10. 20x (x+1)= 30 x (x-1); etc. Divide by x. 13. (x+4)(x+4)=8x+80; etc. 15. 6x2+36=5x2+72. 16. x2-6x+9-(x2-10x+25)= 12; removing the parenthesis, x2-6x+9-x2+10x-25 = 12; etc. х 18. The common denominator is 36 x. Clearing of fractions, 9x2+1444x2+324; etc. 2. Let x = the length of one edge. The area of one face = x2; that of six faces is 6x2, and is equal to 96 sq. in. 3x 7. Let x= the length of the perpendicular; of the base. The area = Х the length 3x 3x2 4 8 3x2 = 96; 3x2=768; x2 256; x = 16. Neglecting the negative result, the perpendicular measures 16 rd., and the base 12 rd. The hypotenuse = √162 + 122 rd. 9. (x+9)2= x2 + 152; x2 + 18x+81 = x2+225; etc. 10. (x+1)2x2-49; etc. 1238. The pupils should be informed that the product of the numbers represented by two letters is represented by writing the letters together; thus a times b is written ab, m times n is written mn, just as 3 times x is written 3x. 1242. 1. x2+6x+9. 2. x2-12x+36. 3. x 8x+16. 6. x2+2x+1. 7. x2-4x+4. 8. x10x + 25. 1244. 1. x+6x+9=49; x+3=±7. Ans. 2. x2-12x+36 64; x-6=±8. Ans. = 5. x2+18x+8119+81 = 100; x+9=10. Ans. 6. x2+2x+1=24+1=25; x+1=±5. Ans. 7. x2-14x+49 15+49; x-7±8. Ans. = 1246. 1. x2-6x+9=7+9; x-3=±4; etc. 2. x-12x+36 108+ 36; etc. = 3. x2+2x+1=48+1; etc. 1247. The first member is made a complete square by adding square of of the coefficient of x. the 1248. 1. x2+x+4=12+1=42. x + z = ± 7; x =, or 3 or 4. Ans. 2. x2-3x+2=10+2=42; x-3=±7; etc. 3. x2+5x+()2=-4+ (5)2; etc. = 1249. 1. x2- x = 6; x2 -x+1=6+1=25; etc. 1250. 1. 12x-x2 = 32. Changing the signs, and rearranging, x2-12x: = - 32. Completing the square, x2 - 12x + 36 = − 32 + 36 = 4. 2. x2+50x + 625 = 2400 + 625: 8 and 4, or 4 and 8. Ans. = 3025. x+25=±55; x= 30 or 80. Neglecting the negative result, the altitude is 30 ft. Ans. 3. x2+225 +30x+x2=5625. Completing the square, x2+15x + (15)2 = 2700+(1,5)2; etc. 4. Perpendicular = √1 § x2 — x2 = √√x2=&x. = Base 20 yd.; hypotenuse = 20 yd. × 14 = 25 yd. Ans. 5. The convex surface = 6 (x + x + x + x) = 24x; the surface of the two bases 2x2; the entire surface = 2x2+24x=170; x2+12x=85; etc. 6. The area of the walk = area of outside rectangle - area of inner rectangle. (40+2x) (50+2x) - 40 x 50=784; 4x2+180x784; x2+45x = 196; etc. 7. 12 acres = 1920 sq. rd. 1920; 15x2 = 15360; x2 = 1024; x =± 32. Base = 32 rd. ; perpendicular = 32 rd. × 17 = 60 rd.; hypotenuse= √32+602 rd. = 68 rd. Diagonal 68 rd. Ans. = = AC=16 ft., CB, the part broken off = 50 ft. - 16 ft. - 34 ft. Ans. Or, making BC=x, AC= 50— x. x = 34, the length in feet of the part broken off. 9. 602+(58-x)2=562x2; 36003364 116 x + x2 = 3136+ x2; The length of the ladder in feet = √562 + 332 = √3136 +1089 10. From ABD, the square of BD = 132 — (15 - x)2. From BCD, the square of BD 42x2. Therefore or, or, Removing the parenthesis, 169-225+ 30 x - x2=16-x2. Transposing and combining, 30 x 16-169 +225 = 72; = x = 23. BD=√BC — CD = √42 — 222 = √16 — 144 = 16 = 3}. Altitude = 3 ft. Ans. 11. AF=√AB2 – BF2 = √1156 – 256 = √900 = 30 ; Let FC=√BC2 — BF2 = √400 – 256 = √144 = 12; AC AFFC=30+12=42. = 42 ft. Ans. AE= x; EC= 42 — x ; ED AD AE2 262 - x2 = 676 — x2; ED Therefore ED=√262-102 = √576 = 24; =√402 — 322 = √576 = 24. 24 ft. Ans. |