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Bài 2:
Chiều cao trung bình của 8 bạn trong tổ 1 là:
115 : 8 = \(\dfrac{115}{8}\) (dm)
Chiều cao trung bình của 10 bạn trong tổ 2 là:
138 : 10 = \(\dfrac{69}{5}\) (dm)
\(\dfrac{115}{8}\) = \(\dfrac{115\times5}{8\times5}\) = \(\dfrac{575}{40}\)
\(\dfrac{69}{5}\) = \(\dfrac{69\times8}{5\times8}\) = \(\dfrac{552}{40}\)
Vì \(\dfrac{575}{40}\) > \(\dfrac{552}{40}\)
Vậy chiều cao trung bình của các bạn tổ 1 lớn hơn chiều cao trung bình của các bạn tổ 2
Bài 3:
a; \(\dfrac{-11}{5}\) < \(\dfrac{-10}{5}\) = -2
\(\dfrac{-7}{4}\) > \(\dfrac{-8}{4}\) = - 2
\(\Rightarrow\) \(\dfrac{-11}{5}\) < \(\dfrac{-7}{4}\)
b; \(\dfrac{2020}{-2021}\) > - 1
\(\dfrac{-2022}{2021}\) < -1
Vậy \(\dfrac{2020}{-2021}\) > \(\dfrac{-2022}{2021}\)
a) 3/8 = 81/216
5/27 = 40/216
b) 17/420 = 68/1680
-9/80 = -189/1680
c) 11/120
7/40 = 21/120
d) -7/10 = -231/330
1/33 = 10/330
g) 3/(-7) = -9/21
2/3 = 14/21
-1/3 = -7/21
h) -4/7 = -36/63
8/9 = 72/63
-10/21 = -30/63
l) 10/42 = 220/924
-3/28 = -99/924
-55/132 = -385/924
m) 5/(2².3) = 5/12 = 110/264
7/(2³.11) = 7/88 = 21/264
Câu 1:
\(M=132-\left\{100-\left[\left(78-73\right)^2:5+9\right]\right\}\)
\(=132-\left\{100-\left[5^2:5+9\right]\right\}\)
\(=132-100+5+9\)
=32+14
=46
Câu 2:
105-[(2x+7)-13]=25
=>(2x+7)-13=105-25=90
=>2x-6=90
=>2x=96
=>x=96/2=48
Câu 4:
\(N=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{99\cdot101}\)
\(=\dfrac{1}{2}\cdot\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{99\cdot101}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)
\(=\dfrac{1}{2}\left(1-\dfrac{1}{101}\right)=\dfrac{1}{2}\cdot\dfrac{100}{101}=\dfrac{50}{101}\)
Câu 5:
\(xy-x+2y=3\)
\(\Rightarrow xy-x+2y-2=3-2\)
\(\Rightarrow\left(xy-x\right)+\left(2y-2\right)=1\)
\(\Rightarrow x\left(y-1\right)+2\left(y-1\right)=1\)
\(\Rightarrow\left(x+2\right)\left(y-1\right)=1\)
Ta có bảng sau:
| \(x+2\) | \(1\) | \(-1\) |
| \(y-1\) | \(1\) | \(-1\) |
| \(x\) | \(-1\) | \(-3\) |
| \(y\) | \(2\) | \(0\) |
Vậy các cặp (x;y) là (-1;2) ; (-3;0)
#YM
Bài 3:
Để A là số nguyên thì \(2n+7⋮n+3\)
=>\(2n+6+1⋮n+3\)
=>\(1⋮n+3\)
=>\(n+3\in\left\{1;-1\right\}\)
=>\(n\in\left\{-2;-4\right\}\)
Bài 4:
Để A là số nguyên thì \(2n+7⋮n+1\)
=>\(2n+2+5⋮n+1\)
=>\(5⋮n+1\)
=>\(n+1\in\left\{1;-1;5;-5\right\}\)
=>\(n\in\left\{0;-2;4;-6\right\}\)
Bài 5:
Để A là số nguyên thì \(6n-3⋮3n+1\)
=>\(6n+2-5⋮3n+1\)
=>\(-5⋮3n+1\)
=>\(3n+1\in\left\{1;-1;5;-5\right\}\)
=>\(3n\in\left\{0;-2;4;-6\right\}\)
=>\(n\in\left\{0;-\dfrac{2}{3};\dfrac{4}{3};-2\right\}\)
mà n nguyên
nên \(n\in\left\{0;-2\right\}\)
Bài 6:
Để A là số nguyên thì \(3n+4⋮n-1\)
=>\(3n-3+7⋮n-1\)
=>\(7⋮n-1\)
=>\(n-1\in\left\{1;-1;7;-7\right\}\)
=>\(n\in\left\{2;0;8;-6\right\}\)
Bài 1:
\(A=3+3^2+...+3^{100}\)
=>\(3\cdot A=3^2+3^3+...+3^{101}\)
=>\(3A-A=3^2+3^3+...+3^{101}-3-3^2-...-3^{100}\)
=>\(2A=3^{101}-3\)
=>\(2A+3=3^{101}\)
mà \(2A+3=3^n\)
nên n=101
Bài 2:
a: \(M=3+3^2+3^3+3^4+...+3^{100}\)
\(=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^{99}+3^{100}\right)\)
\(=\left(3+3^2\right)+3^2\left(3+3^2\right)+...+3^{98}\left(3+3^2\right)\)
\(=12\left(1+3^2+...+3^{98}\right)⋮12\)
=>\(M=4\cdot3\cdot\left(1+3^2+...+3^{98}\right)⋮4\)
b: \(M=3+3^2+...+3^{100}\)
=>\(3M=3^2+3^3+...+3^{101}\)
=>\(3M-M=3^2+3^3+...+3^{101}-3-3^2-...-3^{100}\)
=>\(2M=3^{101}-3\)
=>\(2M+3=3^{101}\)
=>n=101
Bài 4:
a) 2x + 7 ⋮ x + 2
⇒ 2x + 4 + 3 ⋮ x + 2
⇒ 2(x + 2) + 3 ⋮ x + 2
⇒ 3 ⋮ x + 2
⇒ x + 2 ∈ Ư(3) = {1; -1; 3; -3}
⇒ x ∈ {-1; -3; 1; -5}
b) 2x + 7 ⋮ x - 3
⇒ 2x - 6 + 13 ⋮ x - 3
⇒ 2(x - 3) + 13 ⋮ x - 3
⇒ 13 ⋮ x - 3
⇒ x - 3 ∈ Ư(13) = {1; -1; 13; -13}
⇒ x ∈ {4; 2; 16; -10}
Bài 6:
a: \(3x-13⋮x+3\)
=>\(3x+9-22⋮x+3\)
=>\(-22⋮x+3\)
=>\(x+3\in\left\{1;-1;2;-2;11;-11;22;-22\right\}\)
=>\(x\in\left\{-2;-4;-1;-5;8;-14;19;-25\right\}\)
b: \(2x+24⋮x-4\)
=>\(2x-8+32⋮x-4\)
=>\(32⋮x-4\)
=>\(x-4\in\left\{1;-1;2;-2;4;-4;8;-8;16;-16;32;-32\right\}\)
=>\(x\in\left\{5;3;6;2;8;0;12;-4;20;-12;36;-28\right\}\)
Bài 5:
a: \(4x+3⋮x-2\)
=>\(4x-8+11⋮x-2\)
=>\(11⋮x-2\)
=>\(x-2\in\left\{1;-1;11;-11\right\}\)
=>\(x\in\left\{3;1;13;-9\right\}\)
b: \(2x+7⋮x-3\)
=>\(2x-6+13⋮x-3\)
=>\(13⋮x-3\)
=>\(x-3\in\left\{1;-1;13;-13\right\}\)
=>\(x\in\left\{4;2;16;-10\right\}\)
Bài 4:
a: \(2x+7⋮x+2\)
=>\(2x+4+3⋮x+2\)
=>\(3⋮x+2\)
=>\(x+2\in\left\{1;-1;3;-3\right\}\)
=>\(x\in\left\{-1;-3;1;-5\right\}\)
b: \(2x+7⋮x-3\)
=>\(2x-6+13⋮x-3\)
=>\(13⋮x-3\)
=>\(x-3\in\left\{1;-1;13;-13\right\}\)
=>\(x\in\left\{4;2;16;-10\right\}\)
Bài 2:
\(a,\dfrac{-1}{3}.\dfrac{5}{7}=\dfrac{-5}{21}\\ b,\dfrac{1}{2}.\dfrac{-3}{4}=\dfrac{-3}{8}\\ c,\dfrac{19}{7}.\dfrac{7}{15}=\dfrac{19.1}{1.15}=\dfrac{19}{15}\\ d,\dfrac{5}{11}:\left(-9\right)=\dfrac{5}{11}.\dfrac{-1}{9}=\dfrac{-5}{99}\\ e,-1:\dfrac{3}{5}=-1.\dfrac{5}{3}=-\dfrac{5}{3}\\ f,\dfrac{-2}{9}:\dfrac{2}{9}:\dfrac{-9}{14}=-\left(\dfrac{2}{9}:\dfrac{2}{9}\right).\dfrac{-14}{9}=-1.\dfrac{-14}{9}=\dfrac{14}{9}\\ k,\left(-\dfrac{2}{7}\right)^2=\left(-1\right)^2.\left(\dfrac{2}{7}\right)^2=1.\dfrac{2^2}{7^2}=\dfrac{4}{49}\\ l,\dfrac{1}{3}.\left(\dfrac{1}{3}\right)^3=\left(\dfrac{1}{3}\right)^4=\dfrac{1^4}{3^4}=\dfrac{1}{243}\\ m,\left(-\dfrac{1}{2}\right)^2.\left(\dfrac{1}{2}\right)^3=\left(-1\right)^2.\left(\dfrac{1}{2}\right)^{2+3}=1.\left(\dfrac{1}{2}\right)^5=1.\dfrac{1^5}{2^5}=\dfrac{1}{32}\)
Bài 1:
\(a,\dfrac{1}{-8}+\dfrac{-5}{8}=\dfrac{-1}{8}+\dfrac{-5}{8}=\dfrac{-\left(1+5\right)}{8}=-\dfrac{6}{8}=\dfrac{-6:2}{8:2}=-\dfrac{3}{4}\\ b,\dfrac{1}{7}+\dfrac{-3}{7}=\dfrac{1-3}{7}=-\dfrac{2}{7}\\ c,\dfrac{-12}{35}+\dfrac{-7}{35}=\dfrac{-\left(12+7\right)}{35}=\dfrac{-19}{35}\\ d,\dfrac{1}{6}+\dfrac{2}{5}=\dfrac{1.5+2.6}{6.5}=\dfrac{5+12}{30}=\dfrac{17}{30}\\ e,\dfrac{3}{5}+\dfrac{-7}{4}=\dfrac{3.4-7.5}{5.4}=\dfrac{12-35}{20}=\dfrac{-23}{20}\\ g,-2-\left(-\dfrac{1}{5}\right)=-2+\dfrac{1}{5}=\dfrac{-2.5+1}{5}=\dfrac{-9}{5}\\ h,\dfrac{2}{3}-\left(-1\right)=\dfrac{2}{3}+1=\dfrac{5}{3}\\ i,4-\dfrac{2}{3}=\dfrac{4.3-2}{3}=\dfrac{12-2}{3}=\dfrac{10}{3}\\ j,\dfrac{3}{4}-2=\dfrac{3-2.4}{4}=\dfrac{-5}{4}\\ k,-1-\left(-\dfrac{2}{3}\right)=-1+\dfrac{2}{3}=\dfrac{-1.3+2}{3}=\dfrac{-3+2}{3}=-\dfrac{1}{3}\)