\(a)\frac{7}{10^2+6.10}\)giúp mik với các bn ơi.
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Ta có: \(\dfrac{3}{2\cdot6}+\dfrac{3}{6\cdot10}+\dfrac{3}{10\cdot14}+...+\dfrac{3}{26\cdot30}\)
\(=\dfrac{3}{4}\left(\dfrac{4}{2\cdot6}+\dfrac{4}{6\cdot10}+\dfrac{4}{10\cdot14}+...+\dfrac{4}{26\cdot30}\right)\)
\(=\dfrac{3}{4}\left(\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{14}+...+\dfrac{1}{26}-\dfrac{1}{30}\right)\)
\(=\dfrac{3}{4}\left(\dfrac{1}{2}-\dfrac{1}{30}\right)\)
\(=\dfrac{3}{4}\cdot\dfrac{7}{15}=\dfrac{21}{60}=\dfrac{7}{20}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a)Ta có : \(A=\frac{10^{2014}+5}{10^{2014}-2}\)
=> \(A-1=\frac{10^{2014}+5-\left(10^{2014}-2\right)}{10^{2014}-2}=\frac{7}{10^{2014}-2}\)
Lại có : \(B=\frac{10^{2014}}{10^{2014}-7}\)
=> B - 1 = \(\frac{10^{2014}-\left(10^{2014}-7\right)}{10^{2014}-7}=\frac{7}{10^{2014}-7}\)
Vì : \(\frac{7}{10^{2014}-2}< \frac{7}{10^{2014}-7}\)
nên A - 1 < B - 1
=> A < B
b) Ta có : 4x + 1295 = 6y
=> 6y - 4x = 1295
Với x ; y \(\inℕ\)
=> 4x ; 6y \(\inℕ\)
mà 6y - 4x = 1295 (1)
=> 6y > 4x ; 6y > 1295
Vì 6y > 1295
=> \(y\ge4\)
Ta xét các trường hợp
Nếu \(x;y>0\)
=> 6y ; 4x chẵn
=> 6y - 4x chẵn (loại vì 1295 lẻ)
Nếu x = 0 ; y > 0
Khi đó (1) <=> 6y - 1 = 1295
=> 6y = 1296
=> 6y = 64
=> y = 4 (tm)
Vậy x = 0 ; y = 4
![](https://rs.olm.vn/images/avt/0.png?1311)
\(-\frac{2}{3}.\left|-\frac{1}{2}x-\frac{1}{3}\right|=0\)
\(\Rightarrow\left|-\frac{1}{2}x-\frac{1}{3}\right|=0\)
\(\Rightarrow-\frac{1}{2}x-\frac{1}{3}=0\)
\(\Rightarrow-\frac{1}{2}x=\frac{1}{3}\)
\(\Rightarrow x=-\frac{2}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{10}{7}\cdot\frac{2}{3}+\frac{5}{6}:\frac{3}{10}-\frac{2}{3}\cdot\frac{3}{7}\)
\(=\left(\frac{10}{7}\cdot\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{7}\right)+\frac{5}{6}\cdot\frac{10}{3}\)
\(=\frac{2}{3}\left(\frac{10}{7}-\frac{3}{7}\right)+\frac{5\cdot10}{6\cdot3}\)
\(=\frac{2}{3}\cdot1+\frac{25}{9}\)
\(=\frac{2}{3}+\frac{25}{9}\)
\(=\frac{31}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(\frac{-3}{42}+\frac{10}{-21}-\frac{-9}{14}\right).\left(\frac{-7}{5}\right).\)
\(=\left(\frac{-1}{14}-\frac{10}{21}+\frac{9}{14}\right).\left(\frac{-7}{5}\right)\)
\(\left(\frac{12}{21}-\frac{10}{21}\right).\left(\frac{-7}{5}\right)=\frac{2.\left(-7\right)}{21.5}=\frac{-2}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{1}{7}\cdot\frac{2}{3}+\frac{5}{6}:\frac{3}{10}-\frac{2}{3}\cdot\frac{3}{7}\)
\(=\left(\frac{1}{7}\cdot\frac{2}{3}-\frac{2}{3}\cdot\frac{3}{7}\right)+\frac{5}{6}\cdot\frac{10}{3}\)
\(=\frac{2}{3}\cdot\left(-\frac{2}{7}\right)+\frac{5}{3}\cdot\frac{5}{3}\)
\(=-\frac{4}{21}+\frac{25}{6}=\frac{167}{42}\)
Xin lỗi không nhanh được
![](https://rs.olm.vn/images/avt/0.png?1311)
Tính bằng các thuận tiện nhất: 10/7 x 2/3 + 6/5 : 3/10 - 2/3 x 3/7
trả lời:
10/7 x 2/3 + 6/5 : 3/10 - 2/3 x 3/7=10/7 x 2/3 + 6/5. 10/3 - 2/3 x 3/7=10/7 x 2/3 + 2/3.2- 2/3 x 3/7
=2/3.(10/7+2-3/7)=2/3.3=2
10/7 x 2/3 + 6/5 : 3/10 - 2/3 x 3/7
= 10/7 x 2/3 + 6/5 x 10/3 - 2/3 x 3/7
= 10/7 x 2/3 + 6/5 x 5 x 2/3 - 2/3 x 3/7
= 10/7 x 2/3 + 6 x 2/3 - 2/3 x 3/7
= 2/3 x (6 + 10/7 - 3/7)
= 2/3 x (6 + 1)
= 2/3 x 7
= 14/3
CHúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
a)x : 3 - 7 * 2 = 1,56
x : 3 - 14 = 1,56
x : 3 = 1,56 + 14
x : 3 = 15,56
x = 15,56 * 3
x = 46,68
b)nếu dấu chấm trên đề là dấu phẩy thì:
x : 6,4 = 1,248
x = 1,248 * 6,4
x = 7,9872
c)(x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 40
x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 40
(x + x + x + x + x) + (1 + 2 + 3 + 4 + 5) = 40
5 * x + 15 = 40
5 * x = 40 - 15
5 * x = 25
x = 25 : 5
x = 5
A) X:3 - 7 * 2 = 1,56
X:3-14=1,56
X:3=1,56+14
X:3=5,56
X= 5,56* 3 =16,68
B) X : 6 . 4 = 1 ,248
X = 1,248 :4 *6
X=1,872
C) ĐỀ DÀI LÀM LUN
= 5X + (1+2+3+4+5) =40
5X+15 =40
5X= 40-15=25
X= 25:5=5
7/-500 nhá
`Answer:`
\(\frac{7}{10^2-6.10^2}\) (Mình sửa đề nhé.)
\(=\frac{7}{100-6.100}\)
\(=\frac{7}{100.1-6.100}\)
\(=\frac{7}{\left(1-6\right).100}\)
\(=\frac{7}{\left(-5\right).100}\)
\(=\frac{7}{-500}\)