Question

Someone help please

Now that you have helped Bernard design the pool, he presents you with a situation. There are x number of communities that will be designing homes with the pools. The number of homes within each community is six more than the number of communities. The number of hours that will be required to build each home is double the number of homes in each community.

B. Using the three expressions, interpret the meaning of each grouping of factors as a single unit, and also simplify each expression by finding their product.

Answer 1

C. Explain how polynomials demonstrated the closure property throughout this exploration.


I've already solved A

Answer 2

@hari5719 @SolomonZelman @zepdrix @triciaal @mathmate @mathstudent55 @mathmale @pooja195 @Awolflover1 @satellite73 @ParthKohli

Answer 3

@sleepyjess @dan815 @SithsAndGiggles

Answer 4

@boldjon @DannyO19

Answer 5

might be long but take ur time
tell me if u don't get it
x = number of communities
x + 6 = number of houses per community
2(x + 6) = Hours required to build

Alright, so you got the above information. Now, the question asks you to combine them via multiplication to get some other measure. For example:

If we take the expression "x" for the number of communities and the expression (x + 6) for the number of houses per community, we can multiply them together to yield:

x(x+6) = x^2 + 6x = The number of houses altogether

You can do the same for 2(x+6) and (x+6), as multiplying them together will yield the total time needed to build all the houses in a single community:

2(x+6)(x+6) = 2(x^2 + 12x + 36) = 2x^2 + 24x + 72 is the expression for the amount of hours needed per community.

The question asks for a grouping of all the the above expressions. To do this, you do the same as I showed above, but you use all three expressions. This will yield the total time needed to build all houses in all of the communities:

2(x+6) * (x+6) * x = 2x^2 + 24x + 72 [from previous] (x)
= 2x^3 + 24x^2 + 72x

As for the closure property question, all of the products that we just generated are polynomials. So a multiplication of polynomials yields a closed set of polynomials since their multiplication yields another polynomial. This can be understood through the simple addition of exponents when multiplying by said exponents, and since non-negative exponents are present, their results must also be positive (since you can't subtract exponents under these conditions and get a non-polynomial answer).

Answer 6

Alright, @boldjon I'm gonna try understanding what you just said, tell me if I'm wrong

Answer 7

k

Answer 8

oh one more thing
SUMMARY:
x = # of communities
x + 6 = H
2H = T

Answer 9

So the grouping thing in Part B just wants me to multiply the number of hours * the number of houses * the number of communities, correct?

Answer 10

yup

Answer 11

Wait

Answer 12

Wuts the difference between that and:

and also simplify each expression by finding their product.

???

Answer 13

Oh wait nvm

Answer 14

XD u got it?

Answer 15

Basically, I am supposed to give equations, like the number of hours per house could be calculated using:

2(x + 6)

In that, I could simplify it to 2x + 12, that's what that part is asking, right?

Answer 16

yeah, it's easy once u get it

Answer 17

Alright.

Now Part C

Answer 18

Too much work scrolling up but:

"As for the closure property question, all of the products that we just generated are polynomials. So a multiplication of polynomials yields a closed set of polynomials since their multiplication yields another polynomial. This can be understood through the simple addition of exponents when multiplying by said exponents, and since non-negative exponents are present, their results must also be positive (since you can't subtract exponents under these conditions and get a non-polynomial answer).
"

Answer 19

O_O part c?

Answer 20

Yea, we only did Part B

Answer 21

I'm analyzing ur block of text that answers Part C, hold on

"As for the closure property question, all of the products that we just generated are polynomials. So a multiplication of polynomials yields a closed set of polynomials since their multiplication yields another polynomial. This can be understood through the simple addition of exponents when multiplying by said exponents, and since non-negative exponents are present, their results must also be positive (since you can't subtract exponents under these conditions and get a non-polynomial answer).
"

Answer 22

k take ur time

Answer 23

Okay, so basically, all of the polynomials multiplied leads to another polynomial, which means that they are closed, correct?

Answer 24

@boldjon ??

Answer 25

sorry, i was helping someone and yes ur right

Answer 26

Alright, thanks again!

Answer 27

fan me so u can call on me whenever u need help

Answer 28

byeee

Answer 29

@boldjon Yea I did :)

bye