Using analytical geometry, prove that the sum of the squares of a parallelograms diagonals equal the sum of the squares of the side lengths.

Define the derangement sum to be the sum of all permutations of the digits of such that no digit appears in its original spot. For example, and . What is ?

So I was working my way through mass points, and I found a rule that basically says:

"If transversal line EF crosses cevian AD in triangle ABC, you must split mass A into Mass ab and Mass ac. Could someone explain to me why this makes sense/why we couldn't just use mass A?

Solve for x and y given that xy=923, x+y=84

if x/(3^3+4^3) + y/(3^3+6^3) =1

and

x/(5^3+4^3) + y/(5^3+6^3) =1

find the 2 values of x and y.

Hello, I needed some help understanding this concept from Chapter 12, Geometry:

Points P, Q and R are on circle O such that

Arc PQ = 78°, arc QR = 123°, and arc PQR = 201°.

1. Find ∠PQO
2. Find ∠POR

Please help me understand HOW to solve these 2 problems.

does anyone know how to quickly identify prime numbers?

thanks.

This is the problem 2.771 from the book Competition Math For Middle School. The printed answer is 16, which is obtained by going through the triangle. I have no idea about what's going on there. Can anyone help explain please?

BTW, my understanding about a way to spell COUNT is simply to choose an order of those letters and write down them one by one at their designated locations, like writing down U first at the 3rd location, then O at the 2nd position, N at 4th, T at 5th, and C at 1st. Therefore, in total we should have 5! ways to spell the word.

The number of factors from 2024 that are greater than are

A store sells a strawberry flavoured candy for 1 dollar each. The store offers a promo where every 4 candy wrappers can be exchanged for one candy. If there is no limit to how many times you can exchange candy wrappers for candies, what is the maximum number of candies I can obtain with 100 dollars?