Question

What is the original length of a 4x6 note card?

Answer 1

huh?

Answer 2

Ummm 4 by 6?

Answer 3

Well these are the question i need help with

Answer 4

Wow - sorry for making a little fun there.
Oh well I see that comes with an explanation and a diagram. That changes things considerably.
Original length is 6" (or 6 inches).

Answer 5

lol its okay, i know im not smart in any type of math /:

Answer 6

so then the original length is 6'' and the original width is 4" ?

Answer 7

B) Four pieces have been cut.
C) We are not told the length of 'x' so we have to call the resulting length 6 inches minus 2x.
D) Original width - 4 inches.
E) Four pieces have been cut.
F) Resulting width = 4 inches minus 2x.

Answer 8

thank you so much! for C, would the resulting length be 2 since it was originally 6 inches and four pieces were cut?

Answer 9

Since we don't know the length of 'x', we can't say definitely what the length or width is.
If x is a half inch the resulting width = 6 minus 2*half = 6 -1 = 5.

Answer 10

oh, i see, that completely makes sense! thank you so much! :)

Answer 11

Okay, glad to have helped out.
:-)

Answer 12

well now I am confused because the next question says "Use your answers to parts c and f to express the new dimensions of the box. "

Answer 13

how do i do that if we dont know the true length and width?

Answer 14

I'd answer it by what I stated in part c and f

Answer 15

so then it would 6''-2x by 4"-2x?

Answer 16

Yes or as it might be stated in algebra (6-2x)" by (4-2x)"

Answer 17

that makes sense, but the last question in that section is "The area of the bottom of the box is the product of the new length and width. Write this area as a function in the form: A(x) = your answer"

Answer 18

so how would i go about that if i dont know the exact dimensions of the box?

Answer 19

Multiply (6-2x)" by (4-2x)"
Is this an intro to algebra course?

Answer 20

it's pre calculus

Answer 21

I guess they want you to think in the abstract.
Let me multiply (6-2x)" by (4-2x)"

Answer 22

okay!

Answer 23

If we say x is 3/4 of an inch then width = 4 - 2*.75 = 2.5"
and length = 6 -2*.75 = 6 -1.5 = 4.5"
The area of the bottom of that box is 2.5 times 4.5 * 2.5 = 11.25

Answer 24

(6-2x)" by (4-2x)" =
24 -8x -12x -4x² =
24 -20x +4x²

Let's say x = .75
24 -20*.75 +4*.75*.75
=3.75 + 2.25
=6

Answer 25

thank you so much!! that was very helpful :)

Answer 26

(6-2x)" by (4-2x)" =
24 -8x -12x -4x² =
24 -20x +4x²

Let's say x = .75
24 -20*.75 +4*.75*.75 =
24 -15 + 2.25 = 11.25

Answer 27

Could you help me with these 2 questions? I promise these are the last ones for this problem! lol it is just so confusing

Answer 28

It seems there must be a Part II to that attachment because it talks about "set your question from Part II"

Answer 29

we just did part II

Answer 30

No - that was Part I

Answer 31

Part I-III

Answer 32

See it says "Part I (6 points)"

Answer 33

Yes, and then right under it is part II for 8 points

Answer 34

My answer (I don't think) was submitted by you and I think it can be used for part II A and B


(6-2x)" by (4-2x)" =
24 -8x -12x +4x² =
24 -20x +4x²

Answer 35

Part III
A. and B.

Setting this up in conventional form:
Area = 4x² -20x + 24

If we want an area of 16 square inches then
16 = 4x² -20x + 24
4x² -20x + 8

Solving by quadratic formula
a=4 b=-20 c=8

x = [--20 +-sqrt(400 - 4 * 4 * 8)] / 2*4

x = [20 +- sqrt(272)] / 8

The 2 answers are:
x1 = 4.5615528128

and x2 = 0.4384471872

Answer x1 can't be used because 2 * 4.56 is greater than 4 or 6 so the note card couldn't have ANY dimension.

So the only usable answer is
x2 = 0.4384471872

Answer 36

thank you so much!

Answer 37

u r welcome and thanks for the medal :-)