{"id":1785,"date":"2021-12-02T19:39:26","date_gmt":"2021-12-03T00:39:26","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-4-5\/"},"modified":"2022-11-02T10:37:35","modified_gmt":"2022-11-02T14:37:35","slug":"answer-key-4-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-4-5\/","title":{"raw":"Answer Key 4.5","rendered":"Answer Key 4.5"},"content":{"raw":"
    \n \t
  1. [latex]L=2W-3 \\text{ and } P=2L+2W \\Rightarrow 54=2(2W-3)+2W[\/latex]<\/li>\n \t
  2. [latex]L=2W-8 \\text{ and } P=2L+2W \\Rightarrow 64=2(2W-8)+2W[\/latex]<\/li>\n \t
  3. [latex]L=2W+4 \\text{ and } P=2L+2W \\Rightarrow 32=2(2W+4)+2W[\/latex]<\/li>\n \t
  4. [latex]A_1=2A_2, A_1=10^{\\circ}+A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow[\/latex]\n[latex]A_1+\\dfrac{A_1}{2}+A_1- 10^{\\circ}=180^{\\circ}[\/latex]<\/li>\n \t
  5. [latex]A_1=\\dfrac{1}{2}A_2, A_1=20^{\\circ}+A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow[\/latex]\n[latex]A_1+2A_1+A_1-20^{\\circ}=180^{\\circ}[\/latex]<\/li>\n \t
  6. [latex]A_1+A_2=\\dfrac{1}{2}A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow[\/latex]\n[latex]\\dfrac{3}{2}A_3=180^{\\circ}\\hspace{0.34in} A_1 \\text{ and } A_2?[\/latex]<\/li>\n \t
  7. [latex]x_1+x_2=140, x_1=5x_2 \\Rightarrow 5x_2+x_2=140[\/latex]<\/li>\n \t
  8. [latex]x_1+x_2=48, x_2=5+x_1 \\Rightarrow x_1+5+x_1=48[\/latex]<\/li>\n \t
  9. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrrrr}\nA_2&=&A_1&&&&&&&&&& \\\\\nA_3&=&A_1&+&12&&&&&&&& \\\\ \\\\\nA_1&+&A_2&+&A_3&&&=&180&&&& \\\\\nA_1&+&A_1&+&A_1&+&12&=&180&&&& \\\\\n&&&&&-&12&&-12&&&& \\\\\n\\hline\n&&&&&&3A_1&=&168&&&& \\\\ \\\\\n&&&&&&A_1&=&\\dfrac{168}{3}&=&56&& \\\\\nA_1&=&56^{\\circ}&&&&&&&&&& \\\\\nA_2&=&56^{\\circ}&&&&&&&&&& \\\\\nA_3&=&56^{\\circ}&+&12^{\\circ}&=&68^{\\circ}&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  10. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrrrr}\nA_1&=&A_2&&&&&&&& \\\\\nA_3&=&A_1&-&12&&&&&& \\\\ \\\\\nA_1&+&A_2&+&A_3&&&=&180&& \\\\\nA_1&+&A_1&+&A_1&-&12&=&180&& \\\\\n&&&&&+&12&&+12&& \\\\\n\\hline\n&&&&&&3A_1&=&192&& \\\\ \\\\\n&&&&&&A_1&=&\\dfrac{192}{3}&=&64 \\\\\nA_1&=&64^{\\circ}&&&&&&&& \\\\\nA_2&=&64^{\\circ}&&&&&&&& \\\\\nA_3&=&64^{\\circ}&-&12^{\\circ}&=&52^{\\circ}&&&&\n\\end{array}[\/latex]<\/li>\n \t
  11. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlrrrrrrrr}\nA_1&=&A_2&&&&&&&& \\\\\nA_3&=&3A_1&&&&&&&& \\\\ \\\\\nA_1&+&A_2&+&A_3&=&180&&&& \\\\\nA_1&+&A_1&+&3A_1&=&180&&&& \\\\\n&&&&5A_1&=&180&&&& \\\\ \\\\\n&&&&A_1&=&\\dfrac{180}{5}&=&36&& \\\\\nA_1&=&36^{\\circ}&&&&&&&& \\\\\nA_2&=&36^{\\circ}&&&&&&&& \\\\\nA_3&=&3(36^{\\circ})&=&108^{\\circ}&&&&&&\n\\end{array}[\/latex]<\/li>\n \t
  12. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrcrrrrrrr}\nA_2&=&2A_1&&&&&&&& \\\\\nA_3&=&A_1&+&20&&&&&& \\\\ \\\\\nA_1&+&A_2&+&A_3&&&=&180&& \\\\\nA_1&+&2A_1&+&A_1&+&20&=&180&& \\\\\n&&&&&-&20&=&-20&& \\\\\n\\hline\n&&&&&&4A_1&=&160&& \\\\ \\\\\n&&&&&&A_1&=&\\dfrac{160}{4}&=&40 \\\\\nA_1&=&40^{\\circ}&&&&&&&& \\\\\nA_2&=&2(40^{\\circ})&=&80^{\\circ}&&&&&& \\\\\nA_3&=&20^{\\circ}&+&40^{\\circ}&=&60^{\\circ}&&&&\n\\end{array}[\/latex]<\/li>\n \t
  13. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlllrr}\n^{\\text{1}}L&=&W&+&15&& \\\\ \\\\\n^{\\text{2}}P&=&2L&+&2W&& \\\\\n150&=&2(W&+&15)&+&2W \\\\\n150&=&2W&+&30&+&2W \\\\\n-30&&&-&30&& \\\\\n\\hline\n120&=&4W&&&& \\\\ \\\\\nW&=&\\dfrac{120}{4}&=&30\\text{ cm}&& \\\\ \\\\\n^{\\text{3}}L&=&30&+&15&& \\\\\nL&=&45\\text{ cm}&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  14. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlllrr}\n^{\\text{1}}L&=&W&+&40&& \\\\ \\\\\n^{\\text{2}}P&=&2L&+&2W&& \\\\\n304&=&2(W&+&40)&+&2W \\\\\n304&=&2W&+&80&+&2W \\\\\n-80&&&-&80&& \\\\\n\\hline\n224&=&4W&&&& \\\\ \\\\\nW&=&\\dfrac{224}{4}&=&56\\text{ cm}&& \\\\ \\\\\n^{\\text{3}}L&=&56&+&40&& \\\\\nL&=&96\\text{ cm}&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  15. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlllrr}\n^{\\text{1}}W&=&L&-&22&& \\\\ \\\\\n^{\\text{2}}P&=&2L&+&2W&& \\\\\n152&=&2L&+&2(L&-&22) \\\\\n152&=&2L&+&2L&-&44 \\\\\n+44&&&&&+&44 \\\\\n\\hline\n196&=&4L&&&& \\\\ \\\\\nL&=&\\dfrac{196}{4}&=&49\\text{ m}&& \\\\ \\\\\n^{\\text{3}}W&=&49&-&22&& \\\\\nL&=&27\\text{ m}&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  16. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrlllrr}\n^{\\text{1}}W&=&L&-&26&& \\\\ \\\\\n^{\\text{2}}P&=&2L&+&2W&& \\\\\n280&=&2L&+&2(L&-&26) \\\\\n280&=&2L&+&2L&-&52 \\\\\n+52&&&&&+&52 \\\\\n\\hline\n332&=&4L&&&& \\\\ \\\\\nL&=&\\dfrac{332}{4}&=&83\\text{ m}&& \\\\ \\\\\n^{\\text{3}}W&=&83&-&26&& \\\\\nL&=&57\\text{ m}&&&& \\\\\n\\end{array}[\/latex]<\/li>\n \t
  17. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrr}\nx&+&2x&=&12&&& \\\\\n&&3x&=&12&&& \\\\ \\\\\n&&x&=&\\dfrac{12}{3}&=&4\\text{ cm}& \\\\ \\\\\n&\\therefore &2x&=&2(4)&=&8\\text{ cm}& \\\\ \\\\\n\\end{array}\\\\ \\text{Pieces are 4 cm and 8 cm}[\/latex]\"\"<\/li>\n \t
  18. [latex]\\phantom{a}[\/latex]\n[latex]\\begin{array}[t]{rrrrrrrrcrr}\nx&+&x&+&2&=&30&&&& \\\\\n&&&-&2&&-2&&&& \\\\\n\\hline\n&&&&2x&=&28&&&& \\\\ \\\\\n&&&&x&=&\\dfrac{28}{2}&=&14\\text{ m}&& \\\\ \\\\\n&\\therefore &x&+&2&=&14&+&2&=&16 \\text{ m}\\\\ \\\\\n\\end{array}\\\\ \\text{Pieces are 14 m and 16 m}[\/latex]\"\"<\/li>\n<\/ol>","rendered":"
      \n
    1. [latex]L=2W-3 \\text{ and } P=2L+2W \\Rightarrow 54=2(2W-3)+2W[\/latex]<\/li>\n
    2. [latex]L=2W-8 \\text{ and } P=2L+2W \\Rightarrow 64=2(2W-8)+2W[\/latex]<\/li>\n
    3. [latex]L=2W+4 \\text{ and } P=2L+2W \\Rightarrow 32=2(2W+4)+2W[\/latex]<\/li>\n
    4. [latex]A_1=2A_2, A_1=10^{\\circ}+A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow[\/latex]
      \n[latex]A_1+\\dfrac{A_1}{2}+A_1- 10^{\\circ}=180^{\\circ}[\/latex]<\/li>\n
    5. [latex]A_1=\\dfrac{1}{2}A_2, A_1=20^{\\circ}+A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow[\/latex]
      \n[latex]A_1+2A_1+A_1-20^{\\circ}=180^{\\circ}[\/latex]<\/li>\n
    6. [latex]A_1+A_2=\\dfrac{1}{2}A_3, A_1+A_2+A_3=180^{\\circ} \\Rightarrow[\/latex]
      \n[latex]\\dfrac{3}{2}A_3=180^{\\circ}\\hspace{0.34in} A_1 \\text{ and } A_2?[\/latex]<\/li>\n
    7. [latex]x_1+x_2=140, x_1=5x_2 \\Rightarrow 5x_2+x_2=140[\/latex]<\/li>\n
    8. [latex]x_1+x_2=48, x_2=5+x_1 \\Rightarrow x_1+5+x_1=48[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrrrr} A_2&=&A_1&&&&&&&&&& \\\\ A_3&=&A_1&+&12&&&&&&&& \\\\ \\\\ A_1&+&A_2&+&A_3&&&=&180&&&& \\\\ A_1&+&A_1&+&A_1&+&12&=&180&&&& \\\\ &&&&&-&12&&-12&&&& \\\\ \\hline &&&&&&3A_1&=&168&&&& \\\\ \\\\ &&&&&&A_1&=&\\dfrac{168}{3}&=&56&& \\\\ A_1&=&56^{\\circ}&&&&&&&&&& \\\\ A_2&=&56^{\\circ}&&&&&&&&&& \\\\ A_3&=&56^{\\circ}&+&12^{\\circ}&=&68^{\\circ}&&&&&& \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrr} A_1&=&A_2&&&&&&&& \\\\ A_3&=&A_1&-&12&&&&&& \\\\ \\\\ A_1&+&A_2&+&A_3&&&=&180&& \\\\ A_1&+&A_1&+&A_1&-&12&=&180&& \\\\ &&&&&+&12&&+12&& \\\\ \\hline &&&&&&3A_1&=&192&& \\\\ \\\\ &&&&&&A_1&=&\\dfrac{192}{3}&=&64 \\\\ A_1&=&64^{\\circ}&&&&&&&& \\\\ A_2&=&64^{\\circ}&&&&&&&& \\\\ A_3&=&64^{\\circ}&-&12^{\\circ}&=&52^{\\circ}&&&& \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlrrrrrrrr} A_1&=&A_2&&&&&&&& \\\\ A_3&=&3A_1&&&&&&&& \\\\ \\\\ A_1&+&A_2&+&A_3&=&180&&&& \\\\ A_1&+&A_1&+&3A_1&=&180&&&& \\\\ &&&&5A_1&=&180&&&& \\\\ \\\\ &&&&A_1&=&\\dfrac{180}{5}&=&36&& \\\\ A_1&=&36^{\\circ}&&&&&&&& \\\\ A_2&=&36^{\\circ}&&&&&&&& \\\\ A_3&=&3(36^{\\circ})&=&108^{\\circ}&&&&&& \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrcrrrrrrr} A_2&=&2A_1&&&&&&&& \\\\ A_3&=&A_1&+&20&&&&&& \\\\ \\\\ A_1&+&A_2&+&A_3&&&=&180&& \\\\ A_1&+&2A_1&+&A_1&+&20&=&180&& \\\\ &&&&&-&20&=&-20&& \\\\ \\hline &&&&&&4A_1&=&160&& \\\\ \\\\ &&&&&&A_1&=&\\dfrac{160}{4}&=&40 \\\\ A_1&=&40^{\\circ}&&&&&&&& \\\\ A_2&=&2(40^{\\circ})&=&80^{\\circ}&&&&&& \\\\ A_3&=&20^{\\circ}&+&40^{\\circ}&=&60^{\\circ}&&&& \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlllrr} ^{\\text{1}}L&=&W&+&15&& \\\\ \\\\ ^{\\text{2}}P&=&2L&+&2W&& \\\\ 150&=&2(W&+&15)&+&2W \\\\ 150&=&2W&+&30&+&2W \\\\ -30&&&-&30&& \\\\ \\hline 120&=&4W&&&& \\\\ \\\\ W&=&\\dfrac{120}{4}&=&30\\text{ cm}&& \\\\ \\\\ ^{\\text{3}}L&=&30&+&15&& \\\\ L&=&45\\text{ cm}&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlllrr} ^{\\text{1}}L&=&W&+&40&& \\\\ \\\\ ^{\\text{2}}P&=&2L&+&2W&& \\\\ 304&=&2(W&+&40)&+&2W \\\\ 304&=&2W&+&80&+&2W \\\\ -80&&&-&80&& \\\\ \\hline 224&=&4W&&&& \\\\ \\\\ W&=&\\dfrac{224}{4}&=&56\\text{ cm}&& \\\\ \\\\ ^{\\text{3}}L&=&56&+&40&& \\\\ L&=&96\\text{ cm}&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlllrr} ^{\\text{1}}W&=&L&-&22&& \\\\ \\\\ ^{\\text{2}}P&=&2L&+&2W&& \\\\ 152&=&2L&+&2(L&-&22) \\\\ 152&=&2L&+&2L&-&44 \\\\ +44&&&&&+&44 \\\\ \\hline 196&=&4L&&&& \\\\ \\\\ L&=&\\dfrac{196}{4}&=&49\\text{ m}&& \\\\ \\\\ ^{\\text{3}}W&=&49&-&22&& \\\\ L&=&27\\text{ m}&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrlllrr} ^{\\text{1}}W&=&L&-&26&& \\\\ \\\\ ^{\\text{2}}P&=&2L&+&2W&& \\\\ 280&=&2L&+&2(L&-&26) \\\\ 280&=&2L&+&2L&-&52 \\\\ +52&&&&&+&52 \\\\ \\hline 332&=&4L&&&& \\\\ \\\\ L&=&\\dfrac{332}{4}&=&83\\text{ m}&& \\\\ \\\\ ^{\\text{3}}W&=&83&-&26&& \\\\ L&=&57\\text{ m}&&&& \\\\ \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} x&+&2x&=&12&&& \\\\ &&3x&=&12&&& \\\\ \\\\ &&x&=&\\dfrac{12}{3}&=&4\\text{ cm}& \\\\ \\\\ &\\therefore &2x&=&2(4)&=&8\\text{ cm}& \\\\ \\\\ \\end{array}\\\\ \\text{Pieces are 4 cm and 8 cm}[\/latex]\"\"<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrcrr} x&+&x&+&2&=&30&&&& \\\\ &&&-&2&&-2&&&& \\\\ \\hline &&&&2x&=&28&&&& \\\\ \\\\ &&&&x&=&\\dfrac{28}{2}&=&14\\text{ m}&& \\\\ \\\\ &\\therefore &x&+&2&=&14&+&2&=&16 \\text{ m}\\\\ \\\\ \\end{array}\\\\ \\text{Pieces are 14 m and 16 m}[\/latex]\"\"<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":34,"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-1785","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\/1785","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\/1785\/revisions"}],"predecessor-version":[{"id":1786,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1785\/revisions\/1786"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1785\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1785"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1785"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1785"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}