MeowLover17
  • MeowLover17
The lengths of two sides of a triangle are shown below: Side 1: 8x2 − 5x − 2 Side 2: 7x − x2 + 3 The perimeter of the triangle is 4x3 − 3x2 + 2x − 6. Part A: What is the total length of the two sides, 1 and 2, of the triangle? Part B: What is the length of the third side of the triangle? Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
MeowLover17
  • MeowLover17
@welshfella
Hero
  • Hero
@MeowLover17, What is (8x^2 - 5x - 2) + (7x - x^2 + 3) ?
MeowLover17
  • MeowLover17
One moment

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Jhannybean
  • Jhannybean
Rearrange your terms to combine like terms with eachother. It makes it easier to evaluate.
MeowLover17
  • MeowLover17
I got +6x^2+2x+1 @Hero
MeowLover17
  • MeowLover17
Sorry my computer died
MeowLover17
  • MeowLover17
@Jhannybean
MeowLover17
  • MeowLover17
Hello hero i got what i wrote above
MeowLover17
  • MeowLover17
So would that be the total length of the two sides??
Hero
  • Hero
You should have gotten 7x^2 + 2x + 1
MeowLover17
  • MeowLover17
Oh sorry yes i see
MeowLover17
  • MeowLover17
So hero 7x^2 + 2x + 1 <- This is my answer for part A correct?
MeowLover17
  • MeowLover17
how would i find the length of the third side?
Hero
  • Hero
To find the length of the third side subtract the result you got for part A from the perimeter.
MeowLover17
  • MeowLover17
That's what i was thinking let me do that
MeowLover17
  • MeowLover17
so i would receive -4x^3+10^2+7?
MeowLover17
  • MeowLover17
for the length of the third side
Hero
  • Hero
Subtract this way: |dw:1441579511663:dw|
MeowLover17
  • MeowLover17
ok
MeowLover17
  • MeowLover17
-4x^3 -4x^2-5x-3
MeowLover17
  • MeowLover17
Is what i got
MeowLover17
  • MeowLover17
and if thats correct please help me with part C because i dont understand what its asking.
Hero
  • Hero
What is 4x^3 minus zero?
Hero
  • Hero
|dw:1441579942249:dw|
MeowLover17
  • MeowLover17
+4x^3
MeowLover17
  • MeowLover17
4x^3 -4x^2-5x-3
Hero
  • Hero
What is -3x^2 -(-x^2) ?
MeowLover17
  • MeowLover17
-2x^2
Hero
  • Hero
Yes. When you're subtracting one expression from the other, you have to flip the signs.
MeowLover17
  • MeowLover17
Oh i understand i forgot to change the signs
MeowLover17
  • MeowLover17
Yes :/
MeowLover17
  • MeowLover17
so i get 4x^3-2x^2-5x-9
MeowLover17
  • MeowLover17
For the third side
mathstudent55
  • mathstudent55
|dw:1441580340586:dw|
mathstudent55
  • mathstudent55
|dw:1441580483756:dw|
mathstudent55
  • mathstudent55
To find the third side, subtract the sum of the lengths of the first two sides (Part A) from the perimeter.
MeowLover17
  • MeowLover17
Okay so i would recieve 4x^3-10x^2-7
MeowLover17
  • MeowLover17
Right?
Hero
  • Hero
Somehow I wrote the second term incorrectly.
MeowLover17
  • MeowLover17
I just noticed that lol
MeowLover17
  • MeowLover17
But hero now that i have done gotten part B how do i do part 3?
MeowLover17
  • MeowLover17
Part B is 4x^3-10x^2-7 correct?
mathstudent55
  • mathstudent55
|dw:1441580817818:dw|
mathstudent55
  • mathstudent55
Correct. Your Part B is good. 4x^3 - 10x^2 - 7 is correct.
MeowLover17
  • MeowLover17
yes now how do i do part C?
MeowLover17
  • MeowLover17
please help
mathstudent55
  • mathstudent55
For Part C, you need to understand what this sentence means: "polynomials are closed under addition and subtraction"
MeowLover17
  • MeowLover17
i don't understand what it means :/
mathstudent55
  • mathstudent55
Here is an example. The set of integers is closed under addition, subtraction and multiplication. That means that when you add two integers, or when you subtract integers, or when you multiply integers, the answer is an integer. Integers are not closed under division because when you divide integers, you may get a non-integer answer. For example, 3/4 is not an integer.
MeowLover17
  • MeowLover17
oh i see
mathstudent55
  • mathstudent55
Now think of your problem and the set of all polynomials. If you add two polynomials, is the sum always a polynomial?
MeowLover17
  • MeowLover17
So yes part A and B are closed under subtraction and addition since when i receive the sum of one problem it is still an integer.
MeowLover17
  • MeowLover17
Is that answer correct for part c?
mathstudent55
  • mathstudent55
Above, for Part A, we did add two polynomials. The sum was a polynomial. This leads you to think that adding any polynomials together will result is a polynomial.
mathstudent55
  • mathstudent55
In Part B, we subtracted polynomials and the difference was a polynomial. That makes us think that polynomials are closed under subtraction.
MeowLover17
  • MeowLover17
yes the sum is always a polynomial isnt it?
mathstudent55
  • mathstudent55
Your statement shows you have the right idea, but we are dealing with polynomials, not integers, so I'd modify it this way: "Parts A and B show that polynomials are closed under addition and subtraction since when I added or subtracted polynomials, the result is still a polynomial."
MeowLover17
  • MeowLover17
Thanks you :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.