{"id":1791,"date":"2019-08-12T16:56:37","date_gmt":"2019-08-12T20:56:37","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/?post_type=back-matter&p=1791"},"modified":"2019-08-13T17:07:42","modified_gmt":"2019-08-13T21:07:42","slug":"answer-key-10-7","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/back-matter\/answer-key-10-7\/","title":{"raw":"Answer Key 10.7","rendered":"Answer Key 10.7"},"content":{"raw":"[latexpage]\r\n
    \r\n \t
  1. \\(\\begin{array}{rrrrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx&+&y&=&22&\\Rightarrow &x&=&22&-&y \\\\\r\nx&-&y&=&120&&&&&& \\\\ \\\\\r\n(22&-&y)y&=&120&&&&&& \\\\\r\n22y&-&y^2&=&120&&&&&& \\\\ \\\\\r\n&&0&=&y^2&-&22y&+&120&& \\\\\r\n&&0&=&y^2&-&12y&-&10y&+&120 \\\\\r\n\\midrule\r\n&&0&=&y(y&-&12)&-&10(y&-&12) \\\\\r\n&&0&=&(y&-&12)(y&-&10)&& \\\\ \\\\\r\n&&y&=&12,&10&&&&&\r\n\\end{array}\\)\r\n\r\n\\(\\therefore \\text{ numbers are }10, 12\\)<\/li>\r\n \t
  2. \\(\\begin{array}{rrrrccrrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&x&-&y&=&4&\\Rightarrow &x&=&y&+&4 \\\\\r\n&&&&x&\\cdot &y&=&140&&&&&& \\\\ \\\\\r\n&&&&(y&+&4)y&=&140&&&&&& \\\\\r\n&&&&y^2&+&4y&=&140&&&&&& \\\\ \\\\\r\n&&y^2&+&4y&-&140&=&0&&&&&& \\\\\r\ny^2&-&10y&+&14y&-&140&=&0&&&&&& \\\\\r\n\\midrule\r\ny(y&-&10)&+&14(y&-&10)&=&0&&&&&& \\\\\r\n&&(y&-&10)(y&+&14)&=&0&&&&&& \\\\ \\\\\r\n&&&&&&y&=&10,&-14&&&&& \\\\ \\\\\r\n&&&&&&y&=&10,&x&=&10&+&4&= 14 \\\\\r\n&&&&&&y&=&-14,&x&=&-14&+&4&= -10 \\\\\r\n\\end{array}\\)\r\n\r\n\\(\\therefore \\text{ numbers are }10, 14\\text{ and }-10, -14\\)<\/li>\r\n \t
  3. \\(\\begin{array}{rrrrcrrrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&A&-&B&=&8&\\Rightarrow &A&=&B&+&8 \\\\\r\n&&&&A^2&+&B^2&=&320&&&&&& \\\\ \\\\\r\n&&(B&+&8)^2&+&B^2&=&320&&&&&& \\\\\r\nB^2&+&16B&+&64&+&B^2&=&320&&&&&& \\\\\r\n&&&-&320&&&&-320&&&&&& \\\\\r\n\\midrule\r\n&&2B^2&+&16B&-&256&=&0&&&&&& \\\\\r\n&&2(B^2&+&8B&-&128)&=&0&&&&&& \\\\\r\n&&2(B&+&16)(B&-&8)&=&0&&&&&& \\\\ \\\\\r\n&&&&&&B&=&-16,&8&&&&& \\\\ \\\\\r\n&&&&&&\\therefore A&=&B&+&8&&&& \\\\\r\n&&&&&&A&=&-8,&16&&&&&\r\n\\end{array}\\)\r\n\r\n\\(\\therefore (-16, -8)\\text{ and }(8,16)\\)<\/li>\r\n \t
  4. \\(\\begin{array}{rrrrcrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx, &x&+&2&&&&&&&&&& \\\\ \\\\\r\n&&x^2&+&(x&+&2)^2&=&244&&&&& \\\\\r\nx^2&+&x^2&+&4x&+&4&=&244&&&&& \\\\\r\n&&&&&&-244&&-244&&&&& \\\\\r\n\\midrule\r\n&&2x^2&+&4x&-&240&=&0&&&&& \\\\\r\n&&2(x^2&+&2x&-&120)&=&0&&&&& \\\\\r\n&&2(x&-&10)(x&+&12)&=&0&&&&& \\\\ \\\\\r\n&&&&&&x&=&10, &-12&&&& \\\\ \\\\\r\n&&&&&&x&=&10, &x&+&2&=&12 \\\\\r\n&&&&&&x&=&-12, &x&+&2&=&-10\r\n\\end{array}\\)\r\n\r\n\\(\\therefore \\text{ numbers are }10, 12\\text{ or }-12, -10\\)<\/li>\r\n \t
  5. \\(\\begin{array}{rrrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx,&x&+&2&&&&&&&& \\\\ \\\\\r\n&&x^2&-&(x&+&2)^2&=&60&&& \\\\\r\nx^2&-&(x^2&+&4x&+&4)&=&60&&& \\\\\r\nx^2&-&x^2&-&4x&-&4&=&60&&& \\\\\r\n&&&&&+&4&&+4&&& \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{-4x}{-4}&=&\\dfrac{64}{-4}&&& \\\\ \\\\\r\n&&&&&&x&=&-16&&& \\\\ \\\\\r\n&&&&x&+&2&\\Rightarrow &-16&+&2& \\\\\r\n&&&&&&&\\Rightarrow &-14&&& \\\\\r\n\\end{array}\\)\r\n\r\n\\(-16, -14\\)<\/li>\r\n \t
  6. \\(\\begin{array}{rrrrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx,&x&+&2&&&&& \\\\ \\\\\r\n&&x^2&+&(x&+&2)^2&=&\\phantom{-}452 \\\\\r\nx^2&+&x^2&+&4x&+&4&=&\\phantom{-}452 \\\\\r\n&&&&&-&452&&-452 \\\\\r\n\\midrule\r\n&&2x^2&+&4x&-&448&=&0 \\\\\r\n&&2(x^2&+&2x&-&224)&=&0 \\\\\r\n&&2(x&-&14)(x&+&16)&=&0 \\\\ \\\\\r\n&&&&&&x&=&14, -16 \\\\ \\\\\r\n&&&&&&x&=&14 \\\\\r\n&&&&x&+&2&=&16 \\\\ \\\\\r\n&&&&&&x&=&-16 \\\\\r\n&&&&x&+&2&=&-14\r\n\\end{array}\\)\r\n\r\n\\(14,16\\text{ and }-16,-14\\)<\/li>\r\n \t
  7. \\(\\begin{array}{rrcrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nx,&x&+&2,&x&+&4&&&& \\\\ \\\\\r\n&&x(x&+&2)&=&38&+&x&+&4 \\\\\r\nx^2&+&2x&&&=&42&+&x&& \\\\\r\n&-&x&-&42&&-42&-&x&& \\\\\r\n\\midrule\r\nx^2&+&x&-&42&=&0&&&& \\\\\r\n(x&+&7)(x&-&6)&=&0&&&& \\\\\r\n&&&&x&=&\\cancel{-7},&6&&& \\\\\r\n\\end{array}\\)\r\n\r\n\\(\\therefore \\text{ numbers are }6,8,10\\)<\/li>\r\n \t
  8. \\(x, x+2, x+4\\)\\(\\begin{array}{rrrrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&(x)(x&+&2)&=&52&+&x&+&4 \\\\ \\\\\r\nx^2&+&2x&&&=&56&+&x&& \\\\\r\n&-&x&-&56&&-56&-&x&& \\\\\r\n\\midrule\r\nx^2&+&x&-&56&=&0&&&& \\\\\r\n(x&+&8)(x&-&7)&=&0&&&& \\\\ \\\\\r\n&&&&x&=&\\cancel{-8}, 7&&&&\r\n\\end{array}\\)\r\n\r\n\\(\\therefore \\text{ numbers are }7,9,11\\)<\/li>\r\n \t
  9. \\(\\begin{array}{rrrrrrrrlrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&A&=&T&+&4&&&&& \\\\ \\\\\r\nA&\\cdot &T&=&80&+&(A&-&4)&(T&-&4) \\\\\r\n(T&+&4)T&=&80&+&(T&+&\\cancel{4-4})&(T&-&4) \\\\ \\\\\r\nT^2&+&4T&=&80&+&T^2&-&4T&&& \\\\\r\n-T^2&+&4T&&&-&T^2&+&4T&&& \\\\\r\n\\midrule\r\n&&\\dfrac{8T}{8}&=&\\dfrac{80}{8}&&&&&&& \\\\ \\\\\r\n&&T&=&10&&&&&&& \\\\ \\\\\r\n&&\\therefore A&=&T&+&4&&&&& \\\\\r\n&&A&=&10&+&4&=&14&&&\r\n\\end{array}\\)<\/li>\r\n \t
  10. \\(\\begin{array}{rrcrrrcrcrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&C&=&K&+&3&&&&&& \\\\\r\n&&CK&=&(C&+&5)&&(K&+&5)&-&130 \\\\ \\\\\r\n(K&+&3)K&=&(K&+&3&+&5)(K&+&5)&-&130 \\\\\r\nK^2&+&3K&=&K^2&+&13K&+&40&-&130&& \\\\\r\n-K^2&-&13K&&-K^2&-&13K&&&&&& \\\\\r\n\\midrule\r\n&&\\dfrac{-10K}{-10}&=&\\dfrac{-90}{-10}&&&&&&&& \\\\ \\\\\r\n&&K&=&9&&&&&&&& \\\\ \\\\\r\n&&\\therefore C&=&9&+&3&=&12&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  11. \\(\\begin{array}{rrrrcrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&J&=&S&+&1&& \\\\ \\\\\r\n&&(J&+&5)(S&+&5)&=&230&+&J&\\cdot &S \\\\\r\n(S&+&1&+&5)(S&+&5)&=&230&+&(S&+&1)S \\\\\r\n&&(S&+&6)(S&+&5)&=&230&+&S^2&+&S \\\\ \\\\\r\n&&S^2&+&11S&+&30&=&S^2&+&S&+&230 \\\\\r\n&&-S^2&-&S&-&30&&-S^2&-&S&-&30 \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{10S}{10}&=&\\dfrac{200}{10}&&&& \\\\ \\\\\r\n&&&&&&S&=&20&&&& \\\\\r\n&&&&&&J&=&21&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  12. \\(\\begin{array}{rrcrcrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&J&=&S&+&2&& \\\\\r\n&&(S&+&2)(J&+&2)&=&48&+&S&\\cdot &J \\\\ \\\\\r\n(S&+&2)(S&+&2&+&2)&=&48&+&S(S&+&2) \\\\\r\n&&(S&+&2)(S&+&4)&=&48&+&S^2&+&25 \\\\ \\\\\r\n&&S^2&+&6S&+&8&=&48&+&S^2&+&25 \\\\\r\n&&-S^2&-&2S&-&8&&-8&-&S^2&-&25 \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{4S}{4}&=&\\dfrac{40}{4}&&&& \\\\ \\\\\r\n&&&&&&S&=&10&&&& \\\\\r\n&&&&&&J&=&12&&&&\r\n\\end{array}\\)<\/li>\r\n \t
  13. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&d&=&r\\cdot t \\\\ \\\\\r\n&&&&r&\\cdot &t&=&240\\ \\\\\r\n&&&&&&\\therefore r&=&\\dfrac{240}{t} \\\\ \\\\\r\n&&(r&+&20)(t&-&1)&=&240 \\\\\r\n&&(\\dfrac{240}{t}&+&20)(t&-&1)&=&240 \\\\ \\\\\r\n\\cancel{240}&+&20t&-&\\dfrac{240}{t}&-&20&=&\\cancel{240} \\\\ \\\\\r\n&&(20t&-&\\dfrac{240}{t}&-&20&=&0)(t) \\\\ \\\\\r\n&&(20t^2&-&240&-&20t&=&0)(\\div 20)\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrcrcrl}\r\nt^2&-&12&-&t&=&0 \\\\\r\n(t&-&4)(t&+&3)&=&0 \\\\ \\\\\r\n&&&&t&=&4, \\cancel{-3} \\\\ \\\\\r\n&&&&r&=&\\dfrac{240}{4}\\text{ or }60\\text{ km\/h} \\\\ \\\\\r\n&&&&\\text{faster}&=&80\\text{ km\/h}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  14. \\(\\begin{array}{ll}\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&d&=&r\\cdot t \\\\\r\n&&&&r&\\cdot &t&=&100 \\\\\r\n&&&&&&r&=&\\dfrac{100}{t} \\\\ \\\\\r\n&&(r&+&20)(t&-&0.5)&=&120 \\\\\r\n&&(\\dfrac{100}{t}&+&20)(t&-&0.5)&=&120 \\\\\r\n100&+&20t&-&\\dfrac{50}{t}&-&10&=&120 \\\\\r\n&&&&&-&120&&-120 \\\\\r\n\\midrule\r\n&&20t&-&30&-&\\dfrac{50}{t}&=&0 \\\\ \\\\\r\n&&(20t&-&30&-&\\dfrac{50}{t}&=&0)(t) \\\\ \\\\\r\n&&(20t^2&-&30t&-&50&=&0)(\\div 10)\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrl}\r\n2t^2&-&3t&-&5&=&0 \\\\\r\n&&&&t&=&\\dfrac{-(-3)\\pm \\sqrt{(-3)^2-4(2)(-5)}}{2(2)} \\\\ \\\\\r\n&&&&t&=&\\dfrac{3\\pm 7}{4}=\\dfrac{10}{4}\\text{ or }\\cancel{\\dfrac{-4}{4}} \\\\ \\\\\r\n&&&&t&=&2.5\\text{ h}\r\n\\end{array}\r\n\\end{array}\\)\r\n\r\n\\(\\text{Answer: }\\dfrac{100\\text{ km}}{2.5\\text{ h}}=\\dfrac{40\\text{ km}}{\\text{h}}, \\dfrac{120\\text{ km}}{2\\text{ h}}=\\dfrac{60\\text{ km}}{\\text{h}}\\)<\/li>\r\n \t
  15. \\(\\begin{array}{ll}\r\n\\\\ \\\\ \\\\ \\\\\r\n\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&d&=&r\\cdot t \\\\\r\n&&&&r&\\cdot &t&=&150 \\\\\r\n&&&&&&r&=&\\dfrac{150}{t} \\\\ \\\\\r\n&&(r&+&5)(t&-&1.5)&=&150 \\\\\r\n&&(\\dfrac{150}{t}&+&5)(t&-&1.5)&=&150 \\\\ \\\\\r\n\\cancel{150}&+&5t&-&\\dfrac{225}{t}&-&7.5&=&\\cancel{150} \\\\ \\\\\r\n&&(5t&-&\\dfrac{225}{t}&-&7.5&=&0)(t) \\\\ \\\\\r\n&&(5t^2&-&7.5t&-&225&=&0)(2) \\\\\r\n&&(10t^2&-&15t&-&450&=&0)(\\div 5)\r\n\\end{array}\r\n&\\hspace{0.25in}\r\n\\begin{array}{rrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n2t^2&-&3t&-&90&=&0 \\\\\r\n(t&+&6)(2t&-&15)&=&0 \\\\\r\n&&&&t&=&\\cancel{-6}, \\dfrac{15}{2} \\\\ \\\\\r\n&&&&r&=&\\dfrac{150}{t} \\\\ \\\\\r\n&&&&r&=&\\dfrac{150}{\\dfrac{15}{2}} \\\\ \\\\\r\n&&&&r&=&\\dfrac{150}{1}\\cdot \\dfrac{2}{15} \\\\ \\\\\r\n&&&&r&=&20\\text{ km\/h}\r\n\\end{array}\r\n\\end{array}\\)<\/li>\r\n \t
  16. \\(\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&d&=&r\\cdot t \\\\\r\n&&&&r&\\cdot &t&=&180\\Rightarrow r=\\dfrac{180}{t} \\\\ \\\\\r\n&&(r&+&15)(t&-&1)&=&180 \\\\\r\n&&(\\dfrac{180}{t}&+&15)(t&-&1)&=&180 \\\\ \\\\\r\n\\cancel{180}&+&15t&-&\\dfrac{180}{t}&-&15&=&\\cancel{180} \\\\\r\n&&(15t&-&15&-&\\dfrac{180}{t}&=&0)(t) \\\\\r\n&&(15t^2&-&15t&-&180&=&0)(\\div 15) \\\\ \\\\\r\n&&t^2&-&t&-&12&=&0 \\\\\r\n&&(t&-&4)(t&+&3)&=&0 \\\\\r\n&&&&&&t&=&4, \\cancel{-3} \\\\ \\\\\r\n&&&&&&r&=&\\dfrac{180}{4}=45\r\n\\end{array}\\)<\/li>\r\n \t
  17. \\(\\begin{array}{rrrrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&r&\\cdot &t&=&72\\Rightarrow r=\\dfrac{72}{t} \\\\ \\\\\r\n&&(r&+&12)(9&-&t)&=&72 \\\\ \\\\\r\n&&(\\dfrac{72}{t}&+&12)(9&-&t)&=&72 \\\\\r\n\\dfrac{648}{t}&+&108&-&72&-&12t&=&72 \\\\\r\n&&&-&72&&&&-72 \\\\\r\n\\midrule\r\n&&(-12t&-&36&+&\\dfrac{648}{t}&=&0)(t) \\\\ \\\\\r\n&&(-12t^2&-&36t&+&648&=&0)(\\div -12) \\\\ \\\\\r\n&&t^2&+&3t&-&54&=&0 \\\\\r\n&&(t&+&9)(t&-&6)&=&0 \\\\\r\n&&&&&&t&=&\\cancel{-9}, 6 \\\\ \\\\\r\n&&&&&&r&=&\\dfrac{72}{6}=12\\text{ (there)} \\\\ \\\\\r\n&&&&&&r&=&24\\text{ (return)}\r\n\\end{array}\\)<\/li>\r\n \t
  18. \\(\\begin{array}{rrrrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&r&\\cdot &t&=&120\\Rightarrow r=\\dfrac{120}{t} \\\\\r\n&&(r&+&10)(7&-&t)&=&120 \\\\ \\\\\r\n&&(\\dfrac{120}{t}&+&10)(7&-&t)&=&120 \\\\\r\n\\dfrac{840}{t}&+&70&-&120&-&10t&=&120 \\\\\r\n&&&-&120&&&&-120 \\\\\r\n\\midrule\r\n&&(-10t&-&170&+&\\dfrac{840}{t}&=&0)(t) \\\\\r\n&&(-10t^2&-&170t&+&840&=&0)(\\div -10) \\\\ \\\\\r\n&&t^2&+&17t&-&84&=&0 \\\\\r\n&&(t&+&21)(t&-&4)&=&0 \\\\\r\n&&&&&&t&=&\\cancel{-21}, 4 \\\\ \\\\\r\n&&&&&&r&=&\\dfrac{120}{4}\\text{ or }30\\text{ km\/h} \\\\ \\\\\r\n&&&&r&+&10&=&40\\text{ km\/h} \\\\\r\n\\end{array}\\)<\/li>\r\n \t
  19. \\(\\begin{array}{rrrrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&r&\\cdot &t&=&240\\Rightarrow r=\\dfrac{240}{t} \\\\ \\\\\r\n&&(r&+&20)(t&-&1)&=&240 \\\\\r\n&&(\\dfrac{240}{t}&+&20)(t&-&1)&=&240 \\\\\r\n\\cancel{240}&+&20t&-&\\dfrac{240}{t}&-&20&=&\\cancel{240} \\\\ \\\\\r\n&&(20t&-&20&-&\\dfrac{240}{t}&=&0)(t) \\\\\r\n&&(20t^2&-&20t&-&240&=&0)(\\div 20) \\\\ \\\\\r\n&&t^2&-&t&-&12&=&0 \\\\\r\n&&(t&-&4)(t&+&3)&=&0 \\\\\r\n&&&&&&t&=&4, \\cancel{-3} \\\\ \\\\\r\n&&&&&&r&=&\\dfrac{240}{4}\\text{ or }60\\text{ km\/h}\r\n\\end{array}\\)<\/li>\r\n \t
  20. \\(\\begin{array}{rrrrcrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&r&\\cdot &t&=&600\\Rightarrow r=\\dfrac{600}{t} \\\\ \\\\\r\n&&(r&-&50)(7&-&t)&=&600 \\\\\r\n&&(\\dfrac{600}{t}&-&50)(7&-&t)&=&600 \\\\\r\n\\dfrac{4200}{t}&-&350&-&600&+&50t&=&600 \\\\\r\n&&&-&600&&&&-600 \\\\\r\n\\midrule\r\n&&(50t&-&1550&+&\\dfrac{4200}{t}&=&0)(t) \\\\\r\n&&(50t^2&-&1550t&+&4200&=&0)(\\div 50) \\\\ \\\\\r\n&&t^2&-&31t&+&84&=&0 \\\\\r\n&&(t&-&3)(t&-&28)&=&0 \\\\\r\n&&&&&&t&=&3, \\cancel{28} \\\\ \\\\\r\n&&&&&&r&=&\\dfrac{600}{3}\\text{ or }200\\text{ km\/h}\r\n\\end{array}\\)<\/li>\r\n \t
  21. \\(\\begin{array}{rrrrlrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nL&=&4&+&W&&&& \\\\\r\n\\text{Area}&=&L&\\cdot &W&&&& \\\\ \\\\\r\n60&=&(4&+&W)W&&&& \\\\\r\n60&=&4W&+&W^2&&&& \\\\ \\\\\r\n0&=&W^2&+&4W&-&60&& \\\\\r\n0&=&W^2&+&10W&-&6W&-&60 \\\\\r\n\\midrule\r\n0&=&W(W&+&10)&-&6(W&+&10) \\\\\r\n0&=&(W&+&10)(W&-&6)&& \\\\ \\\\\r\nW&=&\\cancel{-10},&6&&&&& \\\\\r\nL&=&6&+&4&=&10&&\r\n\\end{array}\\)<\/li>\r\n \t
  22. \\(\\begin{array}{rrrrcrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\nW&=&L&-&10&&&& \\\\\r\n\\text{Area}&=&L&\\cdot &W&&&& \\\\ \\\\\r\n200&=&L(L&-&10)&&&& \\\\\r\n200&=&L^2&-&10L&&&& \\\\ \\\\\r\n0&=&L^2&-&10L&-&200&& \\\\\r\n0&=&L^2&+&10L&-&20L&-&200 \\\\\r\n\\midrule\r\n0&=&L(L&+&10)&-&20(L&+&10) \\\\\r\n0&=&(L&+&10)(L&-&20)&& \\\\ \\\\\r\nL&=&\\cancel{-10},&20&&&&& \\\\\r\nW&=&20&-&10&=&10&&\r\n\\end{array}\\)<\/li>\r\n \t
  23. \\(\\begin{array}{rrrrcrcrcrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&\\text{Area}_{\\text{large}}&-&\\text{Area}_{\\text{small}}&=&2800\\text{ m}^2 \\\\ \\\\\r\n&&(150&+&2x)(120&+&2x)&-&(150)(120)&=&2800 \\\\\r\n\\cancel{18000}&+&240x&+&300x&+&4x^2&-&\\cancel{18000}&=&2800 \\\\\r\n&&&&&&&-&2800&&-2800 \\\\\r\n\\midrule\r\n&&&&4x^2&+&540x&-&2800&=&0 \\\\\r\n&&&&x^2&+&135x&-&700&=&0 \\\\\r\n&&&&(x&-&5)(x&+&140)&=&0 \\\\\r\n&&&&&&&&x&=&5, \\cancel{-140}\r\n\\end{array}\\)\r\n\r\n\\(\\text{walkway}=5\\text{ m}\\)<\/li>\r\n \t
  24. \\(\\begin{array}{rrrrcrcrcrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&\\text{Area}_{\\text{large}}&-&\\text{Area}_{\\text{small}}&=&74\\text{ m}^2 \\\\ \\\\\r\n&&(25&+&2x)(10&+&2x)&-&(25)(10)&=&74 \\\\\r\n\\cancel{250}&+&20x&+&50x&+&4x^2&-&\\cancel{250}&=&74 \\\\\r\n&&&&&&&-&74&&-74 \\\\\r\n\\midrule\r\n&&&&4x^2&+&70x&-&74&=&0 \\\\\r\n&&&&2x^2&+&35x&-&37&=&0 \\\\\r\n&&&&(x&-&1)(2x&+&37)&=&0 \\\\\r\n&&&&&&&&x&=&1, \\cancel{-\\dfrac{37}{2}} \\\\\r\n\\end{array}\\)\r\n\r\n\\(\\text{the overlap}=1\\text{ m}\\)<\/li>\r\n \t
  25. \\(\\begin{array}{rrrrrrrrl}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&L&=&W&+&4 \\\\\r\n&&L&\\cdot &W&=&60&& \\\\ \\\\\r\n&&(W&+&4)W&=&60&& \\\\\r\nW^2&+&4W&&&=&60&& \\\\\r\n&&&-&60&&-60&& \\\\\r\n\\midrule\r\nW^2&+&4W&-&60&=&0&& \\\\\r\n(W&-&6)(W&+&10)&=&0&& \\\\ \\\\\r\n&&&&W&=&6,&\\cancel{-10}& \\\\\r\n&&&&L&=&6&+&4=10\r\n\\end{array}\\)<\/li>\r\n \t
  26. \\(\\begin{array}{rrrrrrrrcrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&(x&+&5)^2&=&4(x)^2&&&& \\\\ \\\\\r\nx^2&+&10x&+&25&=&4x^2&&&& \\\\\r\n-x^2&-&10x&-&25&&-x^2&-&10x&-&25 \\\\\r\n\\midrule\r\n&&&&0&=&3x^2&-&10x&-&25 \\\\\r\n&&&&0&=&(x&-&5)(3x&+&5) \\\\\r\n&&&&x&=&5, &\\cancel{-\\dfrac{5}{3}}&&&\r\n\\end{array}\\)<\/li>\r\n \t
  27. \\(\\begin{array}{rrrrrrlll}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&L&=&20&+&W \\\\\r\n&&L&\\cdot &W&=&2400&& \\\\ \\\\\r\n&&(20&+&W)W&=&2400&& \\\\\r\nW^2&+&20W&&&=&2400&& \\\\\r\n&&&-&2400&&-2400&& \\\\\r\n\\midrule\r\nW^2&+&20W&-&2400&=&0&& \\\\\r\n(W&+&60)(W&-&40)&=&0&& \\\\ \\\\\r\n&&&&W&=&\\cancel{-60},&40& \\\\\r\n&&&&L&=&20&+&40=60\r\n\\end{array}\\)<\/li>\r\n \t
  28. \\(\\begin{array}{rrrrcrrrrrrrr}\r\n\\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\ \\\\\r\n&&&&&&L&=&W&+&8&& \\\\\r\n&&(L&+&2)(W&+&2)&=&L&\\cdot &W&+&60 \\\\ \\\\\r\n(W&+&8&+&2)(W&+&2)&=&(W&+&8)W&+&60 \\\\\r\n&&W^2&+&12W&+&20&=&W^2&+&8W&+&60 \\\\\r\n&&-W^2&-&8W&-&20&&-W^2&-&8W&-&20 \\\\\r\n\\midrule\r\n&&&&&&\\dfrac{4W}{4}&=&\\dfrac{40}{4}&&&& \\\\ \\\\\r\n&&&&&&W&=&10&&&& \\\\\r\n&&&&&&L&=&10&+&8&=&18\r\n\\end{array}\\)<\/li>\r\n<\/ol>","rendered":"
      \n
    1. \"\begin{array}{rrrrrrrrrrl}\n

      \"\therefore \text{ numbers are }10, 12\"<\/li>\n

    2. \"\begin{array}{rrrrccrrrrrrrrl}\n

      \"\therefore \text{ numbers are }10, 14\text{ and }-10, -14\"<\/li>\n

    3. \"\begin{array}{rrrrcrrrrrrrrrl}\n

      \"\therefore (-16, -8)\text{ and }(8,16)\"<\/li>\n

    4. \"\begin{array}{rrrrcrrrrrrrrr}\n

      \"\therefore \text{ numbers are }10, 12\text{ or }-12, -10\"<\/li>\n

    5. \"\begin{array}{rrrrrrrrrrrr}\n

      \"-16, -14\"<\/li>\n

    6. \"\begin{array}{rrrrcrrrl}\n

      \"14,16\text{ and }-16,-14\"<\/li>\n

    7. \"\begin{array}{rrcrrrrrrrr}\n

      \"\therefore \text{ numbers are }6,8,10\"<\/li>\n

    8. \"x, x+2, x+4\"\"\begin{array}{rrrrrrrrrrr}\n

      \"\therefore \text{ numbers are }7,9,11\"<\/li>\n

    9. \"\begin{array}{rrrrrrrrlrrr}<\/li>\n
    10. \"\begin{array}{rrcrrrcrcrrrr}<\/li>\n
    11. \"\begin{array}{rrrrcrrrrrrrr}<\/li>\n
    12. \"\begin{array}{rrcrcrrrrrrrr}<\/li>\n
    13. \"\begin{array}{ll}<\/li>\n
    14. \"\begin{array}{ll}\n

      \"\text{Answer: }\dfrac{100\text{ km}}{2.5\text{ h}}=\dfrac{40\text{ km}}{\text{h}}, \dfrac{120\text{ km}}{2\text{ h}}=\dfrac{60\text{ km}}{\text{h}}\"<\/li>\n

    15. \"\begin{array}{ll}<\/li>\n
    16. \"\begin{array}{rrrrrrrrl}<\/li>\n
    17. \"\begin{array}{rrrrcrrrl}<\/li>\n
    18. \"\begin{array}{rrrrcrrrl}<\/li>\n
    19. \"\begin{array}{rrrrcrrrl}<\/li>\n
    20. \"\begin{array}{rrrrcrrrl}<\/li>\n
    21. \"\begin{array}{rrrrlrrrl}<\/li>\n
    22. \"\begin{array}{rrrrcrrrr}<\/li>\n
    23. \"\begin{array}{rrrrcrcrcrl}\n

      \"\text{walkway}=5\text{ m}\"<\/li>\n

    24. \"\begin{array}{rrrrcrcrcrl}\n

      \"\text{the overlap}=1\text{ m}\"<\/li>\n

    25. \"\begin{array}{rrrrrrrrl}<\/li>\n
    26. \"\begin{array}{rrrrrrrrcrr}<\/li>\n
    27. \"\begin{array}{rrrrrrlll}<\/li>\n
    28. \"\begin{array}{rrrrcrrrrrrrr}<\/li>\n<\/ol>\n","protected":false},"author":727,"menu_order":94,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-1791","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1791","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/users\/727"}],"version-history":[{"count":8,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1791\/revisions"}],"predecessor-version":[{"id":1805,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1791\/revisions\/1805"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter\/1791\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/media?parent=1791"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/pressbooks\/v2\/back-matter-type?post=1791"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/contributor?post=1791"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatealgebrakpu\/wp-json\/wp\/v2\/license?post=1791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}