1) \(f\left(x\right)=-3x^2-12x+5\)

\(\Rightarrow f\left(x\right)=-3\left(x^2+4x\right)+5\)

\(\Rightarrow f\left(x\right)=-3\left(x^2+4x+4\right)+5+12\)

\(\Rightarrow f\left(x\right)=-3\left(x+2\right)^2+17\le17\left(-3\left(x+2\right)^2\le0,\forall x\right)\)

\(\Rightarrow GTLN\left(f\left(x\right)\right)=17\left(tạix=-2\right)\)

2) \(f\left(x\right)=-8x^2+20x\)\

\(\Rightarrow f\left(x\right)=-8\left(x^2+\dfrac{5}{2}x\right)\)

\(\Rightarrow f\left(x\right)=-8\left(x^2+\dfrac{5}{2}x+\dfrac{25}{16}\right)+\dfrac{25}{2}\)

\(\Rightarrow f\left(x\right)=-8\left(x+\dfrac{5}{4}\right)^2+\dfrac{25}{2}\le\dfrac{25}{2}\left(-8\left(x+\dfrac{5}{4}\right)^2\le0,\forall x\right)\)

\(\Rightarrow GTLN\left(f\left(x\right)\right)=\dfrac{25}{2}\left(tạix=-\dfrac{5}{4}\right)\)

a) ....

=> 14/3 : x = 4/3 + 3/5 = 29/15

=> x = 14/3 : 29/15 = 70/29

b) ...

=> 4/3 + 5/2x = 2

=> 5/2x = 2 - 4/3 = 2/3

=> x = 2/3 : 5/2 = 4/15

c)...

=> x : 10/3 =  31/10

=> x = 31/10 x 10/3 = 31/3 

Ta có :

\(\widehat{A}+\widehat{B}+\widehat{C}+\widehat{D}=360^o\)

\(\Rightarrow\widehat{A}+\widehat{B}=360^o-\left(\widehat{C}+\widehat{D}\right)\)

\(\Rightarrow\widehat{A}+\widehat{B}=360^o-\left(60+80\right)=220^o\)

mà \(\widehat{A}-\widehat{B}=10^o\)

\(\Rightarrow\widehat{A}=\left(220-10\right):2=105^o\)

\(\Rightarrow\widehat{B}=105-10=95^o\)

Vậy \(\left\{{}\begin{matrix}\widehat{A}=105^o\\\widehat{B}=95^o\end{matrix}\right.\)

`a/`

` 7/5 + 3 2/5 - 1 1/2 `

`= (7/5 + 17/5) - 3/2`

`= 24/5 - 3/2 `

`= 48/10 - 15/10 `

`= 33/10 `

`b/`

` 3 xx 2 4/9 xx 3/2 `

` = 3 xx 22/9 xx 3/2 `

` = 22/3 xx 3/2`

`= 11.`

`c/`

` 5/9 xx ( 2 1/6 - 1 2/3 ) `

`= 5/9 xx ( 13/6 -5/3 )`

`= 5/9 xx ( 13/6 - 10/6 ) `

`= 5/9 xx 3/6 `

`= 5/9 xx 1/2 `

`= 5/18`

Hiệu số phần bằng nhau là:

\(7-1=6\left(phần\right)\)

Mẹ có số tuổi là:

\(30:6x7=35\left(tuổi\right)\)

Con có số tuổi là:

\(35-30=5\left(tuổi\right)\)

Đáp số: Mẹ : 35 tuổi

             Con : 5 tuổi

THAM KHẢO nha:

Hiệu số phần bằng nhau là:

7-1=6 phần

Tuổi mẹ là:

30:6x7=35 tuổi

Tuổi con là:

30:6x1=5 tuổi

Đs: Mẹ: 35 tuổi

       Con: 5 tuổi

\(3.2+\left(x+5^2\right)=10^2\)

\(6+\left(x+25\right)=100\)

\(x+25=100-6=94\)

\(x=94-25=69\)

Bạn xem lại đề

a)\(x+\dfrac{2}{3}x\dfrac{5}{6}=7\)

\(x+\dfrac{10}{18}=7\)

\(x=7-\dfrac{10}{18}\)

\(x=\dfrac{58}{9}\)

b)\(9-xx\dfrac{1}{2}=\dfrac{3}{4}\)

\(xx\dfrac{1}{2}=9-\dfrac{3}{4}\)

\(xx\dfrac{1}{2}=\dfrac{33}{4}\)

\(x=\dfrac{33}{4}:\dfrac{1}{2}\)

\(x=\dfrac{33}{2}\)

c)\(18-x:\dfrac{2}{3}=\dfrac{4}{5}-\dfrac{1}{10}\)

\(18-x:\dfrac{2}{3}=\dfrac{7}{10}\)

\(x:\dfrac{2}{3}=18-\dfrac{7}{10}\)

\(x:\dfrac{2}{3}=\dfrac{173}{10}\)

\(x=\dfrac{173}{10}x\dfrac{2}{3}\)

\(x=\dfrac{173}{15}\)

a)\(27.65+27.35+300=27.\left(65+35\right)+300\)

\(=27.100+300=2700+300=3000\)

b)\(3838:\left[\left(190-6.5^2\right):4+3\right]\)

\(=3838:\left[\left(190-6.25\right):4+3\right]\)

\(=3838:\left[\left(190-150\right):4+3\right]\)

\(=3838:\left[40:4+3\right]=3838:\left[10+3\right]\)

\(=3838:13=\dfrac{3838}{13}\)

c)\(2022-x=2021\)

\(x=2022-2021=1\)

d)\(26+14:\left(x-5\right)=33\)

\(14:\left(x-5\right)=33-26=7\)

\(x-5=14+7=2\)

\(x=2+5=7\)

e)đề hỏi làm j thế bạn

\(\dfrac{x-2023}{6}+\dfrac{x-2023}{10}+\dfrac{x-2023}{15}+\dfrac{x-2023}{21}=\dfrac{8}{21}\)

\(\left(x-2023\right)\left(\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}\right)=\dfrac{8}{21}\)

\(\left(x-2023\right).\dfrac{8}{21}=\dfrac{8}{21}\)

\(x-2023=1\)

\(x=2024\)

Vậy..............

\(...\Rightarrow\left(x-2023\right)\left(\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}\right)=\dfrac{8}{21}\)

\(\Rightarrow\left(x-2023\right)\left(\dfrac{35+21+14+1}{210}\right)=\dfrac{8}{21}\)

\(\Rightarrow\left(x-2023\right).\dfrac{71}{210}=\dfrac{8}{21}\)

\(\Rightarrow\left(x-2023\right).\dfrac{71}{210}=\dfrac{8}{21}.\dfrac{210}{71}=\dfrac{80}{71}\)

\(\Rightarrow x-2023=\dfrac{80}{71}\Rightarrow x=\dfrac{80}{71}+2023=\dfrac{143713}{71}\)