3. let n = {0, 1, ,9, 10} consider a relation r on nx n defined by (a, b) r (x, y) iff a + y = b + x i) prove that r is an equivalence relation. ii) describe the equivalence classes geometrically. iii) describe the quotient set nxn/r. iv) what is the index of r?

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

2 1/2 feet

step-by-step explanation: