Of the following numbers, which has the most factors of 3?
a) 81
b) 270
c) 999
d) 3333

81 has the most factors of 3

Step-by-step explanation:

To conclude which of the following options has the most factors of 3, take each of the number's prime factorization, which will help us solve the problem.

( 1 ) 81 is a composite number and is 9 squared. Knowing that 3 squared = 9, we can say that the prime factorization of 81 = 3 3 3 3, which can also be denoted as 3⁴.

( 2 ) 270 is a composite number. The exponents in the prime factorization are 1, 3, and 1, and therefore it's prime factorization is - 3 5 3 2 3, composed of 3 3s.

( 3 ) If we put all of it together we have the factors 3 x 3 x 3 x 37 = 999. It can also be written in exponential form, with 3 to the power of 3 - hence having 3 factors of 3.

And finally the value 3333 has the prime factorization of 3 11 101, and as you can see it has 1 factor of 3. 81, having 4 factors of 3, is present with the most factors, and therefore is our solution.

answerthe vertex form

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.