Sharing your mathematics in MathYouLike

Every week (starting from question 1) I will post 6 - 7 questions to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION THIS TIME IS:

19) Given\(\Delta ABC\) (AB = AC), \(\widehat{A}\) = 20^o. Take point D on AB that AD = BC

Find \(\widehat{ACD}\)

Every solution worths one point

Every week (starting from question 1) I will post 6 - 7 questions to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTIONS TODAY ARE:

17) Prove that: \(G=\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}< 1\)

18) Prove that: \(L=\dfrac{1}{2!}+\dfrac{5}{3!}+\dfrac{11}{4!}+...+\dfrac{n^2+n-1}{\left(n+1\right)!}< 2\)

Every week (starting from question 1) I will post 6 - 7 questions to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTIONS TODAY ARE:

15) A box of chocolate has gone missing from the refrigerator. The suspects have been reduced to 4 children. Only one of them is telling the truth.

John: "I didn't take the chocolate"

Wendy: "John is lying"

Charlies: "Wendy is lying"

Sally: "Wendy took the chocolate"

Who took the chocolate?

16) Given:

8 + 1 + 3 = 3

9 + 0 + 9 = 9

4 + 5 + 3 = 3

1 + 4 + 6 + 2 = ?

Find the missing number

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

14) A rectangle is folded like below. Knowing that the area of figure 2 is \(\dfrac{2}{3}\) the rectangle and the area of the slashed triangle is 24 cm². Find the area of the rectangle

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTIONS TODAY ARE:

12) Given \(\Delta ABC\) (AB = AC). Find\(\widehat{ABC}\)

13) Andy and Beth is in a race at the pool. Andy runs around the pool while Beth swims by the length of the pool. Knowing that:

- Andy is three times as fast as Beth

- The time Beth swims 5 turns is equal to the time that Andy runs 6 turns around the pool

- The length of the pool is 50m

What is the width of the pool?

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

11) Mr. Cook bought a big box of his favourite Halloween candies to hand out to trick-or-treaters. However,
he ate half of all the candies himself before the first child came and took her share. He ate half of what
was left before the second child came, and half of what was left again before the third child came and
took all of the remaining candies. If it is known that each child received the same number of candies,
which of the following statements is certainly true about how many candies Mr. Cook originally bought?
(A) It is a multiple of 3

(B) It is a multiple of 4

(C) It is a multiple of 6

(D) It is a multiple of 7

(E) It is a multiple of 11

(Full answer please)

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

10) Given \(\Delta ABC\) (\(\widehat{A}=90^o\), AB = AC). O is the intersection point of 3 perpendicular bisectors; I is the intersection point of 3 bisectors in the triangle

a/ Given AB = c, BC = a, CA = b, \(p=\dfrac{a+b+c}{2}\), r is the distance from I to BC

Prove that r = p - a

b/ Prove that if \(\Delta ABC\) rights, it must right at I

(Draw the figure if possible)

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

9) Find 3 positive integers x, y, z that satisfy:

- \(x^3-y^3-z^3=3xyz\)

- The area of the square that includes side x = The perimeter of the rectangle with sides y, z

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTIONS TODAY ARE:

7) Given 3 integers a, b and c that satisfy: a² = b² + c². Prove that a.b.c\(⋮\) 60

8) Find the smallest value of \(\overline{abcd}\) that satisfy: \(\overline{abcd}=7\times\overline{ab}\times\overline{ad}\)

Remember: - You just need to answer 1 of these

- One point/answer/question

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

6) Find x that satisfy:

- \(x\in Q\), x² is a square number

- x² + 5 and x²- 5are also square number

Let's see who can solve this

Your IQ will be over 150 if you can

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

5) Given as shown:

square ABCD
equilateral triangle ABE and BDF

Find \(\angle EFD\:\)

(MYTS - 2018 - Grade 7)

A B C D E F

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

4) Find the smallest positive integers N such that:

- \(N⋮99\)

- N doesn't include digit 9

( MYTS - 2018 - Grade 7)

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

3) Find the smallest prime number including 3 digits \(\overline{abc}\) that \(a,\overline{ab},\overline{abc},c,\overline{cb},\overline{cba}\) are also prime numbers

(MYTS - 2018 - Grade 7)

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

2) Given \(\Delta ABC\) right at A

AB = 3 cm & AC = 4 cm

Draw a square BCED outside the triangle A B C D E 4 3

What is the length of AD?

(MYTS - 2018 - Grade 7)

Everyday (starting from question 1) I will post 1 - 2 question(s) to get a point:

- The fastest person who answer correctly will get 1 point/question/answer

- You can still answer my old question at https://mathulike.com/discuss/member/leanhduy0206 and get point

THE QUESTION TODAY IS:

1) The odd numbers is sorted into rows below:

1

3 5

7 9 11

13 15 17 19

21 23 25 27 29

... ... ... ... ... ... ...

What is the sum of the numbers in row 20?

(MYTS - 2018 - Grade 7)

Given \(A=2018^2-2017^2+2016^2-2015^2+...+2^2-1^2\)

Find the last two digits of A

How many prime numbers maximumly are there in 100 consecutive natural numbers?

Find the last two digits of \(7^{107}\)

In this figure, \(\angle GJA=113^o\)

\(\angle A+\angle B+\angle C+\angle D+\angle E+\angle F+\angle G=x^o\)

Find x

A natural number N is called gallant number if N is divisible by its digits and the sum of its digits

Ex: 12 is a gallant number because \(12⋮1;2;1+2\)

102 is not a gallant number because \(102⋮1;2;1+0+2\) but \(102⋮̸0\)

Find the smallest gallant number that is divisible by 11