`#3107.101107`

`76.`

`a)`

\(4,278;4,728;42,78;42,87;427,8;472,8\)

`b)`

\(5,87;5,78;4,2;4,02;4,002;3,5\)

`77.`

`a)`

- Các số được lập ra: \(42,5;24,5;54,2;45,2;52,4;25,4\)

`b)`

- Từ lớn đến bé: \(24,5;25,4;42,5;45,2;52,4;54,2\)

`#3107.101107`

`9)`

Ta có:

`|a| = |41,25| = 41,25`

`|b| = |-53,12| = 53,12`

Vì `53,12 > 41,25 \rightarrow |a| < |b|`

`10)`

Để \(\dfrac{14}{\sqrt{n}-5}\) là số nguyên

\(\Rightarrow\dfrac{14}{\sqrt{n}-5}\in Z\)

\(\Rightarrow\) `14 \vdots (\sqrt{n} - 5)`

`\Rightarrow \sqrt{n} - 5 \in \text{Ư(14)} = {+-1; +-2; +-7; +-14}`

`\Rightarrow`\(\left[{}\begin{matrix}\sqrt{n}-5=1\\\sqrt{n}-5=-1\\\sqrt{n}-5=2\\\sqrt{n}-5=-2\end{matrix}\right.;\left[{}\begin{matrix}\sqrt{n}-5=7\\\sqrt{n}-5=-7\\\sqrt{n}-5=14\\\sqrt{n}-5=-14\end{matrix}\right.\)

`\Rightarrow` \(\left[{}\begin{matrix}\sqrt{n}=6\\\sqrt{n}=4\\\sqrt{n}=7\\\sqrt{n}=3\end{matrix}\right.;\left[{}\begin{matrix}\sqrt{n}=12\\\sqrt{n}=-2\left(\text{loại}\right)\\\sqrt{n}=19\\\sqrt{n}=-9\left(\text{loại}\right)\end{matrix}\right.\)

`\Rightarrow`\(\left[{}\begin{matrix}n=36\\n=16\\n=49\\n=9\end{matrix}\right.;\left[{}\begin{matrix}n=144\\n=361\end{matrix}\right.\)

`#3107.101107`

`x + 30% * x = -1,3`

`=> x + 0,3x = -1,3`

`=> x(1 + 0,3) = -1,3`

`=> x * 1,3 = -1,3`

`=> x = -1,3 \div 1,3`

`=> x = -1`

Vậy, `x = -1.`

`#3107.101107`

`1)`

\(C=\dfrac{5}{18}+\dfrac{8}{19}-\dfrac{7}{21}+\left(\dfrac{-10}{36}+\dfrac{11}{19}+\dfrac{1}{3}\right)-\dfrac{5}{8}\)

`= 5/18 + 8/19 - 1/3 - 5/18 + 11/19 + 1/3 - 5/8`

`= (5/18 - 5/18) + (1/3 - 1/3) + (8/19 + 11/19) - 5/8`

`= 19/19 - 5/8`

`= 1 - 5/8`

`= 3/8`

Vậy, `C = 3/8`

`2)`

`E =`\(\dfrac{1}{13}+\left(-\dfrac{5}{18}-\dfrac{1}{13}+\dfrac{12}{17}\right)-\left(\dfrac{12}{17}-\dfrac{5}{18}+\dfrac{7}{5}\right)\)

`= 1/13 - 5/18 - 1/13 + 12/17 - 12/17 + 5/18 - 7/5`

`= (1/13 - 1/13) + (-5/18 + 5/18) + (12/17 - 12/17) - 7/5`

`= -7/5`

Vậy, `E = -7/5`

`3)`

\(F=\dfrac{15}{14}-\left(\dfrac{17}{23}-\dfrac{80}{87}+\dfrac{5}{4}\right)+\left(\dfrac{17}{23}-\dfrac{15}{14}+\dfrac{1}{4}\right)\)

`= 15/14 - 17/23 + 80/87 - 5/4 + 17/23 - 15/14 + 1/4`

`= (15/14 - 15/14) + (-17/23 + 17/23) + (-5/4 + 1/4) + 80/87`

`= -4/4 + 80/87`

`= -1 + 80/87`

`= -7/87`

Vậy, `F = -7/87`

`4)`

\(G=\dfrac{1}{25}-\dfrac{4}{27}+\left(-\dfrac{23}{27}+\dfrac{-1}{25}-\dfrac{5}{43}\right)+\dfrac{5}{43}-\dfrac{4}{7}\)

`= 1/25 - 4/27 - 23/27 - 1/25 - 5/43 + 5/43 - 4/7`

`= (1/25 - 1/25) - (4/27 + 23/27) + (-5/43 + 5/43) - 4/7`

`= -27/27 - 4/7`

`= -1 - 4/7`

`= -11/7`

Vậy, `G = -11/7.`

`#3107.101107`

\(106-\left(x+7\right)=9\\ \Rightarrow x+7=106-9\\ \Rightarrow x+7=97\\ \Rightarrow x=97-7\\ \Rightarrow x=90\)

Vậy, `x = 90`

___

\(45-\left(x+10\right)=31\\ \Rightarrow x+10=45-31\\ \Rightarrow x+10=14\\ \Rightarrow x=14-10\\ \Rightarrow x=4\)

Vậy, `x = 4`

___

\(156-\left(x+61\right)=82\\ \Rightarrow x+61=156-82\\ \Rightarrow x+61=74\\ \Rightarrow x=74-61\\ \Rightarrow x=13\)

Vậy, `x = 13`

___

\(126-\left(x+32\right)=86\\ \Rightarrow x+32=126-86\\ \Rightarrow x+32=40\\ \Rightarrow x=40-32\\ \Rightarrow x=8\)

Vậy, `x = 8.`

`#3107.101107`

`a)`

\(187+x=320\\ \Rightarrow x=320-187\\ \Rightarrow x=133\)

Vậy, `x = 133`

`b)`

\(765-x=158\\ \Rightarrow x=765-158\\ \Rightarrow x=607\)

Vậy, `x = 607`

`c)`

\(451+\left(x-218\right)=876\\ \Rightarrow x-218=876-451\\ \Rightarrow x-218=425\\ \Rightarrow x=425-218\\ \Rightarrow x=207\)

Vậy, `x = 207.`

`#3107.101107`

`a,`

\(12\cdot53+53\cdot172+184\cdot47\)

\(=53\cdot\left(12+172\right)+184\cdot47\\ =53\cdot184+184\cdot47\\ =184\cdot\left(53+47\right)\\ =184\cdot100\\ =18400\)

`b,`

\(43\cdot29+57\cdot29-73\cdot26-27\cdot26\\ =29\cdot\left(43+57\right)-26\cdot\left(73+27\right)\\ =29\cdot100-26\cdot100\\ =100\cdot\left(29-26\right)\\ =100\cdot3\\ =300\)

`c,`

\(4\cdot22\cdot87+11\cdot8\cdot36-2\cdot44\cdot23\\ =11\cdot4\cdot2\cdot87+11\cdot8\cdot36-11\cdot4\cdot2\cdot23\\ =11\cdot8\cdot87+11\cdot8\cdot36-11\cdot8\cdot23\\ =11\cdot8\cdot\left(87+36-23\right)\\ =88\cdot100\\ =8800\)

`d,`

\(100-96+92-88+84-80+...+12-8+4\)

Gọi tổng sau là A

`A = (100 - 96) + (92 - 88) + (84 - 80) + ... + (12 - 8) + 4`

Số số hạng có trong tổng A:

`(100 - 4) \div 4 + 1 = 25` (số hạng)

Ghép mỗi cặp 2 số lại với nhau, các cặp có trong tổng:

`25 \div 2 = 12` (dư 1 số)

Ta có:

`A = 4 + 4 + 4 + .... + 4 + 4`

Trong đó, có `12` cặp ghép với nhau (dư 1)

`A = 4 \times 12 + 4`

`= 48 + 4`

`= 52`

Vậy, tổng A có giá trị là `52.`

`#3107.101107`

\(\left(2,3\right)^3\cdot x=\left(2,3\right)^4\\ \Rightarrow x=\left(2,3\right)^4\div\left(2,3\right)^3\\ \Rightarrow x=2,3\)

Vậy, `x = 2,3.`

Không nói được gì tử tế thì đừng nói, mất công người khác khinh b ạ. 

`#3107.101107`

\(\dfrac{5}{13}+...=\dfrac{7}{9}\)

\(\dfrac{7}{9}-\dfrac{5}{13}=\dfrac{49}{117}\)

Vậy, chỗ trống cần điền là \(\dfrac{49}{117}.\)