7) 5x=4y ⇒\(\dfrac{x}{4}=\dfrac{y}{5}\)

Nhân cả hai vế với \(\dfrac{x}{4}\), ta có: \(\left(\dfrac{x}{4}\right)^2=\dfrac{x}{4}.\dfrac{y}{5}=\dfrac{xy}{20}=\dfrac{20}{20}=1\)

\(\left(\dfrac{x}{4}\right)^2=1\Rightarrow\left[{}\begin{matrix}\dfrac{x}{4}=1\\\dfrac{x}{4}=-1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

⇒ \(\left[{}\begin{matrix}y=5\\y=-5\end{matrix}\right.\)

4) áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{0,5}=\dfrac{y}{0,3}=\dfrac{z}{0,2}=\dfrac{z-y+x}{0,2-0,3+0,5}=\dfrac{1}{\dfrac{2}{5}}=\dfrac{5}{2}\)

\(\dfrac{x}{0,5}=\dfrac{5}{2}\Rightarrow x=\dfrac{5}{4}\)

\(\dfrac{y}{0,3}=\dfrac{5}{2}\Rightarrow y=\dfrac{3}{4}\)

\(\dfrac{z}{0,2}=\dfrac{5}{2}\Rightarrow z=\dfrac{1}{2}\)

6) áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x+11}{13}=\dfrac{y+12}{14}=\dfrac{z+13}{15}=\dfrac{x+11+y+12+z+13}{13+14+15}=\dfrac{42}{42}=1\)

\(\dfrac{x+11}{13}=1\Rightarrow x=2\)

\(\dfrac{y+12}{13}=1\Rightarrow y=1\)

\(\dfrac{z+13}{15}=1\Rightarrow z=2\)

7) \(5x=4y\Rightarrow\dfrac{x}{4}=\dfrac{y}{5}=k\)

\(\Rightarrow x=4k,y=5k\)

\(x.y=20\\ \Rightarrow4k.5k=20\\ \Rightarrow20k^2=20\\ \Rightarrow k^2=1\\ \Rightarrow\left[{}\begin{matrix}k=-1\\k=1\end{matrix}\right.\)

\(x=4k\Rightarrow\left[{}\begin{matrix}x=-4\\x=4\end{matrix}\right.\)

\(y=5k\Rightarrow\left[{}\begin{matrix}y=-5\\y=5\end{matrix}\right.\)

Vậy \(\left(x,y\right)=\left\{\left(-4;-5\right);\left(4;5\right)\right\}\)

\(\frac{15\times14+30}{15\times14+60}\)

\(=\frac{14\times15+30}{15\times14+60}\)

\(=\frac{30}{60}=\frac{1}{2}\)

\(0,1:3+0,2:3+0,3:3+0,4:3+0,5:3\)

\(=3:\left(0,1+0,2+0,3+0,4+0,5\right)\)

\(=3:\left(\frac{1}{10}+\frac{2}{10}+\frac{3}{10}+\frac{4}{10}+\frac{5}{10}\right)\)

\(=3:\left(\frac{1+2+3+4+5}{10}\right)\)

\(=3:\frac{3}{2}\)

\(=\frac{3\times2}{3}\)

\(=\frac{1\times2}{1}\)

\(=\frac{2}{1}\)

0,3(15)=\(\dfrac{52}{165}\)

3,1(14)=\(\dfrac{311}{99}\)

\(0,3(15)=\dfrac{153-3} {990}=\dfrac{150} {990} \)

\(3,1(14)=3+\dfrac{114-1}{990}=2+\dfrac{113}{990}=\dfrac{2093}{990}\)

Cách làm là như vậy! Nếu không hiểu chỗ nào thì hãy cmt mình sẽ trả lời cho##HiHi!

\(a,\frac{-8}{15}.\left(-30\right).\frac{15}{-8}.\frac{9}{10}\)
\(=-\left(\frac{8}{15}.\frac{15}{8}\right).\left(30.\frac{9}{10}\right)\)
\(=-1.27 =-27\)
\(b,2\frac{1}{18}.\frac{23}{24}.\frac{9}{37}.\frac{48}{-15}\)
\(=\frac{-37.23.9.48}{18.24.37.15}=\frac{23}{15}\)
c, chịu rồi
 

cảm ơn bạn nhé Ghost River

\(\dfrac{\dfrac{7}{13}+\dfrac{7}{14}-\dfrac{7}{15}}{\dfrac{8}{13}+\dfrac{8}{14}-\dfrac{8}{15}}-\dfrac{\dfrac{5}{11}-\dfrac{5}{13}+\dfrac{5}{15}}{\dfrac{8}{11}-\dfrac{8}{13}+\dfrac{8}{15}}\)

\(=\dfrac{7\left(\dfrac{1}{13}+\dfrac{1}{14}-\dfrac{1}{15}\right)}{8\left(\dfrac{1}{13}+\dfrac{1}{14}-\dfrac{1}{15}\right)}-\dfrac{5\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{15}\right)}{8\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{15}\right)}\)

\(=\dfrac{7}{8}-\dfrac{5}{8}\)

\(=\dfrac{2}{8}=\dfrac{1}{4}\)

=7/8 - 5/8 =1/4

Chọn A

a) 13 - 2x = x- 2                                    b)2x-15+8x=7-2x+14                                 c)12-4y+3y=4y-10-8y

<=>13 + 2 = x+2x                                <=>2x +2x+8x =7+14+15                         <=>12+10     =4y-8y+4y-3y

<=> 15     =3x                                       <=>12x           =36                                   <=> 22          =-3y

<=> x=5                                                 <=>x=3                                                  <=>y=-22/3

vậy S=[5]                                             vậy S=[3]                                                vậy S=[-22/3]

hình như giải gòi (:

67/72

37/24

1)\(\dfrac{5}{6}\)

2)\(\dfrac{1}{4}\)

3)\(\dfrac{12}{5}\)

4)\(\dfrac{39}{2}\)

5)\(1\)