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12,65 x X + X x 27,35 = 9
(12,65 + 27,35) x X = 9
40 x X = 9
X = 9 : 40
X = 0,225
a)12,65 x x + x x 27,35 = 9
x x ( 12,65 + 27,35 ) = 9
x x 40 = 9
x=\(\frac{9}{40}\)
b)11x(x-5)=5x(x+11)
11x-55=5x+55
11x-55-5x-55=0
6x-110=0
6x=110
x=\(\frac{55}{3}\)
I.\(B=9,8+8,7+7,6+...+2,1-1,2-2,3-3,4-...-8,9\)
\(B=\left(9,8-8,9\right)+\left(8,7-7,8\right)+\left(7,6-6,7\right)+...+\left(2,1-1,2\right)\)
\(B=0,9+0,9+0,9+...+0,9\) ( 8 số 0,9 )
\(B=7,2\)
II.
\(\left(a\right)\frac{2}{1\cdot2}+\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+...+\frac{2}{19\cdot20}\)
\(=2\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{19\cdot20}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\left(1-\frac{1}{20}\right)\)
\(=2\cdot\frac{19}{20}=\frac{19}{10}\)
\(\left(b\right)\frac{4}{1\cdot3}+\frac{4}{3\cdot5}+\frac{4}{5\cdot7}+...+\frac{4}{17\cdot19}+\frac{4}{19\cdot21}\)
\(=2\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{17\cdot19}+\frac{2}{19\cdot21}\right)\)
\(=2\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\)
\(=2\left(1-\frac{1}{21}\right)\)
\(=2\cdot\frac{20}{21}=\frac{40}{21}\)
\(\left(c\right)\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{16\cdot18}+\frac{4}{18\cdot20}\)
\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=1-\frac{1}{10}=\frac{9}{10}\)
( x + 1) + (x +4) + ...+ ( x + 34) = 222
x*12 + [(1+34) * 12 : 2] = 222
x*12 + 210 = 222
x*12 = 12
x = 1
(x+1)+(x+ 4)+...+(x+34)=222
x*12+(1+4+7...+34)=222
x*12+210=222
x*12=222-210
x*12=12
x=12:12
x=1
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50% \(\times\) \(x\) + 16,8 = 3,4 \(\times\) 2 + \(x\)
0,5 \(\times\) \(x\) + 16,8 = 6,8 + \(x\)
6,8 + \(x\) - 0,5 \(\times\) \(x\) = 16,8
6,8 + \(x\) \(\times\) ( 1 -0,5) = 16,8
6,8 + \(x\) \(\times\) 0,5 = 16,8
\(x\) \(\times\) 0,5 = 16,8 - 6,8
\(x\) \(\times\) 0,5 = 10
\(x\) = 10 : 0,5
\(x\) = 20