1 \\\\ \\\\ &&&(-2y&-&3z&=&1)(3) \\\\ &&&(3y&+&4z&=&0)(2) \\\\ \\\\ &&&-6y&-&9z&=&3 \\\\ &&+&6y&+&8z&=&0 \\\\ \\hline &&&&&-z&=&3 \\\\ &&&&&z&=&-3 \\\\ \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrcrl} 3y&+&4z&=&0 \\\\ 3y&+&4(-3)&=&0 \\\\ 3y&-&12&=&0 \\\\ &&3y&=&12 \\\\ &&y&=&4 \\\\ \\\\ 2x&+&z&=&1 \\\\ 2x&+&(-3)&=&1 \\\\ &&2x&=&4 \\\\ &&x&=&2 \\\\ \\end{array} \\end{array}[\/latex]
      \n[latex](2,4,-3)[\/latex]<\/li>\n
    5. [latex]28-\\{5x-\\cancel{\\left[6x-3(5-2x)\\right]^0}1\\}+5x^2[\/latex]
      \n[latex]28-\\{5x-1\\}+5x^2[\/latex]
      \n[latex]28-5x+1+5x^2[\/latex]
      \n[latex]5x^2-5x+29[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrcrl} &a&-&3&& \\\\ \\times &a&-&3&& \\\\ \\hline &a^2&-&3a&& \\\\ +&&-&3a&+&9 \\\\ \\hline &a^2&-&6a&+&9 \\\\ \\\\ &a^2&-&6a&+&9 \\\\ \\times&&&&&4a^2 \\\\ \\hline &4a^4&-&24a^3&+&36a^2 \\\\ \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrlrrrr} &x^2&+&2x&+&3&&&& \\\\ \\times&x^2&+&2x&+&3&&&& \\\\ \\hline &x^4&+&2x^3&+&3x^2&&&& \\\\ &&&2x^3&+&4x^2&+&6x&& \\\\ +&&&&&3x^2&+&6x&+&9 \\\\ \\hline &x^4&+&4x^3&+&10x^2&+&12x&+&9 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n\"\"<\/li>\n
    9. [latex]a(2b+3c)-2(2b+3c)[\/latex]
      \n[latex](2b+3c)(a-2)[\/latex]<\/li>\n
    10. [latex]a^2-5ab+3ab-15b^2[\/latex]
      \n[latex]a(a-5b)+3b(a-5b)[\/latex]
      \n[latex](a-5b)(a+3b)[\/latex]<\/li>\n
    11. [latex]x^2(x+1)-9(x+1)[\/latex]
      \n[latex](x^2-9)(x+1)[\/latex]
      \n[latex](x+3)(x-3)(x+1)[\/latex]<\/li>\n
    12. [latex](x)^3-(4y)^3[\/latex]
      \n[latex](x-4y)(x^2+4xy+16y^2)[\/latex]<\/li>\n
    13. [latex]B+S=35\\Rightarrow B=35-S[\/latex]
      \n[latex]\\begin{array}{ll} \\begin{array}{rrrrrrrr} &B&-&10&=&2(S&-&10) \\\\ &35-S&-&10&=&2S&-&20 \\\\ &25&-&S&=&2S&-&20 \\\\ +&20&+&S&&S&+&20 \\\\ \\hline &&&45&=&3S&& \\end{array} & \\hspace{0.25in} \\begin{array}{rrl} S&=&\\dfrac{45}{3}\\text{ or }15 \\\\ \\\\ \\therefore B&=&35-S \\\\ B&=&35-15 \\\\ B&=&20 \\\\ \\end{array} \\end{array}[\/latex]<\/li>\n
    14. [latex]D+Q=20\\Rightarrow Q=20-D[\/latex]
      \n[latex]\\begin{array}{ll} \\begin{array}{rrlrr} 10D&+&25Q&=&275 \\\\ 10D&+&25(20-D)&=&275 \\\\ 10D&+&500-25D&=&275 \\\\ &-&500&&-500 \\\\ \\hline &&\\phantom{500}-15D&=&-225 \\end{array} & \\hspace{0.25in} \\begin{array}{rrl} D&=&\\dfrac{-225}{-15}\\text{ or }15 \\\\ \\\\ \\therefore Q&=&20-D \\\\ Q&=&20-15 \\\\ Q&=&5 \\\\ \\end{array} \\end{array}[\/latex]<\/li>\n
    15. [latex]A+B=50\\Rightarrow A=50-B[\/latex]
      \n[latex]\\begin{array}{rrrrrrl} (3.95A&+&3.70(50&-&A)&=&191.25)(100) \\\\ \\\\ 395A&+&370(50&-&A)&=&19125 \\\\ 395A&+&18500&-&370A&=&19125 \\\\ &-&18500&&&&-18500 \\\\ \\hline &&&&25A&=&625 \\\\ \\\\ &&&&A&=&\\dfrac{625}{25}\\text{ or 25 kg} \\\\ \\\\ &&&&B&=&50-25 \\\\ &&&&B&=&25 \\text{ kg} \\\\ \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":69,"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-1921","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\/1921","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\/1921\/revisions"}],"predecessor-version":[{"id":1922,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1921\/revisions\/1922"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1921\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1921"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1921"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1921"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}