Question

V=LWH
17=9*6*2

Rewrite the formula using the variable x for the length. Substitute the value of the volume found in step 2 for V and express the width and height of the object in terms of x plus or minus a constant. For example, if the height measurement is 4 inches longer than the length, then the expression for the height will be (x + 4).

What is this asking?

Answer 1

its looking for the answer of 9 * 6 * 2

Answer 2

then you have to factor it all out

Answer 3

its 17

Answer 4

x * (x - 2) * (x - 8) = 108
i think you have it from here

Answer 5

no you have to multiply them out not add

Answer 6

oh, yea wow, im dumb. idk why i added them

Answer 7

what would be the expression for the height?

Answer 8

it sounds like there is more to this question that you left out.

Answer 9

it does not make sense

Answer 10

Measure and record the length, width and height of the rectangular box you have chosen in inches. Round to the nearest whole number.

Apply the formula of a rectangular box (V = lwh) to find the volume of the object.

Now suppose you knew the volume of this object and the relation of the length to the width and height, but did not know the length. Rewriting the equation with one variable would result in a polynomial equation that you could solve to find the length.

Rewrite the formula using the variable x for the length. Substitute the value of the volume found in step 2 for V and express the width and height of the object in terms of x plus or minus a constant. For example, if the height measurement is 4 inches longer than the length, then the expression for the height will be (x + 4).


This is the whole question. But I already have the L,W & H

Answer 11

It looks like what they want you to do is take the formula \(V=lwh \) and replace it with \(V=(x+c)(6)(2)\).

Answer 12

what is c?

Answer 13

oops! Nevermind that, I think I misread, give me a moment.

Answer 14

Okay so \(x = l = 9\).
This means \(w = x - 3\) and \(h = x-7\) since \(9 - 3 = 6\) and \(9 - 7 = 2\).
Make sense so far?
I think they then want you to multiply them:
\[V = (x)(x-3)(x-7)\]

Answer 15

how did you get 3?

Answer 16

You have length= 9
width=6
height=2

they want you to call the length x
they want width= 6 = x+ something
in other words 6= 9 + s
s= 6-9= -3
so width is (x-3) (where x is 9)

Answer 17

got it. but then its asking me to simplify the equation and write it in standard form. what equation would that be?

Answer 18

before going on, you should fix your original calculation
V= 9*6*2
the volume is length TIMES width TIMES height

Answer 19

that would be 108

Answer 20

yes. So you know the answer is 9, 6 and 2
but they want you to pretend you did not know the length is 9, and call it x
and you know the width is x-3 (9-3 is 6) and the height is x-7 (9-7 is 2)
and when you multiply them you get the volume:

x(x-3)(x-7)= 108

standard form is ax^3 + bx^2+cx + d=0
where a,b,c,d are numbers.
you have to multiply out your x terms. Can you do that?

Answer 21

I would use FOIL to multiply (x-3)*(x-7) first

Answer 22

(x^2-7x-3x+21)

Answer 23

is that right

Answer 24

-7x and -3x are like terms.

Answer 25

yes, but simplify it -7x-3x = -10 x

now multiply it by x

Answer 26

x(x-3)(x-7)= 108
x(x^2-10x+21)=108
now mult by x
then add -108 to both sides of the = sign

Answer 27

what do you mean multiply by x, you mean 9?

Answer 28

is -7x-3x = -10 x, the simplified form?

Answer 29

no, not by 9 (we are pretending we don't know what number x is)
we are doing
x(x-3)(x-7)= 108 here you multiplied (x-3)(x-7)
x(x^2-10x+21)=108 now distribute the x (mult every term inside the parens)

Answer 30

and yes (x^2-7x-3x+21) is x^2 -10x +21 (after simplifying -7x-3x to be -10x)

Answer 31

Here is an example: x(x^2 +2)= x*x^2 +x*2 = x^3 + 2x

Answer 32

hold on sorry, im gonna read this carefully

Answer 33

would it be: x^3-10x^2+21x=108 ?

Answer 34

yes, one last step to put it in standard form
standard form is ax^3 + bx^2+cx + d=0

add -180 to both sides

Answer 35

what do you mean?

Answer 36

you want standard form: stuff on the left side = ZERO
you have: stuff on the left= 108
you want to "move" the 108 to the other side of the = sign.
write down -108 on both sides of the = sign like this
x^3-10x^2+21x -108 =108-108

and simplify

Answer 37

would i add 108 to the left side?, im sorry i dont get this

Answer 38

i mean, add it to the right side

Answer 39

add -108 (if I typed 180 up above, that is supposed to be 108) to both sides

yes. you start with
x^3-10x^2+21x=108

you add -108 to BOTH sides
x^3-10x^2+21x -108 =108-108

Answer 40

This exercise is supposed to help you understand about equations
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/e/one_step_equation_intuition

Answer 41

what both sides? i added it to the -108 before the =sign and i got -216 but im assuming thats wrong

Answer 42

you start with
x^3-10x^2+21x=108

you add -108 to BOTH sides
x^3-10x^2+21x -108 =108-108

Answer 43

ohhhhh, your not telling me to add the -108 just place them their?

Answer 44

yes , to both sides (to keep things in balance or equal)

Answer 45

so that would be standard form?

Answer 46

what did you get?

Answer 47

im so confused on what to solve, im not sure how to solve it

Answer 48

you are practically done
you have
x^3-10x^2+21x -108 =108-108
on the right side 108-108 is 0, and this simplifies to
x^3-10x^2+21x -108 = 0

that is the polynomial they wanted you to create.
If you solve it (find the x that makes the left side =0), you would find x=9
See http://www.wolframalpha.com/input/?i=x%5E3-10x%5E2%2B21x-108%3D0

Answer 49

which one is the standard form?

Answer 50

standard form is ax^3 + bx^2+cx + d=0

can you see that
x^3-10x^2+21x -108 = 0
is in this form?

Answer 51

yes, so i dont have to replace the a,b and c?

Answer 52

no, when I write ax^3 + bx^2+cx + d=0, that is just to show you what the equation should look like (we assume a,b,c,d are numbers)
See http://www.mathsisfun.com/algebra/standard-form.html (scroll down to polynomial)
for more info.

But your answer is

x^3-10x^2+21x -108 = 0

Answer 53

awesome, thanks!!!

Answer 54

notice it is easier to create this problem (though it did take time), than to solve it. Remember, you want to be the person that creates problems, not the one that has to solve them