Question

The length of a pool must be 3x the width plus 3. The depth must be 7 less than 2x the length. How do I write the depth in an algebraic expression?

x=width
3x+3=length
How do I write the depth?
I got 2(3x+3)-7 -- is this correct?

Answer 1

yes you are correct

Answer 2

correct

Answer 3

Thank you both!

Answer 4

welcome

Answer 5

How do I write the volume? I know the formula for the volume of a rectangular prism is LengthxWidthxHight(or depth)

Answer 6

Volume = length x width x height

Answer 7

(x)*(3x+3)*(2(3x+3)-7)

Answer 8

Volume = x (3x+3) 2(3x+3) - 7
= 2x(3x+3)(3x+3) - 7

Answer 9

Thank you @Easyaspi314 !!!

Answer 10

and @nirmalnema !! you guys helped me a lot (:

Answer 11

I got 2(3x+3)-7 -- is this correct?

yes, that is the depth

you could simplify it by distributing the 2
2(3x+3)-7
6x + 6 -7
6x-1 <-- another way to write the depth, after simplifying

Answer 12

with width = x , length= 3x+3= 3(x+1) and depth= (6x-1)
the volume is

width * length * depth
x * 3(x+1)(6x-1)
or

3x(x+1)(6x-1)

Answer 13

@phi I don't under stand how the depth=(6x-1) I understand the 6x but why is it -1 when its supposed to be -7?

Answer 14

@phi nevermind! I didn't see your first reply!! Thank you guys so much!

Answer 15

Now I have to classify the volume polynomial by degree and number of terms.

3x(x+1)(6x-1)
(3x^2+3x) (6x-1)
18x^3-3x^2+18x^2-3x
18x^3+15x^2-3x
3rd degree trinomial.

Is this right? I'm not so confident about this one..

Answer 16

@phi @Easyaspi314 @nirmalnema

Answer 17

yup you r right..

Answer 18

Thanks again! lol

Answer 19

Bernard is realizing that his dimensions are not fitting the way that he wants it to because he forgot about the deck. The deck is going to be a rectangular space that borders the pool. Also, for the pool to fit just right there must be a special product represented when either the area or volume expressions are determined. He wants you to design your own rectangular pool using polynomial expressions, including the deck to borders the pool.

a.Include a diagram or sketch of your pool and deck. Your diagram must have all dimensions represented with polynomials and ensure that a special product will be used.

How do I use a special product for this? @Easyaspi314 @nirmalnema