=>  x + 20 = 100

=> x = 80

We have:

\(\left(a-b\right)^2\ge0\)

=> a² + b² \(\ge2ab\)

=> a² + b² + 2ab \(\ge2\left(2ab\right)=4ab\)

=> \(\left(a+b\right)^2\ge4ab\)

Because a > 0, b > 0 => a+b > 0

\(\Rightarrow\dfrac{a+b}{ab}\ge\dfrac{4}{a+b}\Leftrightarrow\dfrac{a}{ab}+\dfrac{b}{ab}\ge\dfrac{4}{a+b}\)

\(\Rightarrow\dfrac{1}{a}+\dfrac{1}{b}\ge\dfrac{4}{a+b}\)

So, .......

Considering the triangles ABC and MNP, we have:

* AB = MN [suppose]

* AC = MP [suppose]

* \(\widehat{A}< \widehat{C}\left(\text{suppose}\right)\) 

=> \(\Delta ABC< \Delta MNP\)

=> BC < NP

Is it true? 

The circumference of this circle is:

\(2\times2\times3,14=12,56\left(cm\right)\)

Answer: 12,56cm

10 + 35 + 100 : 25

= 10 + 35 + 4

= 45 + 4 = 49

25 + 15 + 10 + 80: 4 

= 40 + 10 + 20

= 50 + 20 = 70

\(2^{45}=\left(2^3\right)^{15}=8^{15}\)

8ⁿ with n \(\in N\) divide for 7 then we have remainder is 1

=> 2⁴⁵ divide for 7 then we have remainder is 1

\(\sqrt{3375}=15\sqrt{15}\)

The average of 23,67,108 is:

\(\dfrac{23+67+108}{3}=66\)

Answer: 66

x + 10 - 20 = 70 - 10

=> x + 10 = 70 - 10 + 20

=> x + 10 = 80

=> x = 70

x - 20 + 40 = 40 + 20

=> x - 20 = 40 + 20 - 40

=> x - 20 = 20

=> x = 40

100 + 200 + 300 + 500 + 700 + 800 + 900

= \(\left(1+2+3+5+7+8+9\right).100\)

\(=35.100=3500\)

200 + 300 + 400 + 100 + 700 + 600 + 900

= \(\left(2+3+4+1+7+6+9\right).100\)

\(=32.100=3200\)

10.2 + 10.3 = 20 + 30 = 50

4.3 + 2.4 = 12 + 8 = 20

10000 + 20000 + 2543 + 125444

= 30000 + 2543 + 125444

= 32543 + 125444

= 157987

4 + 2 + 3 + 200 + 200 + 300 + 12345

= 9 + 400 + 300 + 12345

= 9 + 700 + 12345

= 709 + 12345

= 13054

1 + 2 + 3 + 1000000 = 1000006

If x > 0

2² + 2^x + 11²

= 2[2 + 2^x-1] + 121 \(⋮̸2\)unsatisfactory

If x = 0

=> 2² + 2^x + 11²

= 4 + 1 + 121

= 5 + 121

= 126 \(⋮2\)

So x = 0

100 + 200 + 300 + 400 + 500 + 600 + 700 + 800 + 900

= \(\left(1+2+3+4+5+6+7+8+9\right).100\)

\(=45.100=4500\)

In Vietnam, the plane takes off at 11:00 and cost 8h for a plane of this type to fly this distance

=> In Vietnam when complete this distance is: 11:00 + 8:00 = 19:00

And this times in Toronto is 1:00

=> Time in Vietnam is faster than this in Toronto is18 hours

=> If Vietnam it is 7:00 => In Toronto is:

7:00 + 18:00 = 25:00 or 1:00 next morning

So choose B : 1:00 am

We have:

a : 7 = c [residual d] with c = d and are the minimun. Find a

But c always diffirent from 0 => c = d > 0

=> Min of c and d = 1

=> a : 7 = c [residual d] <=> a : 7 = 1 [residual 1]

=> a = 1.7 + 1 = 8

So choose B

The numbers of apples are left are:

3 - 2 = 1 [apple]

Answer: 1 apple

Choose C