Question

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)

Answer 1

area = product of adjacent sides
so area = (4x + 5)(3x + 10)

can you expand this?

Answer 2

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

Answer 3

r u there?

Answer 4

Sorry yes.

Answer 5

I am confused.

Answer 6

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

Answer 7

A little....

Answer 8

(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)

Answer 9

Ok okay :]

Answer 10

placing them together means they are to be multiplied

Answer 11

O okay :]

Answer 12

(4x + 5)(3x + 10)

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

= 4x(3x + 10) + 5(3x + 10)

Answer 13

ok?

Answer 14

Okay

Answer 15

can you do that?

Answer 16

yes 1 min :]

Answer 17

12x2+55x+50?

Answer 18

yes right

that represents the are of the rectangle

Answer 19

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

so its degree 2

Answer 20

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

Answer 21

yes

Answer 22

OKay :]

Answer 23

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

thats part B

Answer 24

The last two comments you said correct?

Answer 25

First its degree 2 and its classified as a trinomial.

Answer 26

thats answer to part B

Answer 27

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

Answer 28

What part C lol.

Answer 29

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

Answer 30

Thats all for part c?

Answer 31

yes

Answer 32

Can you help me with 1 more?

Answer 33

one polynomial multiplied another polynomial gives another polynomial

Answer 34

sorry i gotta go right now

Answer 35

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)

Answer 36

Oh ok :-/