Sharing your mathematics in MathYouLike

Two consecutive angles of a regular octagon are bisected. What is the degree measure of each of the acute angles formed by the intersection of the two angle bisectors?

Jessica reads 30 pages of her book on the first day. The next day, she reads another 36 pages. On the third day, she reads another 42 pages. If she continues to increase the number of pages she reads each day by 6, how many days will it take her to read a book that has 270 pages?

The perimeter of a particular rectangle is 24 inches. If its length and width are positive integers, how many distinct areas could the rectangle have?

In the following arithmetic sequence, what is the value of m?

-2, 4, m, 16, . . .

A three-digit integer is to be randomly created using each of the digits 2, 3 and 6 once. What is the probability that the number created is even? Express your answer as a common fraction.

Wilhelmina went to the store to buy a few groceries. When she paid for the groceries with a $20 bill, she correctly received $4.63 back in change. How much did the groceries cost?

Prove that exist a number: 20172017.....20170.....0 $⋮2016$

Find all 3-digit number abc such that: $\overline{abc}=\overline{ab}+\overline{ba}+\overline{bc}+\overline{cb}+\overline{ac}+\overline{ca}$

Find all a,b,c such that: $\overline{abc}+\overline{ab}+a=430$

Find all a,b,c such that: $\overline{abc}+\overline{acb}=\overline{ccc}$

These are the results of the number-guessing contest:

FIRST PRICE: 125

SECOND PRICE: 140

THIRD PRICE: 142

FOURTH PRICE: 121

What is the number?

Prove that: $\dfrac{1}{2}+\dfrac{2}{2^2}+\dfrac{3}{2^3}+...+\dfrac{100}{2^{100}}< 2$

Prove that: $\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+...+\dfrac{n-1}{n!}< 1\left(n\in N;n\ge2\right)$

Prove that with a,b,c > 0: $1< \dfrac{a}{a+b}+\dfrac{b}{b+c}+\dfrac{c}{c+a}< 2$

Prove that: $\left(n!\right)^2>n^2\left(\forall n\in N;>2\right)$

Prove that: $1< \dfrac{1}{n+1}+\dfrac{1}{n+2}+...+\dfrac{1}{3n+1}< 2\left(\forall n\in Z+\right)$

Prove that with a,b,c > 0: $\dfrac{a^2}{b^2}+\dfrac{b^2}{a^2}\ge\dfrac{a}{b}+\dfrac{b}{a}$

Prove that: $2\left(a^8+b^8\right)\ge\left(a^3+b^3\right)\left(a^5+b^5\right)$

Given $a^3+b^3=2$ Prove that $a+b\le2$

Prove that there are no $a,b,c>0$ satisfys: $a+\dfrac{1}{b}< 2;b+\dfrac{1}{c}< 2;c+\dfrac{1}{a}< 2$