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Bài 1:

\(A=-\frac25+\frac34\cdot\frac29\)

\(=-\frac25+\frac{6}{36}\)

\(=-\frac25+\frac16=-\frac{12}{30}+\frac{5}{30}=-\frac{7}{30}\)

\(B=\frac38\cdot\frac{-13}{15}-\frac38\cdot\frac{2}{15}+1\frac12\)

\(=\frac38\left(-\frac{13}{15}-\frac{2}{15}\right)+\frac32\)

\(=-\frac38+\frac32=-\frac38+\frac{12}{8}=\frac98\)

\(C=-\frac78+\frac{9}{10}\cdot\frac23\)

\(=-\frac78+\frac93\cdot\frac{2}{10}\)

\(=-\frac78+\frac35=-\frac{35}{40}+\frac{24}{40}=-\frac{11}{40}\)

\(D=\frac{5}{11}\cdot\frac{-17}{31}-\frac{5}{11}\cdot\frac{14}{31}+1\frac12\)

\(=-\frac{5}{11}\left(\frac{17}{31}+\frac{14}{31}\right)+\frac32\)

\(=-\frac{5}{11}+\frac32=-\frac{10}{22}+\frac{33}{22}=\frac{23}{22}\)

Bài 2:

a: \(\frac65-\frac15\cdot\frac{10}{3}\)

\(=\frac65-\frac{10}{5}\cdot\frac13=\frac65-\frac23\)

\(=\frac{18}{15}-\frac{10}{15}=\frac{8}{15}\)

b: \(\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)

\(=\left(\frac{11}{24}+\frac{13}{24}\right)-\left(\frac{5}{41}+\frac{36}{41}\right)+0,5\)

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

c: \(\frac12\cdot\frac{-3}{4}+\frac12\cdot\frac{-1}{4}+\frac23\)

\(=\frac12\left(-\frac34-\frac14\right)+\frac23\)

\(=-\frac12+\frac23=-\frac36+\frac46=\frac16\)

d: \(\frac13\cdot\frac{-5}{6}+\frac13\cdot\frac{-1}{6}+\frac12\)

\(=\frac13\left(-\frac56-\frac16\right)+\frac12\)

\(=-\frac13+\frac12=\frac16\)

Bài 3:

a: \(\frac{6}{x-7}=\frac{-3}{7}\)

=>\(\frac{6}{x-7}=\frac{-6}{14}\)

=>x-7=-14

=>x=-14+7=-7

b: \(-\frac35-x=\frac12\)

=>\(x=-\frac35-\frac12=-\frac{6}{10}-\frac{5}{10}=-\frac{11}{10}\)

c: \(x-\frac{3}{10}=\frac{7}{15}\cdot\frac{3}{14}\)

=>\(x-\frac{3}{10}=\frac{7}{14}\cdot\frac{3}{15}=\frac12\cdot\frac15=\frac{1}{10}\)

=>\(x=\frac{1}{10}+\frac{3}{10}=\frac{4}{10}=\frac25\)

d: \(\frac{5}{14}-x=-\frac{17}{36}:\frac{51}{18}\)

=>\(\frac{5}{14}-x=-\frac{17}{36}\cdot\frac{18}{51}=-\frac{17}{51}\cdot\frac{18}{36}\)

=>\(\frac{5}{14}-x=-\frac13\cdot\frac12=-\frac16\)

=>\(x=\frac{5}{14}+\frac16=\frac{15}{42}+\frac{7}{42}=\frac{22}{42}=\frac{11}{21}\)

e: \(-\frac34x+\frac14\left(x-1\right)=-\frac{12}{5}\)

=>\(-\frac34x+\frac14x-\frac14=-\frac{12}{5}\)

=>\(-\frac24x=-\frac{12}{5}+\frac14=-\frac{48}{20}+\frac{5}{20}=-\frac{43}{20}\)

=>\(\frac{x}{2}=\frac{43}{20}\)

=>\(x=\frac{43}{20}\cdot2=\frac{43}{10}\)

f: \(\left(2x-\frac49\right)\left(3-11x\right)=0\)

=>\(\left[\begin{array}{l}2x-\frac49=0\\ 3-11x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=\frac49\\ 11x=3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac49:2=\frac29\\ x=\frac{3}{11}\end{array}\right.\)

bài 6 làm như thế nào hả các bạn

27 tháng 8

Bài 3:

4; 45 + 5\(x\) = 10\(^3\): 10

45 + 5\(x\) = 100

5\(x\) = 100 - 45

5\(x\) = 55

\(x\) = 55 : 5

\(x\) = 11

Vậy \(x=11\)

5; 4\(x\) - 20 = 2\(^5\) : 2\(^2\)

4\(x\) - 20 = 2\(^3\)

4\(x\) = 8 + 20

4\(x\) = 28

\(x\) = 28 : 4

\(x=7\)

Vậy \(x=7\)

27 tháng 8

Bài 4:

1; 82 - (25 + 4\(x^{}\)) = 17

25 + 4\(x\) \(^{}\) = 82 - 17

4\(x^{}\) = 65 - 25

4\(x^{}\) = 40

\(x=40:4\)

\(x\) = 10

Vậy \(x=10\)

2; 71 - (24 + 3\(x\)) = 24

24 + 3\(x\) = 71 - 24

24 + 3\(x\) = 47

3\(x\) = 47 - 24

3\(x\) = 23

\(x\) = 23 : 3

Vậy \(x=\frac{23}{3}\)

3; 145 - (125 + \(x\)) = 12

125 + \(x\) = 145 - 12

125 + \(x\) = 133

\(x\) = 133 - 125

\(x\) = 8

Vậy \(x=8\)

c: \(\left(x-1\right)^3=\left(-9\right)^3\)

=>x-1=-9

=>x=-9+1=-8

f: \(3x-2^3=7+\left(-9\right)\)

=>3x-8=7-9=-2

=>3x=-2+8=6

=>x=2

a: \(640=2^7\cdot5;1440=2^5\cdot3^2\cdot5\)

=>ƯCLN(640;1440)\(=2^5\cdot5=32\cdot5=160\)

640⋮a; 1440⋮a

=>a∈ ƯC(640;1440)

mà a lớn nhất

nên a=ƯCLN(640;1440)=160

b: \(450=2\cdot3^2\cdot5^2;210=2\cdot3\cdot5\cdot7\)

=>ƯCLN(450;210)\(=2\cdot3\cdot5=30\)

450⋮a; 210⋮a

=>a∈ ƯC(450;210)

mà a lớn nhất

nên a=ƯCLN(450;210)=30

c: \(128=2^7;210=2\cdot3\cdot5\cdot7\)

=>ƯCLN(128;210)=2

128⋮a; 210⋮a

=>a∈ ƯC(128;210)

=>a∈ Ư(2)

mà 6<a<15

nên a∈∅

d: \(2350=2\cdot5^2\cdot47;1260=2^2\cdot3^2\cdot5\cdot7\)

=>ƯCLN(2350;1260)=\(2\cdot5=10\)

2350⋮a; 1260⋮a

=>a ∈ƯC(2350;1260)

=>a∈ Ư(10)

mà 80<a<140

nên a∈∅

e: \(112=2^4\cdot7;140=2^2\cdot5\cdot7\)

=>ƯCLN(112;140)\(=2^2\cdot7=28\)

112⋮a; 140⋮a

=>a ∈ƯC(112;140)

=>a∈ Ư(28)

mà 10<a<20

nên a=14

f: \(144=2^4\cdot3^2;192=2^6\cdot3\)

=>ƯCLN(144;192)\(=2^4\cdot3=16\cdot3=48\)

144⋮a; 192⋮a

=>a∈ ƯC(144;192)

=>a∈ Ư(48)

mà a<20

nên a∈{1;2;3;4;6;8;12;16}

g: \(420=2^2\cdot3\cdot5\cdot7;700=2^2\cdot5^2\cdot7\)

=>ƯCLN(420;700)\(=2^2\cdot5\cdot7=4\cdot5\cdot7=20\cdot7=140\)

420⋮a; 700⋮a

=>a∈ ƯC(420;700)

=>a∈ Ư(140)

mà a lớn nhất

nên a=140

S
22 tháng 8

bài 14:

\(a.\left(x-1\right)\cdot100=0\)

\(x-1=0\Rightarrow x=1\)

\(b.200-11x=24\)

\(11x=200-24\)

\(11x=176\)

\(x=\frac{176}{11}=16\)

\(c.165:\left(2x+1\right)=15\) (đkxđ: x khác \(-\frac12)\)

\(2x+1=\frac{165}{15}=11\)

\(2x=11-1=10\)

\(x=\frac{10}{2}=5\)

\(d.375:\left(45-4x\right)=15\) (đkxđ: \(x\ne\frac{45}{4})\)

\(45-4x=\frac{375}{15}=25\)

\(4x=45-25=20\)

\(x=20:4=5\)

bài 15:

giá tiền 125 chiếc điện thoại là:

125 x 2350000=293750000 (đồng)

giá tiền 250 chiếc máy tính bảng là:

250 x 4950000 = 1237500000 (đồng)

tổng số tiền mà cửa hàng phải trả cho số điện thoại và máy tính trên là:

293750000 + 1237500000 = 1531250000 (đồng)

đáp số: 1531250000 đồng

Bài 5:

a: \(37\cdot146+46\cdot2-46\cdot37\)

\(=37\left(146-46\right)+46\cdot2\)

\(=37\cdot100+92=3700+92=3792\)

b: \(2\cdot5\cdot71+5\cdot18\cdot2+10\cdot11\)

\(=10\cdot71+10\cdot18+10\cdot11\)

\(=10\left(71+18+11\right)=10\cdot100=1000\)

c: \(135+360+65+40\)

=135+65+360+40

=200+400

=600

d: \(27\cdot75+25\cdot27-450\)

\(=27\left(75+25\right)-450\)

=2700-450

=2250

Bài 4:

a: \(32\cdot163+32\cdot837\)

\(=32\cdot\left(163+837\right)\)

\(=32\cdot1000=32000\)

b: \(2\cdot3\cdot4\cdot5\cdot25=2\cdot5\cdot4\cdot25\cdot3=3\cdot10\cdot100=3000\)

c: \(25\cdot27\cdot4=27\cdot100=2700\)

Bài 3:

a: \(128\cdot19+128\cdot41+128\cdot40\)

\(=128\cdot\left(19+41+40\right)=128\cdot100=12800\)

b: \(375+693+625+307\)

=375+625+693+307

=1000+1000

=2000

c: \(37+42-37+22\)

=37-37+42+22

=0+64

=64

d: \(21\cdot32+21\cdot68\)

\(=21\cdot\left(32+68\right)=21\cdot100=2100\)

Bài 2:

a: \(17\cdot85+15\cdot17-120\)

\(=17\left(85+15\right)-120\)

=1700-120

=1580

b: \(189+73+211+127\)

=189+211+73+127

=400+200

=600

c: \(38\cdot73+27\cdot38\)

\(=38\left(73+27\right)=38\cdot100=3800\)

Bài 1:

a: \(28\cdot76+23\cdot28-28\cdot13\)

\(=28\left(76+23-13\right)=28\cdot86=2408\)

b: \(39\cdot50+25\cdot39+75\cdot61\)

\(=39\left(50+25\right)+75\cdot61\)

\(=39\cdot75+75\cdot61=75\left(39+61\right)=75\cdot100=7500\)

c: \(32\cdot163+837\cdot32\)

\(=32\left(163+837\right)=32\cdot1000=32000\)

d: \(63+118+37+82\)

=63+37+118+82

=100+200

=300

NV
5 tháng 9

20.

a.

\(4^{n}=256\)

\(4^{n}=4^4\)

\(n=4\)

b.

\(9^{5n-8}=81\)

\(9^{5n-8}=9^2\)

5n-8=2

5n=10

n=2

c.

\(3^{n+2}:27=3\)

\(3^{n+2}=27.3\)

\(3^{n+2}=81\)

\(3^{n+2}=3^4\)

n+2=4

n=2

d.

\(8^{n+2}.2^3=8^5\)

\(8^{n+2}=8^5:2^3\)

\(8^{n+2}=8^4\)

n+2=4

n=2

NV
5 tháng 9

21.

a.

\(30-2x^2=12\)

\(2x^2=30-12\)

\(2x^2=18\)

\(x^2=18:2=9\)

\(x^2=3^2\)

\(x=\pm3\)

b.

\(\left(9-2x\right)^3=125\)

\(\left(9-2x\right)^3=5^3\)

\(9-2x=5\)

2x=9-5=4

x=2

c.

\(\left(2x-2\right)^4=0\)

2x-2=0

2x=2

x=1

d.

\(\left(x+5\right)^3=\left(2x\right)^3\)

x+5=2x

2x-x=5

x=5