If the surface area of a cube is 496 square inches, then which best describes the length of the side of the cube?

The answer to your question is letter D. greater than 9 in

Step-by-step explanation:

Data

Surface area = 496 in²

length of a side = ?

Process

1.- Write the formula to calculate the surface area of a cube

     Surface area = 6 [ side x side]

or   Surface area = 6 side²

2.- Substitution

              496 = 6 side²

3.- Solve for side

              side² = 496/6

              side² = 82.67

4.- Find side

               side = √82.67

               side = 9.09 in

∠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.

tip $2.90

total $17.40