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Số cam trong vườn là :
450 . \(\frac{2}{5}\) = 180 ( cây )
Số hồng xiêm trong vườn là :
450 . 50% = 225 ( cây )
Số bưởi trong vườn là :
450 - 180 - 225 = 45 ( cây )
Đ/s : 45 cây bưởi
a, \((\dfrac{-1}{2})\)2 -\(\dfrac{5}{6}\).\((\dfrac{-6}{7})-\dfrac{3}{4}:1\dfrac{2}{3}\)
=\(\dfrac{1}{4}+\dfrac{5}{7}-\dfrac{9}{20}\)
=\(\dfrac{35}{140}+\dfrac{100}{140}-\dfrac{63}{140}\)
=\(\dfrac{72}{140}\)= \(\dfrac{18}{35}\)
B5
a)\(A=\left(1-\dfrac{1}{2010}\right)\left(1-\dfrac{2}{2010}\right)\left(1-\dfrac{3}{2010}\right)\cdot...\cdot\left(1-\dfrac{2010}{2010}\right)\left(1-\dfrac{2011}{2010}\right)\\ =\left(1-\dfrac{1}{2010}\right)\left(1-\dfrac{2}{2010}\right)\left(1-\dfrac{3}{2010}\right)\cdot...\cdot\left(1-1\right)\left(1-\dfrac{2011}{2010}\right)\\ =\left(1-\dfrac{1}{2010}\right)\left(1-\dfrac{2}{2010}\right)\left(1-\dfrac{3}{2010}\right)\cdot...\cdot0\cdot\left(1-\dfrac{2011}{2010}\right)\\ =0\)
b)
\(A=\dfrac{1946}{1986}=\dfrac{1986-40}{1986}=\dfrac{1986}{1986}-\dfrac{40}{1986}=1-\dfrac{40}{1986}\\ B=\dfrac{1968}{2008}=\dfrac{2008-40}{2008}=\dfrac{2008}{2008}-\dfrac{40}{2008}=1-\dfrac{40}{2008}\)
Vì \(\dfrac{40}{1986}>\dfrac{40}{2008}\) nên \(1-\dfrac{40}{1986}< 1-\dfrac{40}{2008}\) hay \(A< B\)
B6
a) Đề sai
Sửa lại:
\(B=\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{3}{7\cdot10}+...+\dfrac{3}{28\cdot31}\\ =\dfrac{1}{1}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{28}-\dfrac{1}{31}\\ =1-\dfrac{1}{31}\\ =\dfrac{30}{31}\)
b)
\(B=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+\dfrac{1}{8^2}\)
Ta thấy:
\(\dfrac{1}{2^2}< \dfrac{1}{1\cdot2}=\dfrac{1}{1}-\dfrac{1}{2}\)
\(\dfrac{1}{3^2}< \dfrac{1}{2\cdot3}=\dfrac{1}{2}-\dfrac{1}{3}\)
\(\dfrac{1}{4^2}< \dfrac{1}{3\cdot4}=\dfrac{1}{3}-\dfrac{1}{4}\)
...
\(\dfrac{1}{8^2}< \dfrac{1}{7\cdot8}=\dfrac{1}{7}-\dfrac{1}{8}\)
\(\Rightarrow B< \dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}\\ B< 1-\dfrac{1}{8}\\ B< \dfrac{7}{8}\left(1\right)\)
Mà \(\dfrac{7}{8}< 1\left(2\right)\)
Từ (1) và (2) ta có \(B< 1\)
Gọi thứ tự các ô trong dãy lần lượt là :
01;02;03;04;05;06;07 thì ta có:
01=04=07; 02=05 =176 ; 03=06=324;
Mà 01+02+03=1000 hay 01+176+324=1000
=>01+500=1000 => 01 = 500;
Số thích hợp để điền vào ô thứ nhất là 500...
Theo bài ra ta có:
\(\left(x+y\right)=3\left(x-y\right)=\dfrac{2x}{y}\)
Xét 2 vế đầu là x+y =3(x-y ); Ta có:
=> x+y = 3x - 3y
=> (x+y) - (3x - 3y) =0 hay 2x -4y =0;
=>4y -2x=0 => 2(2y - x) =0;
Vậy 2y - x=0 => 2y=x ..Thay vào ta được biểu thức mới:
\(\left(2y+y\right)=3\left(2y-y\right)=\dfrac{4y}{y}=4\)
=> 3y = 4 \(=>y=\dfrac{4}{3};x=\dfrac{4}{3}.2=\dfrac{8}{3}\)
Vậy x\(=\dfrac{8}{3}\); y\(=\dfrac{4}{3}\)
CHÚC BẠN HỌC TỐT .....
Từ đề bài ta có:
\(T=\dfrac{1+2}{2}.\dfrac{1+3}{3}.\dfrac{1+4}{4}...\dfrac{1+98}{98}.\dfrac{1+99}{99}\)
\(=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}...\dfrac{99}{98}.\dfrac{100}{99}\)
\(=\dfrac{100}{2}\)
\(=50\).
\(T=\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)\left(\dfrac{1}{4}+1\right)...\left(\dfrac{1}{98}+1\right)\left(\dfrac{1}{99}+1\right)\)
\(T=\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}....\dfrac{99}{98}.\dfrac{100}{99}\)
\(T=\dfrac{3.4.5......99}{3.4.5......99}.\dfrac{100}{2}\)
\(T=50\)
BÀI 1:
a)
\(\dfrac{1}{2}-\dfrac{2}{3}+\dfrac{3}{4}\\ =\dfrac{6}{12}-\dfrac{8}{12}+\dfrac{9}{12}\\ =\dfrac{6-8+9}{12}\\ =\dfrac{7}{12}\)
b)
\(-4\dfrac{1}{2}+1,2\cdot\left(-5\right)-30\%\\ =\dfrac{-9}{2}+\dfrac{6}{5}\cdot\left(-5\right)-\dfrac{3}{10}\\ =\dfrac{-9}{2}+\left(-6\right)-\dfrac{3}{10}\\ =\dfrac{-45}{10}+\dfrac{-60}{10}-\dfrac{3}{10}\\ =\dfrac{\left(-45\right)+\left(-60\right)-3}{10}\\ =\dfrac{-108}{10}\\ =\dfrac{54}{5}\)
c)
\(\dfrac{-7}{9}\cdot\dfrac{6}{13}+\dfrac{-7}{9}\cdot\dfrac{7}{13}+5\dfrac{7}{9}\\ =\dfrac{-7}{9}\cdot\left(\dfrac{6}{13}+\dfrac{7}{13}\right)+5\dfrac{7}{9}\\ =\dfrac{-7}{9}\cdot1+5\dfrac{7}{9}\\ =\dfrac{-7}{9}+5\dfrac{7}{9}\\ =5\)
BÀI 2
a)
\(\dfrac{3}{2}x-\dfrac{2}{3}=\dfrac{2}{3}:\dfrac{3}{2}\\ \dfrac{3}{2}x-\dfrac{2}{3}=\dfrac{4}{9}\\ \dfrac{3}{2}x=\dfrac{4}{9}+\dfrac{2}{3}\\ \dfrac{3}{2}x=\dfrac{10}{9}\\ x=\dfrac{10}{9}:\dfrac{3}{2}\\ x=\dfrac{20}{27}\)
b)
\(\left(\dfrac{9}{11}-x\right):\left(\dfrac{-10}{11}\right)=1-\dfrac{4}{5}\\ \left(\dfrac{9}{11}-x\right):\left(\dfrac{-10}{11}\right)=\dfrac{1}{5}\\ \dfrac{9}{11}-x=\dfrac{1}{5}\cdot\left(\dfrac{-10}{11}\right)\\ \dfrac{9}{11}-x=\dfrac{-2}{11}\\ x=\dfrac{9}{11}-\dfrac{-2}{11}\\ x=1\)
c)
\(\left(1,2x-\dfrac{4}{7}\right):\dfrac{4}{7}=75\%\\ \left(\dfrac{6}{5}x-\dfrac{4}{7}\right):\dfrac{4}{7}=\dfrac{3}{4}\\ \dfrac{6}{5}x:\dfrac{4}{7}-\dfrac{4}{7}:\dfrac{4}{7}=\dfrac{3}{4}\\ \dfrac{6}{5}x:\dfrac{4}{7}-1=\dfrac{3}{4}\\ \dfrac{6}{5}x:\dfrac{4}{7}=\dfrac{3}{4}+1\\ \dfrac{6}{5}x:\dfrac{4}{7}=\dfrac{7}{4}\\ \dfrac{6}{5}x=\dfrac{7}{4}\cdot\dfrac{4}{7}\\ \dfrac{6}{5}x=1\\ x=1:\dfrac{6}{5}\\ x=\dfrac{5}{6}\)