{"id":1928,"date":"2021-12-02T19:40:02","date_gmt":"2021-12-03T00:40:02","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-c-answer-key\/"},"modified":"2022-11-02T10:38:29","modified_gmt":"2022-11-02T14:38:29","slug":"midterm-two-version-c-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-two-version-c-answer-key\/","title":{"raw":"Midterm 2: Version C Answer Key","rendered":"Midterm 2: Version C Answer Key"},"content":{"raw":"
    \n \t
  1. \n\n\n\n\n\n
    [latex]2x-y-2=0[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n\u22122<\/td>\n<\/tr>\n
    1<\/td>\n0<\/td>\n<\/tr>\n
    2<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n
    [latex]2x+3y+6=0[\/latex]<\/caption>\n
    [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
    0<\/td>\n\u22122<\/td>\n<\/tr>\n
    \u22123<\/td>\n0<\/td>\n<\/tr>\n
    \u22126<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Graph<\/li>\n \t
  2. [latex]x+y=2\\Rightarrow x=2-y[\/latex]\n[latex]\\begin{array}{rrrrrrl}\n3(2&-&y)&-&4y&=&13 \\\\\n6&-&3y&-&4y&=&13 \\\\\n-6&&&&&&-6 \\\\\n\\hline\n&&&&-7y&=&\\phantom{-}7 \\\\\n&&&&y&=&-1 \\\\ \\\\\n&&&&x&=&2--1 \\\\\n&&&&x&=&3\n\\end{array}[\/latex]\n[latex](3,-1)[\/latex]<\/li>\n \t
  3. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrr}\n&4x&-&3y&=&6 \\\\\n+&4x&+&3y&=&2 \\\\\n\\hline\n&&&8x&=&8 \\\\\n&&&x&=&1 \\\\ \\\\\n&3y&+&4(1)&=&2 \\\\\n&&-&4&&-4 \\\\\n\\hline\n&&&3y&=&-2 \\\\ \\\\\n&&&y&=&-\\dfrac{2}{3}\n\\end{array}[\/latex]\n[latex]\\left(1,-\\dfrac{2}{3}\\right)[\/latex]<\/li>\n \t
  4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrrrrrrl}\n\\left[1\\right]&(x&+&y&+&z&=&\\phantom{-}6)(-2) \\\\\n\\left[2\\right]&&&(-2x&+&z&=&-3)(-1) \\\\ \\\\\n\\left[1\\right]&-2x&-&2y&-&2z&=&-12 \\\\\n+&&&2y&+&4z&=&\\phantom{-}10 \\\\\n\\hline\n&&&-2x&+&2z&=&-2 \\\\\n+&&\\left[2\\right]&2x&-&z&=&\\phantom{-}3 \\\\\n\\hline\n&&&&&z&=&1 \\\\\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrr}\n2y&+&4z&=&10 \\\\\n2y&+&4(1)&=&10 \\\\\n&-&4&&-4 \\\\\n\\hline\n&&2y&=&6 \\\\\n&&y&=&3 \\\\ \\\\\n-2x&+&z&=&-3 \\\\\n-2x&+&1&=&-3 \\\\\n&-&1&&-1 \\\\\n\\hline\n&&-2x&=&-4 \\\\\n&&x&=&2 \\\\\n\\end{array}\n\\end{array}[\/latex]\n[latex](2,3,1)[\/latex]<\/li>\n \t
  5. [latex]36+\\{\\cancel{-2x-\\left[6x-3(5-2x)\\right]\\}^0}1+6x^3[\/latex]\n[latex]36+1+6x^3\\Rightarrow 6x^3+37[\/latex]<\/li>\n \t
  6. [latex]6a^2b(a^2-9)[\/latex]\n[latex]6a^4b-54a^2b[\/latex]<\/li>\n \t
  7. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrlrrrr}\n&x^2&+&3x&+&5&&&& \\\\\n\\times &x^2&+&3x&+&5&&&& \\\\\n\\hline\n&x^4&+&3x^3&+&5x^2&&&& \\\\\n&&&3x^3&+&9x^2&+&15x&& \\\\\n+&&&&&5x^2&+&15x&+&25 \\\\\n\\hline\n&x^4&+&6x^3&+&19x^2&+&30x&+&25\n\\end{array}[\/latex]<\/li>\n \t
  8. [latex]\\phantom{a}[\/latex]\n\"\"<\/li>\n \t
  9. [latex]x^2-x+18x-18[\/latex]\n[latex]x(x-1)+18(x-1)[\/latex]\n[latex](x-1)(x+18)[\/latex]<\/li>\n \t
  10. [latex]2(a^2-2ab-15b^2)[\/latex]\n[latex]2(a^2-5ab+3ab-15b^2)[\/latex]\n[latex]2\\left[a(a-5b)+3b(a-5b)\\right][\/latex]\n[latex]2(a-5b)(a+3b)[\/latex]<\/li>\n \t
  11. [latex](2x)^3-y^3[\/latex]\n[latex](2x-y)(4x^2+2xy+y^2)[\/latex]<\/li>\n \t
  12. [latex](4y^2-x^2)(4y^2+x^2)[\/latex]\n[latex](2y-x)(2y+x)(4y^2+x^2)[\/latex]<\/li>\n \t
  13. [latex]B+S=30\\Rightarrow B=30-S[\/latex]\n[latex]\\begin{array}{rrrrrrr}\nB&-&10&=&4(S&-&10) \\\\\n30-S&-&10&=&4S&-&40 \\\\\n+S&+&40&&+S&+&40 \\\\\n\\hline\n&&60&=&5S&& \\\\ \\\\\n&&S&=&\\dfrac{60}{5}&=&12 \\\\ \\\\\n&&\\therefore B&=&30&-&S \\\\\n&&B&=&30&-&12 \\\\\n&&B&=&18&&\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrl}\n&(D&+&N&=&\\phantom{1}18)(-1) \\\\\n&(10D&+&5N&=&120)(\\div 5) \\\\ \\\\\n&-D&-&N&=&-18 \\\\\n+&2D&+&N&=&\\phantom{-}24 \\\\\n\\hline\n&&&D&=&6 \\\\ \\\\\n\\therefore &D&+&N&=&18 \\\\\n&6&+&N&=&18 \\\\\n&-6&&&&-6 \\\\\n\\hline\n&&&N&=&12\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\text{if }x=5\\%, \\text{ then }10-x=30\\% [\/latex]\n[latex]\\begin{array}{rrrrcrl}\n5x&+&30(10&-&x)&=&25(10) \\\\\n5x&+&300&-&30x&=&\\phantom{-}250 \\\\\n&-&300&&&&-300 \\\\\n\\hline\n&&&&-25x&=&-50 \\\\ \\\\\n&&&&x&=&\\dfrac{-50}{-25}\\text{ or 2 L of 5%} \\\\ \\\\\n&&10&-&x&=&\\text{8 L of 30%}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
      \n
    1. \n\n\n\n\n\n\n
      [latex]2x-y-2=0[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n\u22122<\/td>\n<\/tr>\n
      1<\/td>\n0<\/td>\n<\/tr>\n
      2<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n\n\n\n
      [latex]2x+3y+6=0[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      0<\/td>\n\u22122<\/td>\n<\/tr>\n
      \u22123<\/td>\n0<\/td>\n<\/tr>\n
      \u22126<\/td>\n2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \"Graph<\/li>\n

    2. [latex]x+y=2\\Rightarrow x=2-y[\/latex]
      \n[latex]\\begin{array}{rrrrrrl} 3(2&-&y)&-&4y&=&13 \\\\ 6&-&3y&-&4y&=&13 \\\\ -6&&&&&&-6 \\\\ \\hline &&&&-7y&=&\\phantom{-}7 \\\\ &&&&y&=&-1 \\\\ \\\\ &&&&x&=&2--1 \\\\ &&&&x&=&3 \\end{array}[\/latex]
      \n[latex](3,-1)[\/latex]<\/li>\n
    3. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &4x&-&3y&=&6 \\\\ +&4x&+&3y&=&2 \\\\ \\hline &&&8x&=&8 \\\\ &&&x&=&1 \\\\ \\\\ &3y&+&4(1)&=&2 \\\\ &&-&4&&-4 \\\\ \\hline &&&3y&=&-2 \\\\ \\\\ &&&y&=&-\\dfrac{2}{3} \\end{array}[\/latex]
      \n[latex]\\left(1,-\\dfrac{2}{3}\\right)[\/latex]<\/li>\n
    4. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrrrrrrl} \\left[1\\right]&(x&+&y&+&z&=&\\phantom{-}6)(-2) \\\\ \\left[2\\right]&&&(-2x&+&z&=&-3)(-1) \\\\ \\\\ \\left[1\\right]&-2x&-&2y&-&2z&=&-12 \\\\ +&&&2y&+&4z&=&\\phantom{-}10 \\\\ \\hline &&&-2x&+&2z&=&-2 \\\\ +&&\\left[2\\right]&2x&-&z&=&\\phantom{-}3 \\\\ \\hline &&&&&z&=&1 \\\\ \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrr} 2y&+&4z&=&10 \\\\ 2y&+&4(1)&=&10 \\\\ &-&4&&-4 \\\\ \\hline &&2y&=&6 \\\\ &&y&=&3 \\\\ \\\\ -2x&+&z&=&-3 \\\\ -2x&+&1&=&-3 \\\\ &-&1&&-1 \\\\ \\hline &&-2x&=&-4 \\\\ &&x&=&2 \\\\ \\end{array} \\end{array}[\/latex]
      \n[latex](2,3,1)[\/latex]<\/li>\n
    5. [latex]36+\\{\\cancel{-2x-\\left[6x-3(5-2x)\\right]\\}^0}1+6x^3[\/latex]
      \n[latex]36+1+6x^3\\Rightarrow 6x^3+37[\/latex]<\/li>\n
    6. [latex]6a^2b(a^2-9)[\/latex]
      \n[latex]6a^4b-54a^2b[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrlrrrr} &x^2&+&3x&+&5&&&& \\\\ \\times &x^2&+&3x&+&5&&&& \\\\ \\hline &x^4&+&3x^3&+&5x^2&&&& \\\\ &&&3x^3&+&9x^2&+&15x&& \\\\ +&&&&&5x^2&+&15x&+&25 \\\\ \\hline &x^4&+&6x^3&+&19x^2&+&30x&+&25 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n\"\"<\/li>\n
    9. [latex]x^2-x+18x-18[\/latex]
      \n[latex]x(x-1)+18(x-1)[\/latex]
      \n[latex](x-1)(x+18)[\/latex]<\/li>\n
    10. [latex]2(a^2-2ab-15b^2)[\/latex]
      \n[latex]2(a^2-5ab+3ab-15b^2)[\/latex]
      \n[latex]2\\left[a(a-5b)+3b(a-5b)\\right][\/latex]
      \n[latex]2(a-5b)(a+3b)[\/latex]<\/li>\n
    11. [latex](2x)^3-y^3[\/latex]
      \n[latex](2x-y)(4x^2+2xy+y^2)[\/latex]<\/li>\n
    12. [latex](4y^2-x^2)(4y^2+x^2)[\/latex]
      \n[latex](2y-x)(2y+x)(4y^2+x^2)[\/latex]<\/li>\n
    13. [latex]B+S=30\\Rightarrow B=30-S[\/latex]
      \n[latex]\\begin{array}{rrrrrrr} B&-&10&=&4(S&-&10) \\\\ 30-S&-&10&=&4S&-&40 \\\\ +S&+&40&&+S&+&40 \\\\ \\hline &&60&=&5S&& \\\\ \\\\ &&S&=&\\dfrac{60}{5}&=&12 \\\\ \\\\ &&\\therefore B&=&30&-&S \\\\ &&B&=&30&-&12 \\\\ &&B&=&18&& \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrl} &(D&+&N&=&\\phantom{1}18)(-1) \\\\ &(10D&+&5N&=&120)(\\div 5) \\\\ \\\\ &-D&-&N&=&-18 \\\\ +&2D&+&N&=&\\phantom{-}24 \\\\ \\hline &&&D&=&6 \\\\ \\\\ \\therefore &D&+&N&=&18 \\\\ &6&+&N&=&18 \\\\ &-6&&&&-6 \\\\ \\hline &&&N&=&12 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\text{if }x=5\\%, \\text{ then }10-x=30\\%[\/latex]
      \n[latex]\\begin{array}{rrrrcrl} 5x&+&30(10&-&x)&=&25(10) \\\\ 5x&+&300&-&30x&=&\\phantom{-}250 \\\\ &-&300&&&&-300 \\\\ \\hline &&&&-25x&=&-50 \\\\ \\\\ &&&&x&=&\\dfrac{-50}{-25}\\text{ or 2 L of 5%} \\\\ \\\\ &&10&-&x&=&\\text{8 L of 30%} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":71,"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-1928","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\/1928","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\/1928\/revisions"}],"predecessor-version":[{"id":1929,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1928\/revisions\/1929"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1928\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1928"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1928"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1928"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1928"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}