Question

Please help :)

The lengths of two sides of a triangle are shown.

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? Show your work. (4 points)

Part B: What is the length of the third side of the triangle? Show your work. (4 points)

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer. (2 points)

Answer 1

Refer the pic.

Hope it helps.

Answer 2

Step-by-step explanation:

Given:

The lengths of two sides of a triangle are shown.

Side 1: 8x² − 5x − 2

Side 2: 7x − x²+ 3

The perimeter of the triangle is 4x³− 3x² + 2x − 6.

To find:

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?

Solution:

Part A: What is the total length of the two sides, 1 and 2, of the triangle?

Ans: Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Total length of two sides = 7x²+2x+1

Part B: What is the length of the third side of the triangle?

Ans:

Length of the third side = Perimeter-Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

Length of the third side = 4 x³-10x²-7

Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction?

Ans:

Perimeter of triangle: Side 1+ Side 2+Side 3

=8x² − 5x − 2+ 7x − x²+ 3+4 x³-10x²-7

=4x³-3x²+2x-6

Final answer:

Total length of two sides = 7x²+2x+1

Length of the third side = 4x³-10x²-7

Hope it helps you.

*NOTE: Remember that two terms only add/subtract, if they are having same power.

for eg:

x²+3x² =4x²

But x²+3x= x²+3x ,this does not adds or simplify more.

To learn more on brainly:

1) 6x²+7x- I is a quadratic equations. Write values of a, b, c.

https://brainly.in/question/45594910

2) Answer Fast to be brainliest.

https://brainly.in/question/45608378