The first term on an a. p is p ans its common difference is q. find its 10th term.

p + 9q.

Step-by-step explanation:

The explicit formula for the nth term of an A. P is

an = a1 + d(n - 1) where a1 = the first term and d = the common difference.

So the 10th term when a1 = p and d = q is:

a10 =  p + q(10 - 1)

= p + 9q.

Good morning,

the Tenth term = p+9q.

Step-by-step explanation:

let U₁ be The first term, then U₁=q and U₁₀ be The 10th term

U₁₀=p+(10-1)×U₁

Then,

U₁₀=p+9q.

:)

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−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.