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b, \(\dfrac{x-3}{4}=\dfrac{15}{20}\)
<=> \(\dfrac{x-3}{4}=\dfrac{3}{4}\)
=> x-3=3
<=> x=6
Vậy x=6
\(a,\dfrac{x}{15}=\dfrac{4}{y}=\dfrac{-2}{5}\)
* \(\dfrac{x}{15}=\dfrac{-2}{5}\)
\(\Rightarrow\dfrac{x}{15}=\dfrac{-6}{15}\)
\(\Rightarrow x=-6\)
*\(\dfrac{4}{y}=\dfrac{-2}{5}\)
\(\Rightarrow\dfrac{4}{y}=\dfrac{4}{-10}\)
\(\Rightarrow y=-10\)
Vậy x = - 6 ; y = - 10
\(b,\dfrac{x-3}{4}=\dfrac{15}{20}\)
=> ( x - 3 ) . 20 = 4. 15
=> 20x - 60 = 60
=> 20x = 60 + 60
=> 20x = 120
=> x = 120 : 20
=> x = 6
Vậy x = 6
\(c,\dfrac{-5}{9}+\dfrac{-8}{15}+\dfrac{22}{-9}+\dfrac{-7}{15}< x\le\dfrac{-1}{3}+\dfrac{-1}{4}+\dfrac{-5}{12}\)
\(\Rightarrow\dfrac{-5}{9}+\dfrac{-8}{15}+\dfrac{-22}{9}+\dfrac{-7}{15}< x\le\dfrac{-4}{12}+\dfrac{-3}{12}+\dfrac{-5}{12}\)
\(\Rightarrow\left(\dfrac{-5}{9}+\dfrac{-22}{9}\right)+\left(\dfrac{-8}{15}+\dfrac{-7}{15}\right)< x\le-1\)
\(\Rightarrow-3+\left(-1\right)< x\le-1\)
\(\Rightarrow-4< x\le-1\)
\(\Rightarrow x=-3;-2;-1\)
bài 3:
a, đặt \(\dfrac{x}{12}=\dfrac{y}{9}=\dfrac{z}{5}=k\)
=>x=12k,y=9k,z=5k
ta có: ayz=20=> 12k.9k.5k=20
=> (12.9.5)k^3=20
=>540.k^3=20
=>k^3=20/540=1/27
=>k=1/3
=>x=12.1/3=4
y=9.1/3=3
z=5.1/3=5/3
vậy x=4,y=3,z=5/3
b,ta có: \(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{3}=\dfrac{x^2}{25}=\dfrac{y^2}{49}=\dfrac{z^2}{9}\)
A/D tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x}{5}=\dfrac{y}{7}=\dfrac{z}{3}=\dfrac{x^2}{25}=\dfrac{y^2}{49}=\dfrac{z^2}{9}=\dfrac{x^2+y^2-z^2}{25+49-9}=\dfrac{585}{65}=9\)
=>x=5.9=45
y=7.9=63
z=3*9=27
vậy x=45,y=63,z=27
a: \(\Leftrightarrow\dfrac{a}{10}=\dfrac{7}{b}=\dfrac{c}{20}=\dfrac{1}{2}\)
=>a=5; b=14; c=10
b: \(\Leftrightarrow\dfrac{a}{9}=\dfrac{-8}{b}=\dfrac{c}{-21}=\dfrac{-2}{3}\)
=>a=-6; b=12; c=14
a) \(\dfrac{3}{4}=\dfrac{15}{20}\)
b) \(\dfrac{4}{5}=\dfrac{12}{15}\)
c) \(\dfrac{-4}{9}=\dfrac{-16}{36}\)
d) \(\dfrac{7}{-13}=\dfrac{21}{-39}\)
a ) \(\dfrac{3}{4}\)= \(\dfrac{15}{20}\)
b )\(\dfrac{4}{5}\)= \(\dfrac{12}{15}\)
c) \(\dfrac{-4}{9}\)=\(\dfrac{-16}{36}\)
d) \(\dfrac{7}{-13}\)=\(\dfrac{21}{-39}\)
a,9/5-5/9=81/45-25/45 =56/45 b,7/2+4/5+3/6=105/30+24/30+15/30
=144/30=24/5
c,(5/6-4/24)+1/3=(20/24-4/24)+1/3
=2/3+1/3=1
d,(9/12-10/12)-1/8=-1/12-1/8
=-2/12-3/24
=-5/24
Bài 3 :
a) \(A=\dfrac{1}{3.5}+\dfrac{1}{5.7}+...........+\dfrac{1}{2017.2019}\)
\(\Leftrightarrow2A=\dfrac{2}{3.5}+\dfrac{2}{5.7}+.........+\dfrac{2}{2017.2019}\)
\(\Leftrightarrow2A=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+......+\dfrac{1}{2017}-\dfrac{1}{2019}\)
\(\Leftrightarrow2A=\dfrac{1}{3}-\dfrac{1}{2019}\)
\(\Leftrightarrow2A=\dfrac{672}{2019}\)
\(\Leftrightarrow A=\dfrac{336}{2019}\)
b) \(B=\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+.........+\dfrac{1}{132}\)
\(\Leftrightarrow B=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+............+\dfrac{1}{11.12}\)
\(\Leftrightarrow B=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+......+\dfrac{1}{11}-\dfrac{1}{12}\)
\(\Leftrightarrow B=\dfrac{1}{2}-\dfrac{1}{12}=\dfrac{5}{12}\)
1.
Để \(\overline{25a89b}⋮2\Rightarrow b\in\left\{0;2;4;6;8\right\}\)
Để \(\overline{25a89b}\) chia 5 dư 3 \(\Rightarrow b\in\left\{3;8\right\}\)
Để thỏa mãn hai điều kiện trên thì \(b=8\)
Để \(\overline{25a898}⋮9\Rightarrow\left(2+5+a+8+9+8\right)⋮9\Leftrightarrow32+a⋮9\Rightarrow a=4\)
Vậy \(a=4;b=8\); số cần tìm là \(254898\)
\(a,\left(\dfrac{7}{20}+\dfrac{11}{15}-\dfrac{15}{12}\right):\left(\dfrac{11}{20}-\dfrac{26}{45}\right).\)
\(=\left(\dfrac{21}{60}+\dfrac{44}{60}-\dfrac{75}{60}\right):\left(\dfrac{99}{180}-\dfrac{104}{180}\right).\)
\(=\left(\dfrac{65}{60}-\dfrac{75}{60}\right):\left(-\dfrac{5}{180}\right).\)
\(=-\dfrac{10}{60}:\left(-\dfrac{5}{180}\right).\)
\(=-\dfrac{1}{6}:\left(-\dfrac{1}{36}\right).\)
\(=-\dfrac{1}{6}.\left(-36\right).\)
\(=\dfrac{-1.\left(-36\right)}{6}=\dfrac{36}{6}=6.\)
Vậy......
\(b,\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}.\)
\(=\dfrac{5\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}{8\left(1-\dfrac{1}{3}+\dfrac{1}{9}-\dfrac{1}{27}\right)}:\dfrac{15\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}{16\left(1-\dfrac{1}{11}+\dfrac{1}{121}\right)}.\)
\(=\dfrac{5}{8}:\dfrac{15}{16}.\)
\(=\dfrac{5}{8}.\dfrac{16}{15}=\dfrac{5.16}{8.15}=\dfrac{1.2}{1.3}=\dfrac{2}{3}.\)
Vậy......
c, (làm tương tự câu b).
~ Học tốt!!! ~
\(\dfrac{a}{12}=\dfrac{b}{9}=\dfrac{c}{5}\)
\(\Rightarrow a=12k\)
\(\Rightarrow b=9k\)
\(\Rightarrow c=5k\)
\(\Rightarrow a.b.c=12k.9k.5k=20\)
\(\Rightarrow540.k^3=20\)
\(\Rightarrow k^3=\dfrac{1}{27}\)
\(\Rightarrow k=\dfrac{1}{3}\)
\(a=\dfrac{1}{3}.12=4\)
\(b=\dfrac{1}{3}.9=3\)
\(c=\dfrac{1}{3}.5=\dfrac{5}{3}\)
Ta có : \(\dfrac{a}{12}\)=\(\dfrac{b}{9}\)=\(\dfrac{c}{5}\)=k
=> a= k.12
=>b=k.9
=> c= k.5
Mà a.b.c=20
=> k.12 .k.9.k.5 = 20
=> k3.540 =20
=> k3 = \(\dfrac{1}{27}\)
=> k=\(\dfrac{1}{3}\)
Vì a= k.12 => a= \(\dfrac{1}{3}\).12 => a = 4
b= k.9 => b= \(\dfrac{1}{3}\).9 => b= 3
c=k.5 => c=\(\dfrac{1}{3}\) .5 => c =\(\dfrac{5}{3}\)
Vậy ......................