Question

Examine the figure below and answer the questions that follow. Be sure to write your answers in standard form and write the degree and classification for each answer.

A contractor is putting in a wall in an office building to partition the room into two smaller rooms. The image above shows a 2-dimensional representation of a wall with a cut-out for a door.

Answer 1

2. The contractor is trying to design a scale model of the wall to show the buildings manager. To create this scale, he will have to divide the the area of the wall as calculated in Part A by 4xy4. With the polynomial in standard form, divide the first term only by 4xy4. Then divide the second term only by 4xy4. Show your work for the division of each term by 4xy4 separately.



3. If a window with the area of 12xy4 was placed on this wall, what would be the new area of the wall space left? You must show all work and calculations to receive credit.

Answer 2

Did you calculate the area of the wall?

Answer 3

Im bad at Math sorry.

Answer 4

area= 8000x6y15

Answer 5

good o fresno/madera

Answer 6

You calculated the area of the wall without taking into account the door opening.

Answer 7

You must subtract the area of the door opening from what you got.

Answer 8

what would the area of the door be?

Answer 9

The area of the door is 3x * 4y^4

Answer 10

= 12xy^4

Answer 11

so it would be 800x^6y^15
12x^1y^4 -
--------------
788x^5y^11

Answer 12

No. Look at the variable parts.
You have the large rectangle which is 8000x^6y^15
The the door opening is 12xy^4

In order to combine terms (that means add or subtract terms), the terms must be like terms. Like terms must have the same variables and the same exponents.
x^6y^15 is not the same as xy^4. That means these two expressions are not like terms.

The subtraction is simply

8000x^6y^15 - 12xy^4

It can't be simplified any further.

The area of the wall, taking into account the door opening, is

8000x^6y^15 - 12xy^4

Answer 13

is this the answer for part b?

Answer 14

No. That was the answer to part A, I think, although I can't be sure bec you didn't show the question of part A.

Answer 15

For part 2, you need to divide that expression by 4xy^4.

Answer 16

You are asked to do it one part at a time.

(8000x^6y^15)/(4xy^4) = 2000x^5y^11

(12xy^4)/(4xy^4) = 3

That is the answer to part 2.

Answer 17

I don't understand how you got (12xy^4)/(4xy^4) = 3

Answer 18

wait, nevermind I understand :)

Answer 19

what about part 3? how would I answer that?

Answer 20

For part 3, start with our answer to part 1.
Then subtract the area of the window.

In part 1, we have the area of the wall as

8000x^6y^15 - 12xy^4, right?

Answer 21

Now you need to subtract the area of a window that is 12xy^4.

That means we'll have:

8000x^6y^15 - 12xy^4 - 12xy^4

That is the expression for the wall area after taking off the door opening area and the window area.

Now we notice that we have two like terms.
12xy^4 (from the door opening) and -12xy^4 (from the window)
have the same variables and exponents. They are like terms.
That means they can be combined together.

8000x^6y^15 - 12xy^4 - 12xy^4

= 8000x^6y^15 - 24xy^4

This is the answer to part 3.

Answer 22

okay now these are my answers I would turn it, do I have it right?

A contractor is putting in a wall in an office building to partition the room into two smaller rooms. The image above shows a 2-dimensional representation of a wall with a cut-out for a door.
1. Create the expression that represents the area of the wall space only using the dimensions shown above. Show your work.
First Simplify monomial term number 1: (5x2y3)3
We take each piece of our monomial term inside the parentheses of 5x2y3, and raise it to a power of 3

53 = 5 x 5 x 5 = 125


(x2)3 = x(2 x 3) = x6


(y3)3 = y(3 x 3) = y9

final answer:
(5x2y3)3 = 125x6y9

then we Simplify monomial term number 2: (4y2)3
We take each piece of our monomial term inside the parentheses of 4y2, and raise it to a power of 3

43 = 4 x 4 x 4 = 64


(y2)3 = y(2 x 3) = y6

final answer:
(4y2)3 = 64y6

Our new expression is: (125x6y9)(64y6)
Group constants:
125 x 64 = 8000

Group variables:
x6 = x6
y9 + 6 = y15
final answer:
(5x2y3)3(4y2)3 = 8000x6y15
Then we subtract the area of the door from the area of the wall:
8000x^6y^15 - 12xy^4 It can't be simplified any further.

2. The contractor is trying to design a scale model of the wall to show the buildings manager. To create this scale, he will have to divide the the area of the wall as calculated in Part A by 4xy4. With the polynomial in standard form, divide the first term only by 4xy4. Then divide the second term only by 4xy4. Show your work for the division of each term by 4xy4 separately.
Divide (8000x^6y^15 - 12xy^4) by 4xy^4.
(8000x^6y^15)/(4xy^4) = 2000x^5y^11
(12xy^4)/(4xy^4) = 3




3. If a window with the area of 12xy4 was placed on this wall, what would be the new area of the wall space left? You must show all work and calculations to receive credit.
Now you need to subtract the area of a window 12xy^4 from the area of the wall..
That means we'll have: 8000x^6y^15 - 12xy^4 - 12xy^4
That is the expression for the wall area after taking off the door opening area and the window area.
Now we have two like terms. 12xy^4 (from the door opening) and -12xy^4 (from the window) have the same variables and exponents, which meansThey are like terms.
That means they can be combined together. 8000x^6y^15 - 12xy^4 - 12xy^4 =
8000x^6y^15 - 24xy^4

Answer 23

The piece below (between lines of +++) is from your part 1.

++++++++++++++++++++++++++++++++++++++
Group variables:
x6 = x6
y9 + 6 = y15
final answer:
(5x2y3)3(4y2)3 = 8000x6y15
Then we subtract the area of the door from the area of the wall:
8000x^6y^15 - 12xy^4
It can't be simplified any further.
++++++++++++++++++++++++++++++++++++++++

You need to fix two things.
On the third line, write this: y9 x y6 = y15

Also, you state that you need to subtract the aree of the door, but you did not show its calculation. Remember, the door was given as 4y^4 by 3x, not as an area.

Answer 24

Part 2 is good.

Answer 25

You have the following in part 3.

++++++++++++++++++++++++
Now we have two like terms. 12xy^4 (from the door opening) and -12xy^4 (from the window) have the same variables and exponents, which meansThey are like terms.
+++++++++++++++++

The first term 12xy^4 should also be -12xy^4, like you have for the second one. You left out the minus sign the first time.

Answer 26

Other than those small corrections, it's good. You did a great job.

Answer 27

thank you so much!! :) you helped me out a lot, I really appreciate it

Answer 28

You are very welcome. I am glad to have been of help.