{"id":1811,"date":"2021-12-02T19:39:32","date_gmt":"2021-12-03T00:39:32","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-b-answer-key\/"},"modified":"2022-11-02T10:37:43","modified_gmt":"2022-11-02T14:37:43","slug":"midterm-one-version-b-answer-key","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/midterm-one-version-b-answer-key\/","title":{"raw":"Midterm 1: Version B Answer Key","rendered":"Midterm 1: Version B Answer Key"},"content":{"raw":"
    \n \t
  1. [latex]-6-\\sqrt{6^2-4(5)(1)}\u00a0[\/latex]\n[latex]\\begin{array}[t]{l}\\\\\n-6-\\sqrt{36-20} \\\\ \\\\\n-6-\\sqrt{16} \\\\ \\\\\n-6-4 \\\\ \\\\\n-10\n\\end{array}[\/latex]<\/li>\n \t
  2. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\n&15x&-&18&=&4[-6&+&3x] \\\\\n&15x&-&18&=&-24&+&12x \\\\\n-&12x&+&18&&+18&-&12x \\\\\n\\hline\n&&&\\dfrac{3x}{3}&=&\\dfrac{-6}{3} && \\\\ \\\\\n&&&x&=&-2 &&\n\\end{array}[\/latex]<\/li>\n \t
  3. [latex]\\left(A=\\dfrac{h}{B\\cdot b}\\right)(b)[\/latex]\n[latex]\\begin{array}[t]{l}\\\\\n\\left(Ab=\\dfrac{h}{B}\\right)\\div A \\\\ \\\\\n\\phantom{A}b=\\dfrac{h}{BA}\n\\end{array}[\/latex]<\/li>\n \t
  4. [latex]\\left(\\dfrac{x+3}{5}-\\dfrac{x}{2}=\\dfrac{5-3x}{10}\\right)(10) [\/latex]\n[latex]\\begin{array}{rrcrcrrrr}\n2(x&+&3)&-&5(x)&=&5&-&3x \\\\\n2x&+&6&-&5x&=&5&-&3x \\\\\n&-&3x&+&6&=&5&-&3x \\\\\n&+&3x&-&6&&-6&+&3x \\\\\n\\hline\n&&&&0&=&-1&&\\\\\n\\end{array}[\/latex]\nNo solution<\/li>\n \t
  5. [latex]y=4[\/latex]\n\"-3,<\/li>\n \t
  6. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n\\text{slope}&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\\n\\dfrac{1}{3}&=&\\dfrac{y-4}{x--1}\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrrrrrlrr}\n&&1(x&+&1)&=&3(y&-&4) \\\\\n&&x&+&1&=&3y&-&12 \\\\\n&&&-&1&&&-&1 \\\\\n\\hline\n&&&&x&=&3y&-&13 \\\\ \\\\\nx&-&3y&+&13&=&0&& \\\\ \\\\\n&&&&y&=&\\dfrac{1}{3}x&+&\\dfrac{13}{3}\n\\end{array}\n\\end{array}[\/latex]<\/li>\n \t
  7. [latex]\\text{1st slope }\\dots\\text{ } m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{5-4}{-3-0}\\Rightarrow -\\dfrac{1}{3}[\/latex]\n[latex]\\text{now }\\dots\\text{ } m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow -\\dfrac{1}{3}\\Rightarrow \\dfrac{y-4}{x-0} [\/latex]\n[latex]\\begin{array}{rrl}\n-1(x)&=&3(y-4) \\\\\n-x&=&3y-12 \\\\ \\\\\nx+3y-12&=&0 \\\\\ny&=&-\\dfrac{1}{3}x+4 \\\\\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]{rrrrrrrrrrr}\n6x&-&12&+&8x&>&15&-&20x&+&7 \\\\\n&+&12&+&20x&&&+&20x&+&15 \\\\\n&&&+&6x&&&&&+&12 \\\\\n\\hline\n&&&&34x&>&34&&&& \\\\\n&&&&x&>&1&&&&\n\\end{array}[\/latex]\n\"x 1\" width=\"300\" height=\"69\"><\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrr}\n-3&\\le &2x&+&3&<&9 \\\\\n-3&&&-&3&&-3 \\\\\n\\hline\n\\dfrac{-6}{2}&\\le &&\\dfrac{2x}{2}&&<&\\dfrac{6}{2} \\\\ \\\\\n-3&\\le &&x&&<&3\n\\end{array}[\/latex]\"-3<\/li>\n \t
  11. [latex](-2<\\dfrac{3x+2}{5}<2)(5)[\/latex]\n
      \n \t
    1. [latex]\\begin{array}{rrrrrrr}\n-10&<&3x&+&2&<&10 \\\\\n-2&&&-&2&&-2 \\\\\n\\hline\n\\dfrac{-12}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{8}{3} \\\\ \\\\\n-4&<&&x&&<&\\dfrac{8}{3}\n\\end{array}[\/latex]\n\"-4<\/li>\n<\/ol>\n<\/li>\n \t
    2. \n\n\n\n\n\n\n
      [latex]5x+2y=10[\/latex]<\/caption>\n
      [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
      2<\/td>\n0<\/td>\n<\/tr>\n
      0<\/td>\n5<\/td>\n<\/tr>\n
      \u22122<\/td>\n10<\/td>\n<\/tr>\n
      4<\/td>\n\u22125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\"Line<\/li>\n \t
    3. [latex]x, x+2 [\/latex]\n[latex]\\begin{array}{rrrrrrrrr}\nx&+&(x&+&2)&=&5x&-&16 \\\\\n&&2x&+&2&=&5x&-&16 \\\\\n&+&-5x&-&2&&-5x&-&2 \\\\\n\\hline\n&&&&\\dfrac{-3x}{-3}&=&\\dfrac{-18}{-3}&& \\\\ \\\\\n&&&&x&=&6&& \\\\ \\\\\n\\end{array}[\/latex]\nnumbers are 6, 8<\/li>\n \t
    4. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrl}\n4x+x&=&40\\text{ cm} \\\\\n5x&=&40\\text{ cm} \\\\\nx&=&\\dfrac{40\\text{ cm}}{5}\\text{ or }8\\text{ cm} \\\\ \\\\\n\\therefore 4x&=&4(8)\\text{ or }32\\text{ cm}\n\\end{array}[\/latex]<\/li>\n \t
    5. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{ll}\n\\begin{array}[t]{rrl}\n&&\\underline{\\text{1st}} \\\\ \\\\\nP&=&\\dfrac{kT}{V} \\\\ \\\\\n&&\\underline{\\text{2nd}} \\\\ \\\\\n&&\\textbf{1st data} \\\\\nP&=&100 \\\\\nk&=&\\text{find 1st} \\\\\nT&=&200 \\\\\nV&=&500 \\\\ \\\\\nP&=&\\dfrac{kT}{V} \\\\ \\\\\n100&=&\\dfrac{k(200)}{500} \\\\ \\\\\nk&=&\\dfrac{\\cancel{100}(500)}{\\cancel{200}2} \\\\ \\\\\nk&=&250\n\\end{array}\n& \\hspace{0.25in}\n\\begin{array}[t]{rrl}\n&&\\textbf{2nd data} \\\\\nP&=&\\text{find 2nd} \\\\\nk&=&250 \\\\\nT&=&100 \\\\\nV&=&500 \\\\ \\\\\nP&=&\\dfrac{kT}{V} \\\\ \\\\\nP&=&\\dfrac{(250)(100)}{500} \\\\ \\\\\nP&=&50\n\\end{array}\n\\end{array}[\/latex]<\/li>\n<\/ol>","rendered":"
        \n
      1. [latex]-6-\\sqrt{6^2-4(5)(1)}\u00a0[\/latex]
        \n[latex]\\begin{array}[t]{l}\\\\ -6-\\sqrt{36-20} \\\\ \\\\ -6-\\sqrt{16} \\\\ \\\\ -6-4 \\\\ \\\\ -10 \\end{array}[\/latex]<\/li>\n
      2. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrrrrrrr} &15x&-&18&=&4[-6&+&3x] \\\\ &15x&-&18&=&-24&+&12x \\\\ -&12x&+&18&&+18&-&12x \\\\ \\hline &&&\\dfrac{3x}{3}&=&\\dfrac{-6}{3} && \\\\ \\\\ &&&x&=&-2 && \\end{array}[\/latex]<\/li>\n
      3. [latex]\\left(A=\\dfrac{h}{B\\cdot b}\\right)(b)[\/latex]
        \n[latex]\\begin{array}[t]{l}\\\\ \\left(Ab=\\dfrac{h}{B}\\right)\\div A \\\\ \\\\ \\phantom{A}b=\\dfrac{h}{BA} \\end{array}[\/latex]<\/li>\n
      4. [latex]\\left(\\dfrac{x+3}{5}-\\dfrac{x}{2}=\\dfrac{5-3x}{10}\\right)(10)[\/latex]
        \n[latex]\\begin{array}{rrcrcrrrr} 2(x&+&3)&-&5(x)&=&5&-&3x \\\\ 2x&+&6&-&5x&=&5&-&3x \\\\ &-&3x&+&6&=&5&-&3x \\\\ &+&3x&-&6&&-6&+&3x \\\\ \\hline &&&&0&=&-1&&\\\\ \\end{array}[\/latex]
        \nNo solution<\/li>\n
      5. [latex]y=4[\/latex]
        \n\"-3,<\/li>\n
      6. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} \\text{slope}&=&\\dfrac{\\Delta y}{\\Delta x} \\\\ \\\\ \\dfrac{1}{3}&=&\\dfrac{y-4}{x--1} \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrrrrrlrr} &&1(x&+&1)&=&3(y&-&4) \\\\ &&x&+&1&=&3y&-&12 \\\\ &&&-&1&&&-&1 \\\\ \\hline &&&&x&=&3y&-&13 \\\\ \\\\ x&-&3y&+&13&=&0&& \\\\ \\\\ &&&&y&=&\\dfrac{1}{3}x&+&\\dfrac{13}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
      7. [latex]\\text{1st slope }\\dots\\text{ } m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow \\dfrac{5-4}{-3-0}\\Rightarrow -\\dfrac{1}{3}[\/latex]
        \n[latex]\\text{now }\\dots\\text{ } m=\\dfrac{\\Delta y}{\\Delta x}\\Rightarrow -\\dfrac{1}{3}\\Rightarrow \\dfrac{y-4}{x-0}[\/latex]
        \n[latex]\\begin{array}{rrl} -1(x)&=&3(y-4) \\\\ -x&=&3y-12 \\\\ \\\\ x+3y-12&=&0 \\\\ y&=&-\\dfrac{1}{3}x+4 \\\\ \\end{array}[\/latex]<\/li>\n
      8. [latex]\\phantom{a}[\/latex]
        \n\"Line<\/li>\n
      9. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrrrrrrrrrr} 6x&-&12&+&8x&>&15&-&20x&+&7 \\\\ &+&12&+&20x&&&+&20x&+&15 \\\\ &&&+&6x&&&&&+&12 \\\\ \\hline &&&&34x&>&34&&&& \\\\ &&&&x&>&1&&&& \\end{array}[\/latex]
        \n\"image\" 1″ width=”300″ height=”69″><\/li>\n
      10. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrrcrrr} -3&\\le &2x&+&3&<&9 \\\\ -3&&&-&3&&-3 \\\\ \\hline \\dfrac{-6}{2}&\\le &&\\dfrac{2x}{2}&&<&\\dfrac{6}{2} \\\\ \\\\ -3&\\le &&x&&<&3 \\end{array}[\/latex]\"-3<\/li>\n
      11. [latex](-2<\\dfrac{3x+2}{5}<2)(5)[\/latex]\n\n\n
          \n
        1. [latex]\\begin{array}{rrrrrrr} -10&<&3x&+&2&<&10 \\\\ -2&&&-&2&&-2 \\\\ \\hline \\dfrac{-12}{3}&<&&\\dfrac{3x}{3}&&<&\\dfrac{8}{3} \\\\ \\\\ -4&<&&x&&<&\\dfrac{8}{3} \\end{array}[\/latex]\n\"-4<\/li>\n<\/ol>\n<\/li>\n
        2. \n\n\n\n\n\n\n\n
          [latex]5x+2y=10[\/latex]<\/caption>\n
          [latex]x[\/latex]<\/th>\n[latex]y[\/latex]<\/th>\n<\/tr>\n
          2<\/td>\n0<\/td>\n<\/tr>\n
          0<\/td>\n5<\/td>\n<\/tr>\n
          \u22122<\/td>\n10<\/td>\n<\/tr>\n
          4<\/td>\n\u22125<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

          \"Line<\/li>\n

        3. [latex]x, x+2[\/latex]
          \n[latex]\\begin{array}{rrrrrrrrr} x&+&(x&+&2)&=&5x&-&16 \\\\ &&2x&+&2&=&5x&-&16 \\\\ &+&-5x&-&2&&-5x&-&2 \\\\ \\hline &&&&\\dfrac{-3x}{-3}&=&\\dfrac{-18}{-3}&& \\\\ \\\\ &&&&x&=&6&& \\\\ \\\\ \\end{array}[\/latex]
          \nnumbers are 6, 8<\/li>\n
        4. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{rrl} 4x+x&=&40\\text{ cm} \\\\ 5x&=&40\\text{ cm} \\\\ x&=&\\dfrac{40\\text{ cm}}{5}\\text{ or }8\\text{ cm} \\\\ \\\\ \\therefore 4x&=&4(8)\\text{ or }32\\text{ cm} \\end{array}[\/latex]<\/li>\n
        5. [latex]\\phantom{a}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\underline{\\text{1st}} \\\\ \\\\ P&=&\\dfrac{kT}{V} \\\\ \\\\ &&\\underline{\\text{2nd}} \\\\ \\\\ &&\\textbf{1st data} \\\\ P&=&100 \\\\ k&=&\\text{find 1st} \\\\ T&=&200 \\\\ V&=&500 \\\\ \\\\ P&=&\\dfrac{kT}{V} \\\\ \\\\ 100&=&\\dfrac{k(200)}{500} \\\\ \\\\ k&=&\\dfrac{\\cancel{100}(500)}{\\cancel{200}2} \\\\ \\\\ k&=&250 \\end{array} & \\hspace{0.25in} \\begin{array}[t]{rrl} &&\\textbf{2nd data} \\\\ P&=&\\text{find 2nd} \\\\ k&=&250 \\\\ T&=&100 \\\\ V&=&500 \\\\ \\\\ P&=&\\dfrac{kT}{V} \\\\ \\\\ P&=&\\dfrac{(250)(100)}{500} \\\\ \\\\ P&=&50 \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":38,"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-1811","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\/1811","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\/1811\/revisions"}],"predecessor-version":[{"id":1812,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1811\/revisions\/1812"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1811\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1811"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1811"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1811"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1811"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}