\(\dfrac{5}{8}+\dfrac{9}{8}=\dfrac{5+9}{8}=\dfrac{14}{8}=\dfrac{7}{3}\\ \dfrac{6}{7}-\dfrac{3}{7}=\dfrac{6-3}{7}=\dfrac{3}{7}\)

(x+1).(1+1999)=4000

<=>(x+1).2000=4000

<=>x+1=4000/2000=2

<=>x=2-1=1

Answer:x=1

Number of the male students is:

\(40-\left(40.\dfrac{2}{5}\right)=24\left(students\right)\)

Answer: 24 students.

Number of the male student is:

\(50-\left(50.\dfrac{2}{5}\right)=30\left(students\right)\)

Answer: 30 students.

A square have 4 right angles.

m²+n²

= (m+n)²-2mn

= 11²-2.9

=121-18

=103

(a) 3^x=243

And: 3⁵= 243

=>x=5

(b) 5^m=625

And: 5⁴=625

=>m=4

(123456)² -123457 x 123455

= (123456)² - (123456-1) x (123456+1)

=(123456)² - (123456²-1)

=1

m²-n²=64

<=>m²-n²=8²

=> m= n+2

=> m=17; n=15

5x+2y=19

=> x= 3;y=2

2x+5y=16

=>x=3;y=2

a) (2x+3)²

= 4x² + 12x +9

b) (x-2)³

= (x-2) (x²+2x+4)

The volume is:

11.3.2=66(in³)

Answer: 66 in³

The total number of candy John and Tom ia:

15+31=46( candies)

Tom need to give to John so that each boy will have the same number of candies is:

31-46:2=8(candies)

Answer: 8 candies.

We have : 5^x-3^y= z² (x,y,z: integer)

=> x=2; y=2; z=4

Ok.

S=1+2+3+...+50

=>S= (1+50):2 x 50

S= 51:2x50

S= 1275

P= 1+2+3+...+500

<=>P= (1+500):2 x 500

P= 501:2 x 500

P= 125250

3⁵= 243

5³= 125

10³= 1000

22²=484

342³= 40001688

\(\dfrac{1}{z}=\dfrac{z}{9}\\ < =>1.9=z.z\\ < =>z^2=9\\ =>z=3orz=-3\)

We have:

5³⁰= (5³)¹⁰= 125¹⁰

3⁵⁰= (3⁵)¹⁰= 243¹⁰

For: 125¹⁰<243¹⁰ (125<243)

=> 5³⁰ < 3⁵⁰

We have: 

2³⁰⁰= (2³)¹⁰⁰= 8¹⁰⁰

3²⁰⁰= (3²)¹⁰⁰= 9¹⁰⁰

For: 8¹⁰⁰<9¹⁰⁰

=> 2³⁰⁰ < 3²⁰⁰