If the relation R: A → B, where A = {2, 3, 4} and B = {3, 5} is defined by R = {(x, y):x < y, x ϵ A, y ϵ B}, then find R^-1

The shape of the window shown is a regular polygon. The window has a boundary made of silver wire. How many meters of silver wire are needed for this border if two sides are given to be 

If f(x) = (25 – x2)1/2 then f( ) =…..

Given x = {(2, 7), (3, 9), (5, 13), (0, 3)} be a function from Z to Z defined by f(x) = ax + b for some integral a and b. What are the values of a and b?

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.

 Fundamental Algebra:
1. Add:
(ii) –7y² + 8y + 2 ; 3y² – 7y + 1

A regular polygon has 9 diagonals. Find the number of sides and classify it based on the number of sides.

Find the GCF (GCD) of the given pair of monomials.

A regular polygon has 20 diagonals. Find the number of sides and classify it based on the number of sides.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.

Which of the following relations are functions? Give reasons.
(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}
(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}

Note: All functions are relations but all relations are not functions.

Find the GCF (GCD) of the given pair of monomials.

A square has lines of symmetry

Let R be a relation from N-N defined by R= { (a,b) : a, b belong to N and a= b2 }.Are the following true ?
a) (a,a) ∈R , for all a ∈N
b) (a,b) ∈R implies (b,a) ∈R
c) (a,b) ∈R , (b,c) ∈R implies (a,c) ∈R
Justify your answer in each case.

Fundamental Algebra:
1. Add:
(i) x² – y² – 1 ; y² – 1 – x² ; 1 – x² – y²

Draw and find the number of lines of symmetry for the given regular pentagon.