2^2x+2 *5^x-1=8^x*5^2x

The solution will be "x = 2 and x = -1".

Step-by-step explanation:

The given equation is:

⇒  

On solving "", we get

⇒  

As we know, if the base are same then their powers will be added together.

⇒   ...(equation 1)

⇒   ...(equation 2)

From equation 1, we get

⇒  

⇒  

From equation 2, we get

⇒  

⇒  

So that the correct answer will be "x = 2" and "x = -1".

∠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.

both equations and proportions are better.