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1) \(5-\left(1+\dfrac{1}{3}\right):\left(1-\dfrac{1}{3}\right)\)
\(=5-\dfrac{4}{3}:\dfrac{2}{3}\)
\(=5-\dfrac{4}{3}\cdot\dfrac{3}{2}\)
\(=5-\dfrac{4}{2}\)
\(=5-2\)
\(=3\)
b) \(\left(1+\dfrac{2}{3}-\dfrac{5}{4}\right)-\left(1-\dfrac{5}{4}\right)+2022-\dfrac{2}{3}\)
\(=1+\dfrac{2}{3}-\dfrac{5}{4}-1+\dfrac{5}{4}++2022-\dfrac{2}{3}\)
\(=\left(1-1\right)+\left(\dfrac{2}{3}-\dfrac{2}{3}\right)+\left(-\dfrac{5}{4}+\dfrac{5}{4}\right)+2022\)
\(=0+0+0+2022\)
\(=2022\)
2) \(0,7^2\cdot x=0,49^2\)
\(\Rightarrow x=\dfrac{0,49^2}{0,7^2}\)
\(\Rightarrow x=\left(\dfrac{0,49}{0,7}\right)^2\)
\(\Rightarrow x=\left(0,7\right)^2\)
\(\Rightarrow x=0,49\)
b) \(x:\left(-0,5\right)^3=\left(0,5\right)^2\)
\(\Rightarrow x=\left(0,5\right)^2\cdot\left(-0,5\right)^3\)
\(\Rightarrow x=\left(-0,5\right)^5\)
\(\Rightarrow x=-\dfrac{1}{32}\)
2:
a: =>x*0,49=0,49^2
=>x=0,49
b: =>x=(0,5)^2*(-1)*(0,5)^3=-(0,5)^5
Câu 2:
1: =>x-1=5 hoặc x-1=-5
=>x=-4 hoặc x=6
2: =>|x-2|=6,75-0,75=6
=>x-2=6 hoặc x-2=-6
=>x=-4 hoặc x=8
4: =>|x|=22,5
=>x=22,5 hoặc x=-22,5
a) 5/3 : 0,5 = 4/3 : 0,1 . x
10/3 = 40/3.x
x = 1/4
b) 1816 = 2x.332
216.(32)16 = 2x .332
216.332 = 2x.332
=> 216 = 2.x
=> x = 216 : 2 = 215
\(a.\frac{5}{3}:0,5=\frac{4}{3}:0,1\times x\)
\(\Leftrightarrow\frac{4}{3}:0,1\times x=\frac{10}{3}\)
\(\frac{4}{3}:0,1=\frac{10}{3}:x\)
\(\frac{40}{3}=\frac{10}{3}:x\)
\(\Rightarrow x=\frac{10}{3}:\frac{40}{3}\)
\(x=\frac{1}{4}\)
\(b.18^{16}=2x.3^{32}\)
\(2^{16}.\left(3^{16}\right)^2=2x.3^{32}\)
\(2^{16}.\left(3^{32}\right)=2x.3^{32}\)
\(2^{16}=2x\)
\(\Rightarrow x=2^{16}:2\)
\(x=2^{15}\)
\(\)
a) 15/11 - (5/7 - 18/11) + 27/7
= 15/11 - 5/7 + 18/11 + 27/7
= (15/11 + 18/11) + (-5/7 + 27/7)
= 3 + 22/7
= 43/7
b) 39/5 + (9/4 - 9/5) - (5/4 + 1,2)
= 39/5 + 9/4 - 9/5 - 5/4 - 6/5
= (39/5 - 9/5 - 6/5) + (9/4 - 5/4)
= 24/5 + 1
= 29/5
c) -1,2 - 0,8 + 0,25 + 5,75 - 2022
= (-1,2 - 0,8) + (0,25 + 5,76) - 2022
= -2 + 6 - 2022
= 4 - 2022
= -2018
d) 0,1 + 16/9 + 5,1 + (-20/9)
= (0,1 + 5,1) + (16/9 - 20/9)
= 5,2 - 4/9
= 419/90
a) \(\dfrac{15}{11}-\left(\dfrac{5}{7}-\dfrac{18}{11}\right)+\dfrac{27}{7}=\dfrac{22}{7}+3=\dfrac{43}{77}\)
b) \(\dfrac{39}{5}+\left(\dfrac{9}{4}-\dfrac{9}{5}\right)-\left(\dfrac{5}{4}+\dfrac{6}{5}\right)=\dfrac{24}{5}+1=\dfrac{29}{5}\)
c) \(-1,2-0,8+0,25+5,75-2022=-2+6-2022=-2018\)
d) \(0,1+\dfrac{16}{9}+5,1+\dfrac{-20}{9}=\dfrac{26}{5}-\dfrac{4}{9}=\dfrac{214}{45}\)
1/
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{x-y}{5-6}=\dfrac{36}{-1}=-36\)
\(\Rightarrow\left\{{}\begin{matrix}x=-36\cdot5=-180\\y=-36\cdot6=-216\\z=-36\cdot4=-144\end{matrix}\right.\)
2/
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{y+z}{3+4}=\dfrac{28}{7}=4\)
\(\Rightarrow\left\{{}\begin{matrix}x=4\cdot7=28\\y=4\cdot3=12\\z=4\cdot4=16\end{matrix}\right.\)
3/
\(\dfrac{x}{1,2}=\dfrac{y}{1,3}\Leftrightarrow\dfrac{2x}{2,4}=\dfrac{y}{1,3}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{2x}{2,4}=\dfrac{y}{1,3}=\dfrac{2x-y}{2,4-1,3}=\dfrac{5,5}{1,1}=5\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{5\cdot2,4}{2}=6\\y=5\cdot1,3=6,5\\z=5\cdot1,4=7\end{matrix}\right.\)
4/
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{0,5}=\dfrac{y}{0,3}=\dfrac{x-y}{0,5-0,3}=\dfrac{1}{0,2}=5\)
\(\Rightarrow\left\{{}\begin{matrix}x=5\cdot0,5=2,5\\y=5\cdot0,3=1,5\\z=5\cdot0,2=1\end{matrix}\right.\)
5/
\(z=\dfrac{x}{0,3}\Leftrightarrow z=\dfrac{3x}{0,9}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(z=\dfrac{3x}{0,9}=\dfrac{z-3x}{1-0,9}=\dfrac{1}{0,1}=10\)
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{10\cdot0,9}{3}=3\\y=10\cdot0,7=7\\z=10\end{matrix}\right.\)
a: \(A=-\left|3x-1\right|+0.7< =0,7\)
Dấu '=' xảy ra khi x=1/3
b: |x+0,3|+0,5>=0,5
=>B<=1/0,5=2
Dấu '=' xảy ra khi x=-0,3
c: \(C=0.5\cdot\left|0.3x-2\right|+0.7>=0.7\)
Dấu '=' xảy ra khi x=2/0,3=20/3
Sử dụng máy tính và lần lượt thực hiện như sau:
(3,5)2 = 12.25
(-0,12)3 = -0,001728
(1,5)4 = 5,0625
(-0,1)5 = -0,00001
(1,2)6 = 2,985984
`@` `\text {Ans}`
`\downarrow`
`1)`
`5/7*37 13/23 - 51 13/23*5/7`
`= 5/7* (37 13/23 - 51 13/23)`
`= 5/7* (-14)`
`= -10`
`2)`
`-2/3 +1/3+0,5+2 1/2`
`= -2/3 + 1/3 + 1/2 + 5/2`
`= (-2/3+1/3) + (1/2+5/2)`
`= -1/3 + 3`
`=8/3`
`3)`
`-0,5+2/3+1/2`
`= -1/2 + 2/3 + 1/2`
`= (-1/2 + 1/2) + 2/3`
`= 2/3`
`4)`
`(8+2 1/3-3/5) -(5+0,4)-(3 1/2 -2)`
`= 8+ 7/3 - 3/5 - 5 - 0,4 - 7/2 + 2`
`= (8+2-5) + (-3/5 - 2/5) + (7/3 - 7/2)`
`= 5 - 1 - 7/6`
`= 4 - 7/6 = 17/6`
`5)`
`(2/9-7/12):3/4+(16/9-5/12):3/4`
`= (2/9 - 7/12) \times 4/3 + (16/9 - 5/12) \times 4/3`
`= 4/3 *(2/9 - 7/12 + 16/9 - 5/12)`
`= 4/3 * [(2/9 + 16/9) + (-7/12 - 5/12)]`
`= 4/3 * ( 2 - 1)`
`= 4/3 * 1 = 4/3`
`6)`
`-(2021.0,7+19,75) +0,7- (8-19,75)`
`= -2021*0,7 -19,75 + 0,7 - 8 + 19,75`
`= 0,7*(-2021 + 1) - 8`
`= -1414-8`
`= -1422`
`7)`
`15/34+7/21+19/34-20/15`
`= (15/34 + 19/34) + 7/21 - 20/15`
`= 1 + 7/21 - 20/15`
`= 4/3 - 20/15 =0`
`8)`
`2 5/6+1/6:(-5/8)`
`= 17/6 + (-4/15)`
`= 77/30`
`9)`
`(-2)^2 +2/9. (4/5-2/3)`
`= 4 + 2/9*2/15`
`= 4+4/135`
`= 544/135`
`10)`
`(-1/5+3/7):5/4+(-4/5+4/7):5/4`
`= (-1/5+3/7) * 4/5 + (-4/5+4/7) * 4/5`
`= 4/5*(-1/5 +3/7-4/5+4/7)`
`= 4/5*[(-1/5-4/5)+(3/7+4/7)]`
`= 4/5* (-1+1)`
`= 4/5*0=0`
`11)`
`2022,2021 . 1954,1945+ 2022,2021 . (-1954,1945)`
`= 2022,2021 * [1954,1945 + (-1954,1945)]`
`= 2022,2021*0 `
`= 0`
`12)`
`-5,2 .72 +69,1 +5,2 . (-28)+(-1,1)`
`= -5,2*72 + 69,1 - 5,2*28 - 1,1`
`= -5,2*(72+28) + (69,1 - 1,1)`
`= -5,2*100 + 68`
`= -520 + 68`
`= -452`
`13)`
`(7 -1/2-3/4) : (5-1/4-5/8)`
`= 23/4 \div 33/8`
`=46/33`
`14)`
`(8+ 2 1/3 -3/5) -(5+0,4) -( 3 1/3 - 2)`
`= 8+ 2 1/3 - 3/5 - 5 - 0,4 - 3 1/3 + 2`
`= (8+2-5) + (2 1/3 - 3 1/3) - (0,6 + 0,4) `
`= 5 - 1 - 1`
`= 3`
\(\frac{0,5}{0,7}\)=\(\frac{-0.1}{5.x}\)
→(0,5).5.x=-0,07
2,5.x=0,07
x=0,028
\(\frac{1,2}{x+3}\)=\(\frac{5}{4}\)
→5x+15=4,8
5x=-10,2
x=-2.04