Find the consecutive positive odd integers whose product is 99

9 and 11

Step-by-step explanation:

So let's say that the first integer is x.

That means that the second integer is x+2, since it us the next odd number.

This problem can be easily solved with our mind the answer is 9 and 11, but I'll show you the steps to slove this.

We make an equation using these two numbers:

Now all we gotta do is solve for x:

Now we use either splitting the middle term or quadratic formula:

Now we split each terma and solve for x:

Now the question states positive so we can rule out x = -11.

Now we have the first integer x = 9,

the second integer is x+2 = 9+2 =11

So the two consecutive positive odd integers are 9 and 11

∠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.