Bài 3:

a) Áp dụng t/c dtsbn:

\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{y-x}{5-2}=\dfrac{21}{3}=7\)

\(\Rightarrow\left\{{}\begin{matrix}x=7.2=14\\y=7.5=35\end{matrix}\right.\)

b) Áp dụng t/c dtsbn:

\(\dfrac{x}{3}=\dfrac{y}{7}=\dfrac{x+y}{3+7}=\dfrac{25}{10}=\dfrac{5}{2}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{5}{2}.3=\dfrac{15}{2}\\y=\dfrac{5}{2}.7=\dfrac{35}{2}\end{matrix}\right.\)

Bài 4:

Gọi độ dài 3 cạnh là x,y,z(cm)(a,b,c>0)

Nửa chu vi là: \(45:2=\dfrac{45}{2}\left(cm\right)\)

Áp dụng t/c dtsbn:

\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{z}{6}=\dfrac{x+y+z}{4+5+6}=\dfrac{\dfrac{45}{2}}{15}=\dfrac{3}{2}\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}.4=6\left(cm\right)\\y=\dfrac{3}{2}.5=\dfrac{15}{2}\left(cm\right)\\z=\dfrac{3}{2}.6=9\left(cm\right)\end{matrix}\right.\)

Bài 5:

Gọi số học giỏi, khá, tb là a,b,c(em)(a,b,c∈N*)

Áp dụng t/c dtsbn:

\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}=\dfrac{b+c-a}{5+3-2}=\dfrac{180}{6}=30\)

\(\Rightarrow\left\{{}\begin{matrix}a=30.2=60\\b=30.3=90\\z=30.5=150\end{matrix}\right.\)

#include <bits/stdc++.h>

using namespace std;

long long x,i,n,dem;

int main()

{

cin>>n;

dem=0;

for (i=1; i<=n; i++)

{

cin>>x;

if (x%2==0) dem++;

}

cout<<dem;

return 0;

}

\(3n-2\inƯ\left(15\right)\) \(=\left\{1;-1;3;-3;5;-5;15;-15\right\}.\)

\(\Leftrightarrow n\in\left\{1;\dfrac{1}{3};\dfrac{5}{3};\dfrac{-1}{3};\dfrac{7}{3};-1;\dfrac{17}{3};\dfrac{-13}{3}\right\}.\)

Mà \(n\ne\dfrac{2}{3};n\in Z.\)

\(\Rightarrow n\in\left\{1;-1\right\}.\)

Chỉ fuy nhất bài 5 thôi ạh mik cảm ơn♡

Bài 4: 

a: Xét ΔAKB và ΔAKC có

AK chung

KB=KC

AB=AC

Do đó: ΔAKB=ΔAKC

\(f,=\left(5^2+3\right):7=28:7=4\\ g,=7^2-9+8\cdot25=49-9+200=240\\ h,=600+72+18=690\\ i,=5^2+5-20=10\\ j,=45-28+83=100\)

\(2A=\frac{4}{1.5}+\frac{6}{5.11}+\frac{8}{11.19}+\frac{10}{19.29}+\frac{12}{29.41}\)

\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{19}+...+\frac{1}{29}-\frac{1}{41}=1-\frac{1}{41}=\frac{40}{41}\)

\(\Rightarrow A=\frac{20}{21}\)

\(3B=\frac{3}{1.4}+\frac{6}{4.10}+\frac{9}{10.19}+\frac{12}{19.31}=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{10}+\frac{1}{10}-\frac{1}{19}+\frac{1}{19}-\frac{1}{31}\)

\(=1-\frac{1}{31}=\frac{30}{31}\)

\(\Rightarrow B=\frac{10}{31}=\frac{20}{62}<\frac{20}{41}\)

Do đó $A>B$

Ta có: \(A=\dfrac{2}{1.5}+\dfrac{3}{5.11}+\dfrac{4}{11.19}+\dfrac{5}{19.29}+\dfrac{6}{29.41}\)

\(2A=1-\dfrac{1}{5}+\dfrac{1}{5}+...+\dfrac{1}{29}-\dfrac{1}{41}\)

\(2A=1-\dfrac{1}{41}=\dfrac{40}{41}\)

\(A=\dfrac{20}{41}\)

Lại có: \(B=\dfrac{1}{1.4}+\dfrac{2}{4.10}+\dfrac{3}{10.19}+\dfrac{4}{19.31}\)

\(3B=\dfrac{3}{1.4}+\dfrac{6}{4.10}+\dfrac{9}{10.19}+\dfrac{12}{19.31}\)

\(3B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{10}+...+\dfrac{1}{19}-\dfrac{1}{31}\)

\(3B=1-\dfrac{1}{31}=\dfrac{30}{31}\)

\(B=\dfrac{10}{31}\)

Vì \(\dfrac{20}{41}>\dfrac{10}{31}\) nên...

5:

a: Chiều rộng là 18*1/6=3m

S=18*3=54m²

Số viên gạch cần mua là:

54*10^4:30^2=600 viên

b: Số viên gạch phải giảm đi là:

600*5/6=500 viên