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![](https://rs.olm.vn/images/avt/0.png?1311)
Nửa chu vi hình chữ nhật là 18:2=9(cm)
Chu vi không đổi thì nửa chu vi cũng không đổi
Tỉ số giữa chiều dài mới so với chiều dài cũ là:
100%-20%=0,8
Tỉ số giữa chiều rộng mới so với chiều rộng cũ là:
25%+100%=125%=1,25
0,8xchiềudài+1,25x chiều rộng=9
=>chiều dài+1,5625 chiều rộng=11,25
mà chiều dài+chiều rộng=9
nên 0,5625 lần chiều rộng là 11,25-9=2,25
=>Chiều rộng là 2,25:0,5625=4(cm)
=>Chiều dài là 9-4=5(cm)
Diện tích hình chữ nhật là \(5\cdot4=20\left(cm^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\left(1^1+2^2+3^3+...+2022^{2022}\right)^{2023}\cdot\left(8^2-576:3^2\right)^{2024}\)
\(=\left(1^1+2^2+3^3+...+2022^{2022}\right)^{2023}\cdot\left(64-576:9\right)^{2024}\)
\(=\left(1^1+2^2+3^3+...+2022^{2022}\right)^{2023}\cdot\left(64-64\right)^{2024}\)
=0
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
a: \(45\%\cdot x-0,385=-1,685\)
=>\(0,45x=-1,685+0,385=-1,3\)
=>\(x=-\dfrac{1.3}{0,45}=-\dfrac{26}{9}\)
b: \(\left(3\dfrac{1}{4}+2x\right)\cdot\dfrac{2}{3}=2\)
=>\(2x+\dfrac{13}{4}=2:\dfrac{2}{3}=3\)
=>\(2x=3-\dfrac{13}{4}=-\dfrac{1}{4}\)
=>\(x=-\dfrac{1}{4}:2=-\dfrac{1}{8}\)
c: \(\dfrac{3}{4}+\dfrac{1}{4}:x=-3\)
=>\(\dfrac{1}{4}:x=-3-\dfrac{3}{4}=-\dfrac{15}{4}\)
=>\(x=\dfrac{1}{4}:\dfrac{-15}{4}=\dfrac{-1}{15}\)
d: \(2x-0,75=-\dfrac{7}{12}\)
=>\(2x=-\dfrac{7}{12}+0,75=\dfrac{2}{12}\)
=>\(x=\dfrac{1}{12}\)
e: \(\dfrac{4}{9}-\dfrac{7}{12}x=\dfrac{1}{3}\)
=>\(\dfrac{7}{12}x=\dfrac{4}{9}-\dfrac{1}{3}=\dfrac{1}{9}\)
=>\(x=\dfrac{1}{9}:\dfrac{7}{12}=\dfrac{1}{9}\cdot\dfrac{12}{7}=\dfrac{4}{21}\)
Bài 1:
a: \(\left(\dfrac{7}{5}+\dfrac{-5}{11}\right)-\left(\dfrac{6}{11}-\dfrac{3}{5}\right)-2023^0\)
\(=\dfrac{7}{5}-\dfrac{5}{11}-\dfrac{6}{11}+\dfrac{3}{5}-1\)
\(=2-1-1=0\)
b: \(\dfrac{2}{-9}\cdot\dfrac{7}{15}+\dfrac{-2}{9}\cdot\dfrac{8}{15}+1\dfrac{2}{3}\)
\(=\dfrac{-2}{9}\left(\dfrac{7}{15}+\dfrac{8}{15}\right)+\dfrac{5}{3}\)
\(=-\dfrac{2}{9}+\dfrac{5}{3}=\dfrac{13}{9}\)
c: \(\dfrac{1}{3}+\dfrac{-7}{12}+\dfrac{2}{3}+\dfrac{-5}{12}\)
\(=\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(-\dfrac{7}{12}-\dfrac{5}{12}\right)\)
=1-1
=0
d: \(\dfrac{3}{7}\cdot\dfrac{-9}{13}+\dfrac{3}{7}\cdot\dfrac{-4}{13}+1\dfrac{3}{7}\)
\(=\dfrac{3}{7}\left(-\dfrac{9}{13}-\dfrac{4}{13}\right)+1+\dfrac{3}{7}\)
\(=-\dfrac{3}{7}+1+\dfrac{3}{7}\)
=1
e: \(\dfrac{2}{-5}-\left(\dfrac{5}{2}-\dfrac{12}{5}\right)\)
\(=-\dfrac{2}{5}-\dfrac{5}{2}+\dfrac{12}{5}=2-\dfrac{5}{2}=-\dfrac{1}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
a: \(\dfrac{1}{12}+\dfrac{3}{4}-\dfrac{5}{8}\)
\(=\dfrac{2}{24}+\dfrac{18}{24}-\dfrac{15}{24}=\dfrac{5}{24}\)
bài 2:
a: \(x-\dfrac{12}{3}=\dfrac{1}{3}\)
=>\(x=\dfrac{1}{3}+\dfrac{12}{3}=\dfrac{13}{3}\)
b: \(\left(2,8x-32\right):\dfrac{6}{3}=-30\)
=>\(2,8x-32=-30\cdot2=-60\)
=>2,8x=-28
=>x=-10
Bài 3:
a: Huyện B góp được \(\dfrac{5}{6}\cdot72=60\left(tấn\right)\)
Huyện C góp được \(60:\dfrac{4}{5}=75\left(tấn\right)\)
Cả ba huyện góp được: 72+60+75=207(tấn)
b: Tỉ số phần trăm giữa số rau ở huyện A và số rau ở huyện B là:
\(72:60=120\%\)
![](https://rs.olm.vn/images/avt/0.png?1311)
9: \(A=\dfrac{3^2}{10}+\dfrac{3^2}{40}+...+\dfrac{3^2}{340}\)
\(=3\left(\dfrac{3}{10}+\dfrac{3}{40}+...+\dfrac{3}{340}\right)\)
\(=3\left(\dfrac{3}{2\cdot5}+\dfrac{3}{5\cdot8}+...+\dfrac{3}{17\cdot20}\right)\)
\(=3\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+...+\dfrac{1}{17}-\dfrac{1}{20}\right)\)
\(=3\left(\dfrac{1}{2}-\dfrac{1}{20}\right)=3\cdot\dfrac{9}{20}=\dfrac{27}{20}\)
10: \(A=\dfrac{5^2}{1\cdot6}+\dfrac{5^2}{6\cdot11}+...+\dfrac{5^2}{26\cdot31}\)
\(=5\left(\dfrac{5}{1\cdot6}+\dfrac{5}{6\cdot11}+...+\dfrac{5}{26\cdot31}\right)\)
\(=5\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{25}-\dfrac{1}{31}\right)\)
\(=5\left(1-\dfrac{1}{31}\right)=5\cdot\dfrac{30}{31}=\dfrac{150}{31}\)
11: \(A=\dfrac{6}{15}+\dfrac{6}{35}+\dfrac{6}{63}+\dfrac{6}{99}\)
\(=3\left(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+\dfrac{2}{99}\right)\)
\(=3\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}\right)\)
\(=3\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\right)\)
\(=3\left(\dfrac{1}{3}-\dfrac{1}{11}\right)=3\cdot\dfrac{8}{33}=\dfrac{8}{11}\)
12: \(A=\dfrac{3}{3\cdot5}+\dfrac{3}{5\cdot7}+...+\dfrac{3}{49\cdot51}\)
\(=\dfrac{3}{2}\left(\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{49\cdot51}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{49}-\dfrac{1}{51}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{3}-\dfrac{1}{51}\right)=\dfrac{3}{2}\cdot\dfrac{16}{51}=\dfrac{8}{17}\)
13: \(A=\dfrac{1}{2}+\dfrac{2}{2\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{5}{11\cdot16}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}\)
\(=1-\dfrac{1}{16}=\dfrac{15}{16}\)
14: \(A=\dfrac{1}{2}+\dfrac{2}{8}+\dfrac{3}{28}+\dfrac{4}{77}+\dfrac{5}{176}\)
\(=\dfrac{1}{1\cdot2}+\dfrac{2}{2\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{5}{11\cdot16}\)
15: \(A=\dfrac{3}{54}+\dfrac{5}{126}+\dfrac{7}{294}+\dfrac{8}{609}\)
\(=\dfrac{3}{6\cdot9}+\dfrac{5}{9\cdot14}+\dfrac{7}{14\cdot21}+\dfrac{8}{21\cdot29}\)
\(=\dfrac{1}{6}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{29}\)
\(=\dfrac{1}{6}-\dfrac{1}{29}=\dfrac{23}{174}\)
16: \(A=\dfrac{5}{24}+\dfrac{5}{104}+\dfrac{5}{234}+\dfrac{5}{414}\)
\(=\dfrac{5}{3\cdot8}+\dfrac{5}{8\cdot13}+\dfrac{5}{13\cdot18}+\dfrac{5}{18\cdot23}\)
\(=\dfrac{1}{3}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{23}\)
\(=\dfrac{1}{3}-\dfrac{1}{23}=\dfrac{20}{69}\)
17: \(A=\dfrac{\dfrac{3}{54}+\dfrac{5}{126}+\dfrac{7}{294}}{\dfrac{5}{24}+\dfrac{5}{104}+\dfrac{5}{234}}\)
\(=\dfrac{\dfrac{1}{6}-\dfrac{1}{21}}{\dfrac{1}{3}-\dfrac{1}{18}}=\dfrac{15}{126}:\dfrac{15}{54}=\dfrac{54}{126}=\dfrac{3}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\dfrac{5\cdot4^6\cdot9^4-3^9\cdot\left(-8\right)^4}{4\cdot2^{13}\cdot3^8+2\cdot8^4\cdot\left(-27\right)^3}\)
\(=\dfrac{5\cdot2^{12}\cdot3^8-3^9\cdot2^{12}}{2^{15}\cdot3^8-2^{13}\cdot3^9}\)
\(=\dfrac{2^{12}\cdot3^8\left(5-3\right)}{2^{13}\cdot3^8\left(2^2-3\right)}\)
\(=\dfrac{2^{13}}{2^{13}}=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 1: B
Câu 2: D
Câu 3: B
Câu 4: C
Câu 5: A
Câu 6: B
Câu 7: C
Câu 8: B
Câu 9: C
Câu 10: D
Câu 11: D
Câu 12: C
Bài 1:
a: \(\dfrac{7}{30}+\dfrac{-12}{37}+\dfrac{23}{30}+\dfrac{-25}{37}\)
\(=\left(\dfrac{7}{30}+\dfrac{23}{30}\right)+\left(-\dfrac{12}{37}-\dfrac{25}{37}\right)\)
\(=\dfrac{30}{30}+\dfrac{-37}{37}=1-1=0\)
b: \(\dfrac{-20}{23}+\dfrac{8}{15}-\dfrac{3}{23}+\dfrac{7}{15}+\dfrac{1}{2}\)
\(=\left(-\dfrac{20}{23}-\dfrac{3}{23}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)+\dfrac{1}{2}\)
\(=-1+1+\dfrac{1}{2}=\dfrac{1}{2}\)
c: \(\left(-12,5\right)+17,55+\left(-3,5\right)+2,45\)
\(=\left(-12,5-3,5\right)+\left(17,55+2,45\right)\)
=20-16
=4
d: \(\left(-9,237\right)+3,8+1,237-3,8+1,123\)
\(=\left(-9,237+1,237\right)+\left(3,8-3,8\right)+1,123\)
=-8+1,123
=-6,877
e: \(4,35-\left(2,67-1,65\right)+\left(3,54-6,33\right)\)
\(=4,35-2,67+1,65+3,54-6,33\)
\(=6-9+3,54=3,54-3=0,54\)
g: \(\dfrac{5}{7}\cdot\dfrac{5}{11}+\dfrac{5}{7}\cdot\dfrac{2}{11}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)
\(=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\cdot\dfrac{-7}{11}=-\dfrac{5}{11}\)
h: \(\dfrac{-5}{7}\cdot\dfrac{3}{13}+\dfrac{-5}{7}\cdot\dfrac{10}{13}+1\dfrac{5}{7}\)
\(=-\dfrac{5}{7}\left(\dfrac{3}{13}+\dfrac{10}{13}\right)+\dfrac{12}{7}=-\dfrac{5}{7}+\dfrac{12}{7}=\dfrac{7}{7}=1\)
i: \(3,58\cdot24,45+3,58\cdot75,55+12,42\)
\(=3,58\left(24,45+75,55\right)+12,42\)
\(=358+12,42=370,42\)
k: \(3,4\cdot\left(-23,68\right)-3,4\cdot45,12+\left(-31,2\right)\cdot3,4\)
\(=3,4\left(-23,68-45,12-31,2\right)\)
\(=3,4\cdot\left(-100\right)=-340\)
l: \(1,14\cdot6,4+1,14\cdot3,6+11,4\)
\(=1,14\left(6,4+3,6\right)+1,14\cdot10\)
\(=1,14\cdot20=22,8\)
Giúp mk với!