A rectangle has sides measuring (4x + 5) units and (3x + 10) units.
Part A: What is the expression that represents the area of the rectangle? Show your work to receive full credit. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

- anonymous

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- welshfella

area = product of adjacent sides
so area = (4x + 5)(3x + 10)
can you expand this?

- welshfella

= 4(3x + 10) + 5(3x + 10)
can you continue?

- welshfella

r u there?

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## More answers

- anonymous

Sorry yes.

- anonymous

I am confused.

- welshfella

do you follow why
(4x + 5)(3x + 10) is the expression for the area of the rectangle?

- anonymous

A little....

- welshfella

(4x + 5) is the length of one side and (3x + 10) is the length of the other
and the area of a rectangle = length * width ( which are 2 adjacent aides)

- anonymous

Ok okay :]

- welshfella

placing them together means they are to be multiplied

- anonymous

O okay :]

- welshfella

(4x + 5)(3x + 10)
now we have to first multiply (3x + 10) by 4x then by 5
= 4x(3x + 10) + 5(3x + 10)

- welshfella

ok?

- anonymous

Okay

- welshfella

can you do that?

- anonymous

yes 1 min :]

- anonymous

12x2+55x+50?

- welshfella

yes right
that represents the are of the rectangle

- welshfella

Part B the degree of the expression is the highest power which is in 12x^2
so its degree 2

- anonymous

So that answer is for part a?
12x^2+55x+50?

- welshfella

yes

- anonymous

OKay :]

- welshfella

ant its an example of a polynomial In fact as it has 3 terms so its a trinomial
thats part B

- anonymous

The last two comments you said correct?

- welshfella

First its degree 2 and its classified as a trinomial.

- welshfella

thats answer to part B

- anonymous

OK THANK YOU SO MUCH!!!!!!!!!!!!!!!!!!!!!!!

- anonymous

What part C lol.

- welshfella

yw
Part C in part A we multiplied 2 polynomials (4x + 5) and ( 3x + 10) and obtained another polynomial. This demonstrated the closure property of polynomials

- anonymous

Thats all for part c?

- welshfella

yes

- anonymous

Can you help me with 1 more?

- welshfella

one polynomial multiplied another polynomial gives another polynomial

- welshfella

sorry i gotta go right now

- anonymous

A barrel of tomato sauce has spilled on a tile floor. The sauce flow can be expressed with the function r(t) = 2t, where t represents time in minutes and r represents how far the sauce is spreading.
The spilled sauce is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.
Part A: Find the area of the circle of spilled sauce as a function of time, or A[r(t)]. Show your work. (6 points)
Part B: How large is the area of spilled sauce after 5 minutes? You may use 3.14 to approximate π in this problem. (4 points)

- anonymous

Oh ok :-/

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