Sam decides to build a square garden. If the area of the garden is 25x2 + 30x + 9 square feet, what is the length of one side of the garden?

5x + 3

Step-by-step explanation:

We factor 25x^2 + 3x + 9.

25x^2 is a perfect square; 25x^2 = (5x)^2

9 is a perfect square; 9 = 3^2

This expression may be a perfect square trinomial.

25x^2 + 30x + 9 = (5x + 3)^2

We check the middle term: 2ab = 2 * 5 * 3 = 30

The coefficient, 30, is correct, so we are dealing with a perfect square trinomial.

length = 5x + 3

∠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.

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a