Mathematical Question. All answers must have work shown. Thanks!?

Question

1. Gometry: Supplementary angles are angles whose measures have a sum of 180 degrees. Comlementary angles are angles whose measures have a sum of 90 degrees. Find the measure of an angle whose supplement is 10 degrees more than twice its complement. Let 90-x equal the degree measure of its complement and 180-x equal the degree measure of its supplement. Write and solve an equation.

2. Number Theory: Use for problems 2a and 2b.

Mrs. Simms told her class to find two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer.

2a. Write and solve an equation to find the integers.

2b.Does the equation have one solution, no solution, or is it an identity? Explain please.

Answer 1

Will you show your work by handing in a printout of this page to your teacher?

Answer 2

great schjool start and alreday ppl are askingto do their homework i think we should ban  homework related  questions

Answer 3

1. The supplement is 10 degrees more than twice its complement. This tells us two things about the angle:  something related to the supplement and something related to the complement.

What is the supplement? 180 - x.

What is the complement? 90 - x. So twice the complement is 2 * (90 - x), or 180 - 2x. And then 10 degrees more than that is (180 - 2x) + 10, or 190 - 2x.

We have resolved each piece of information into a simplified expression and we know the two pieces of information equal each other:  let's set them equal to each other in a nice equation and solve for "x."

180 - x = 190 - 2x....subtract 180 from each side

- x = 10 - 2x....add 2x to each side

x = 10

Now substitute x = 10 into the original expressions for the supplement:

180 - x = 180 - 10 = 170.

And into the complement:

90 - x = 90 - 10 = 80.

Is 170 twice 80 plus 10? 2 * 80 + 10 = 160 + 10 = 170. Yes.

So the angle is 10 degrees.

2. First of all, how can we characterize two consecutive even integers that could be any set of two for all we know? Well, since we don't know any of them, let's let a variable like "x" be one of them and see if we can find a way to express the other relative to that. In particular, let's let the smallest of them be "x" and see what the other has to be.

If they are consecutive, and even, they must follow the pattern of "6-8." If you start with 6, the next even integer is 6+2, right? So if "x" is the smallest of them, then we would have:  x and x+2.

Now, the problem states that twice the lesser is 4 less than twice the greater. The lesser is x, so twice it is 2x. The greater is x+2 so twice it is 2*(x + 2) = 2x + 4. That means 4 less than twice the greater is 2x + 4 - 4 which equals 2x.

Our equation then will be pretty simple:

2x = 2x + 4 - 4

2x = 2x

x = x

That's solved.

And that's an identity. "Something equals exactly that same something" is an identity. It could be any pair of consecutive even integers. For instance, 6 and 8:  2*6 = 2*8 - 4? 12 = 16 - 4 = 12. (That's drops "no solution" out of the choosing.) Now try 1,000,000 and 1,000,002:  2*1,000,000 = 2*1,000,002 - 4 or 2,000,000 = 2,000,004 - 4 = 2,000,000. Yep. (That rules out "one solution.") So being an identity is all we are left with. Good thing x = x is an identity!