Bạn chưa đăng nhập. Vui lòng đăng nhập để hỏi bài
Ẩn danh
Nguyễn Lê Phước Thịnh
15 tháng 7 2024 lúc 9:44

Câu 1:

a: \(\dfrac{11}{19}+\dfrac{19}{18}+\dfrac{8}{19}-\dfrac{1}{18}+5,2\)

\(=\left(\dfrac{11}{19}+\dfrac{8}{19}\right)+\left(\dfrac{19}{18}-\dfrac{1}{18}\right)+5,2\)

=1+1+5,2=7,2

b: \(1\dfrac{4}{23}+\dfrac{5}{21}-\dfrac{4}{23}+0,5+\dfrac{16}{21}\)

\(=\left(1+\dfrac{4}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+0,5\)

\(=1+1+0,5=2,5\)

c: \(\dfrac{3}{7}\cdot\dfrac{16}{15}-\dfrac{3}{7}\cdot\dfrac{2}{15}=\dfrac{3}{7}\left(\dfrac{16}{15}-\dfrac{2}{15}\right)\)

\(=\dfrac{3}{7}\cdot\dfrac{14}{15}=\dfrac{3}{15}\cdot\dfrac{14}{7}=\dfrac{2}{5}\)

d: \(\dfrac{3}{7}\cdot19\dfrac{1}{3}-\dfrac{3}{7}\cdot33\dfrac{1}{3}\)

\(=\dfrac{3}{7}\left(19+\dfrac{1}{3}-33-\dfrac{1}{3}\right)=\dfrac{3}{7}\cdot\left(-14\right)=-6\)

e: \(15\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)-25\dfrac{1}{4}:\left(-\dfrac{5}{7}\right)\)

\(=\left(15+\dfrac{1}{4}\right)\cdot\dfrac{-7}{5}-\left(25+\dfrac{1}{4}\right)\cdot\dfrac{-7}{5}\)

\(=\dfrac{-7}{5}\left(15+\dfrac{1}{4}-25-\dfrac{1}{4}\right)=-\dfrac{7}{5}\cdot\left(-10\right)=14\)

f: \(\dfrac{4^2\cdot2^3}{2^6}=\dfrac{2^4\cdot2^3}{2^6}=\dfrac{2^7}{2^6}=2\)

g: \(9\cdot\left(-\dfrac{1}{3}\right)^3+\dfrac{1}{3}=9\cdot\dfrac{-1}{27}+\dfrac{1}{3}=-\dfrac{1}{3}+\dfrac{1}{3}=0\)

h: \(\left(\dfrac{5}{12}:3\dfrac{2}{6}\right)+\left(\dfrac{2}{3}-\dfrac{1}{2}\right)^2\)

\(=\left(\dfrac{5}{12}:\dfrac{10}{3}\right)+\left(\dfrac{4}{6}-\dfrac{3}{6}\right)^2\)

\(=\dfrac{5}{12}\cdot\dfrac{3}{10}+\left(\dfrac{1}{6}\right)^2=\dfrac{1}{8}+\dfrac{1}{36}=\dfrac{11}{72}\)

i: \(\left(-0,375\right)\cdot4\dfrac{1}{3}\cdot\left(-2\right)^3=\dfrac{-3}{8}\cdot\dfrac{13}{3}\cdot\left(-8\right)=13\)

k:

\(\dfrac{8}{9}+\dfrac{15}{23}+\dfrac{1}{9}+\dfrac{-15}{23}+\dfrac{1}{2}\)

\(=\left(\dfrac{8}{9}+\dfrac{1}{9}\right)+\left(\dfrac{15}{23}-\dfrac{15}{23}\right)+\dfrac{1}{2}\)

\(=1+\dfrac{1}{2}=\dfrac{3}{2}\)

l: \(16\dfrac{2}{7}:\dfrac{-3}{5}-28\dfrac{2}{7}:\dfrac{-3}{5}\)

\(=\left(16+\dfrac{2}{7}-28-\dfrac{2}{7}\right):\dfrac{-3}{5}=-12\cdot\dfrac{5}{-3}=\dfrac{60}{3}=20\)

m: \(\dfrac{1}{2}\cdot\sqrt{64}-\sqrt{\dfrac{4}{25}}+1^{2012}\)

\(=\dfrac{1}{2}\cdot8-\dfrac{2}{5}+1=4-\dfrac{2}{5}+1=5-\dfrac{2}{5}=\dfrac{23}{5}\)

Câu 2:

a: \(\dfrac{3}{4}+\dfrac{2}{5}x=\dfrac{29}{60}\)

=>\(\dfrac{2}{5}x=\dfrac{29}{60}-\dfrac{3}{4}=\dfrac{29}{60}-\dfrac{45}{60}=-\dfrac{16}{60}=-\dfrac{8}{15}\)

=>\(x=-\dfrac{8}{15}:\dfrac{2}{5}=-\dfrac{8}{15}\cdot\dfrac{5}{2}=-\dfrac{40}{30}=-\dfrac{4}{3}\)

b: \(\dfrac{1}{2}x+\sqrt{0,04}=\sqrt{1,96}\)

=>\(\dfrac{x}{2}+0,2=1,4\)

=>\(\dfrac{x}{2}=1,4-0,2=1,2\)

=>\(x=1,2\cdot2=2,4\)

c: \(\dfrac{1}{4}:\dfrac{1}{4}+x=5\)

=>x+1=5

=>x=5-1=4

d: \(\left(\dfrac{1}{4}+x\right)^2=25\)

=>\(\left[{}\begin{matrix}x+\dfrac{1}{4}=5\\x+\dfrac{1}{4}=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5-\dfrac{1}{4}=\dfrac{19}{4}\\x=-5-\dfrac{1}{4}=-\dfrac{21}{4}\end{matrix}\right.\)

e: ĐKXĐ: x>=1

\(\sqrt{x-1}=5\)

=>\(x-1=5^2=25\)

=>x=25+1=26

f: 1,2x-2=2,4-x

=>1,2x+x=2,4+2

=>2,2x=4,4

=>x=2

g: 2x-5=x+7

=>2x-x=5+7

=>x=12

h: \(\dfrac{31}{36}-\left(\dfrac{1}{3}-x\right)^2=\dfrac{5}{6}\)

=>\(\left(x-\dfrac{1}{3}\right)^2=\dfrac{31}{36}-\dfrac{5}{6}=\dfrac{31}{36}-\dfrac{30}{36}=\dfrac{1}{36}\)

=>\(\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{1}{6}\\x-\dfrac{1}{3}=-\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}+\dfrac{1}{3}=\dfrac{3}{6}=\dfrac{1}{2}\\x=-\dfrac{1}{6}+\dfrac{1}{3}=-\dfrac{1}{6}+\dfrac{2}{6}=\dfrac{1}{6}\end{matrix}\right.\)

i: \(\left(2x-3\right)\left(\dfrac{3}{4}x+1\right)=0\)

=>\(\left[{}\begin{matrix}2x-3=0\\\dfrac{3}{4}x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\\dfrac{3}{4}x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=-1:\dfrac{3}{4}=-\dfrac{4}{3}\end{matrix}\right.\)

k: \(2^x+2^{x+3}=144\)

=>\(2^x+2^x\cdot8=144\)

=>\(9\cdot2^x=144\)

=>\(2^x=\dfrac{144}{9}=16=2^4\)

=>x=4

m: ĐKXĐ: x>=-1

\(3\sqrt{x+1}-1=38\)

=>\(3\sqrt{x+1}=38+1=39\)

=>\(\sqrt{x+1}=13\)

=>x+1=169

=>x=168(nhận)


Các câu hỏi tương tự
Nguyễn Khôi  Nguyên
Xem chi tiết
vu duc huy
Xem chi tiết
Đinh Thị Mỹ Hạnh
Xem chi tiết
Chu Ngọc Huyền
Xem chi tiết
Han Rosie
Xem chi tiết
Trần Hiếu Anh
Xem chi tiết
hoàng phạm
Xem chi tiết
Hoàng Quốc Chính
Xem chi tiết
Phương Thúy Ngô
Xem chi tiết
Thảo Nguyễn Phương
Xem chi tiết