Anumber is called a perfect number if it equals the sum of all of its factors except itself. for instance, 6 is a perfect number because its factors are 1,2,3 and 6, and 1+2+3=6. what is the next greater perfect number?

28

Step-by-step explanation:

We know that,

A perfect number is a number which is the sum of all of its factors except itself.

Now, as we saw that the first perfect number is 6 because it is the sum of its divisors 1, 2 and 3.

So, we see that the next perfect number is 28.

Now, the divisors of 28 are given by 1, 2, 4, 7, 14 and 28.

Since, 28 = 1 + 2 + 4 + 7 + 14.

i.e. 28 is the sum of all of its divisors except 28 itself.

Thus, 28 is a perfect number.

Hence, the next perfect number is 28.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

congruent segments

step-by-step explanation: