a, x . 9,9 + x : 10 = 12,5

\(x.\frac{99}{10}+x.\frac{1}{10}=\frac{25}{2}\)

\(x\left(\frac{99}{10}+\frac{1}{10}\right)=\frac{25}{2}\)

\(x.10=\frac{25}{2}\)

\(x=\frac{25}{2}:10=\frac{25}{2}.\frac{1}{10}=\frac{5}{4}\)

b, \(x:\frac{1}{4}-x=\frac{78}{5}\)

\(x.4-x=\frac{78}{5}\)

\(x\left(4-1\right)=\frac{78}{5}\)

\(x.3=\frac{78}{5}\)

\(x=\frac{78}{5}:3=\frac{78}{5}.\frac{1}{3}=\frac{26}{5}\)

c, \(x:\frac{1}{10}-x:4-x.\frac{3}{4}=\frac{9}{4}\)

\(=x.10-x.\frac{1}{4}-x.\frac{3}{4}=\frac{9}{4}\)

\(x\left(10-\frac{1}{4}-\frac{3}{4}\right)=\frac{9}{4}\)

\(x.9=\frac{9}{4}\)

\(x=\frac{9}{4}:9=\frac{9}{4}.\frac{1}{9}=\frac{1}{4}\)

**** 

a, x . 9,9 + x : 1 0 = 1 2,5 x. 1 0 9 9 + x. 1 01 = 225 x 1 0 9 9 + 1 01 = 225 x.1 0 = 225 x = 225 :1 0 = 225 . 1 01 = 45 b, x: 41 − x = 578 x.4 − x = 578 x 4 − 1 = 578 x.3 = 578 x = 578 :3 = 578 . 31 = 526 c, x: 1 01 − x:4 − x. 43 = 49 = x.1 0 − x. 41 − x. 43 = 49 x 1 0 − 41 − 43 = 49 x.9 = 49 x = 49 :9 = 49 . 91 = 4

d: =3+2010=2013

Bài 1:
$x^2y+4y=x+6$

$\Leftrightarrow y(x^2+4)=x+6$

$\Leftrightarrow y=\frac{x+6}{x^2+4}$

Để $y$ nguyên thì $\frac{x+6}{x^2+4}$ nguyên

$\Rightarrow x+6\vdots x^2+4(1)$

$\Rightarrow x^2+6x\vdots x^2+4$

$\Rightarrow (x^2+4)+(6x-4)\vdots x^2+4$

$\RIghtarrow 6x-4\vdots x^2+4(2)$

Từ $(1); (2)\Rightarrow 6(x+6)-(6x-4)\vdots x^2+4$

$\Rightarrow 40\vdots x^2+4$

$\Rightarrow x^2+4\in\left\{4; 5; 8; 10; 20;40\right\}$ (do $x^2+4$ là số nguyên $\geq 4$)

$\Rightarrow x\in\left\{0; \pm 1; \pm 2; \pm 4; \pm 6\right\}$

Đến đây thay vào tìm $y$ thôi.

Bài 2:
 

Lấy PT(1) trừ PT (2) theo vế thu được:

$3x=5y-2$
$\Leftrightarrow x=\frac{5y-2}{3}$

Thay vào PT(1) thì:

$(2.\frac{5y-2}{3}+1)(y+2)=9$

$\Leftrightarrow 10y^2+19y-29=0$

$\Leftrightarrow (y-1)(10y+29)=0$

$\Rightarrow y=1$ hoặc $y=\frac{-29}{10}$

Với $y=1\Rightarrow x=\frac{5y-2}{3}=1$

Với $y=\frac{-29}{10}\Rightarrow x=\frac{5y-2}{3}=\frac{-11}{2}$

5×5×5×5÷4×5×5+40-80=

40,28 - 22,5 : 12,5 + 1,7

= 40,28 - 1,8 + 1,7

= 38,48 + 1,7

= 40,18

1) 2,75 - 5/6 × 2/5 = 2,75 - (5/6) × (2/5) = 2,75 - 1/3 = 2,75 - 0,33 = 2,42

2) 1,25 - (5/6 - 0,75) - 3/5 = 1,25 - (5/6 - 0,75) - 3/5 = 1,25 - (5/6 - 3/4) - 3/5 = 1,25 - (5/6 - 9/12) - 3/5 = 1,25 - (10/12 - 9/12) - 3/5 = 1,25 - 1/12 - 3/5 = 1,25 - 0,08 - 0,6 = 1,25 - 0,68 = 0,57

3) 4/9 × 0,75 + 8/5 + 3,125 = (4/9) × 0,75 + 8/5 + 3,125 = 0,44 + 8/5 + 3,125 = 0,44 + 1,6 + 3,125 = 0,44 + 4,725 = 5,165

4) 1,125 - 4/7 - 0,12 = 1,125 - (4/7) - 0,12 = 1,125 - 0,57 - 0,12 = 0,435 - 0,12 = 0,315

5) (1/3 + 0,4) × 3,5 + (1/6 + 0,75) × 6/5

a) \(210:x=2,1:0,25=8,4\)

\(x=210:8,4=25\)

b) \(x.2+x.0,5=6,25\)

\(2,5x=6,25\)

\(x=6,25:2,5=2,5\)

c) \(x:0,25-x=15,6\)

\(3x=15,6\)

\(x=5,2\)

d) \(x:12,5=3,75.4=15\)

\(x=15.12,5=187,5\)

e) \(x.12,6-x.5,6=42\)

\(7x=42\)

\(x=6\)

g) \(x:0,1-x:4-x.0,75=2,25\)

\(10x-\dfrac{x}{4}-\dfrac{3x}{4}=2,25\)

\(9x=2,25\)

\(x=0,25\)

giúp mình gấp mn

wth khó thế

\(\left\{{}\begin{matrix}\dfrac{72}{x}+\dfrac{54}{y}=6\\x-y=6\end{matrix}\right.\left(x,y>0\right)< =>\left\{{}\begin{matrix}x=6+y\left(1\right)\\\dfrac{72}{\left(6+y\right)}+\dfrac{54}{y}=6\left(2\right)\end{matrix}\right.\)(x,y>0,y\(\ne-6\))

giải pt(2) \(\dfrac{72}{\left(6+y\right)}+\dfrac{54}{y}=6< =>\dfrac{72y+54\left(6+y\right)}{y\left(6+y\right)}=6\)

\(< =>\dfrac{126y+324}{y\left(6+y\right)}=6=>126y+324=6y\left(6+y\right)\)

\(< =>126y+324=36y+6y^2\)

\(< =>-6y^2+90y+324=0\)

\(\Delta=90^2-4\left(-6\right).324=15876>0\)

=>x1=\(\dfrac{-90+\sqrt{15876}}{2\left(-6\right)}=-3\left(loai\right)\)

x2=\(\dfrac{-90-\sqrt{15876}}{2\left(-6\right)}=18\left(TM\right)\)

=>x=x2=18 thay vào pt(1)=>x=6+18=24

vậy (x,y)=(24,18)

x:0,25 + X x0,25=3,4

(0,25+0,25) :x=3,4

0,5:x=3,4

x=3,4:0,5

x=6,8

a) \(x:0,25+x.0,25=3,4\)

\(\Leftrightarrow x:\dfrac{1}{4}+\dfrac{1}{4}x=3,4\)

\(\Leftrightarrow4x+\dfrac{1}{4}x=3,4\Leftrightarrow\dfrac{17}{4}x=3,4\Leftrightarrow x=3,4:\dfrac{17}{4}\)

\(\Leftrightarrow x=0,8\)

b) \(0,7:x+0,5:x=0,75\)

<=> \(\left(0,7+0.5\right):x=0,75\)

<=> \(1,2:x=0,75\)

<=> \(x=1,6\)

mình có việc gấp

\(a,x\times12,5=15\\ x=15:12,5\\ x=1,2\\ b,x\times\left(2,3+5,7+2\right)=234,7\\ x\times10=234,7\\ x=23,47\)

a,x×12,5=15x=15:12,5x=1,2b,x×(2,3+5,7+2)=234,7x×10=234,7x=23,47

a: =152,3+7,7+2021,19-2021,19

=160

b: =7/15*3/14*20/13

\(=\dfrac{7}{14}\cdot\dfrac{3}{15}\cdot\dfrac{20}{13}=\dfrac{1}{2}\cdot\dfrac{1}{5}\cdot\dfrac{20}{13}=\dfrac{2}{13}\)

c: \(=\dfrac{7}{4}\left(\dfrac{13}{12}-\dfrac{10}{12}\right)+\dfrac{5}{6}=\dfrac{7}{16}+\dfrac{5}{6}=\dfrac{61}{48}\)