Question

i'll post the question and a picture of it

Answer 1

A. express the new length of the long side of the note card once the two corners are removed.
B. Express the new width of the short side of the note card once the two corners are removed

Answer 2

so for A i got 6-2x and for B i got 4-2x... right?

Answer 3

new length ? After what transformation ?

Answer 4

so my question is, suppose you want the bottom of your box to cover a total area of 16 in ^2 set up an equation that will help you find the size(x) of the corner you need to cut in order for this to happen. Solve this equation and take note of any extraneous solutions

Answer 5

After the two corners are removed

Answer 6

Ohh, I see after removing the 2 corners

Answer 7

yea from the long side and the short side

Answer 8

So, each corner on the side 6" is x. We have 2 of these so
6 - (x + x) then simplify the expression... makes sense? Do the same for the side of 4".

Answer 9

so for A i got 6-2x and for B i got 4-2x. i already knew that. so my question is, suppose you want the bottom of your box to cover a total area of 16 in ^2 set up an equation that will help you find the size(x) of the corner you need to cut in order for this to happen. Solve this equation and take note of any extraneous solutions

Answer 10

i got (6-2x)(4-2x)=16 and my answers are 0.44 and 4.56.... extraneous solution...?

Answer 11

if area is supposed to be 16,
then
(6-2x)(4-2x)=16 is right.

Answer 12

\(\normalsize\color{black}{(6-2x)(4-2x)=16}\) \(\LARGE\color{white}{ \rm │ }\)
\(\normalsize\color{black}{2(3-x)2(2-x)=16}\) \(\LARGE\color{white}{ \rm │ }\)
\(\normalsize\color{black}{4(3-x)(2-x)=16}\) \(\LARGE\color{white}{ \rm │ }\)
\(\normalsize\color{black}{(3-x)(2-x)=4}\) \(\LARGE\color{white}{ \rm │ }\)
\(\normalsize\color{black}{6-5x+x^2=4}\) \(\LARGE\color{white}{ \rm │ }\)
\(\normalsize\color{black}{x^2-5x+6=4}\) \(\LARGE\color{white}{ \rm │ }\)
\(\normalsize\color{black}{x^2-5x+2=0}\) \(\LARGE\color{white}{ \rm │ }\) so far we get a quadratic.

Answer 13

(-5)²-4(1)(2) = 25-8 = 17.

So,

-(-5)± √17
__________
2

Answer 14

(5±√17)½

Answer 15

I would not approximate it, but if you really need to.
√17 ≈ 4.12

(5±4.12)½
(2.25 ± 2.06)

4.31 0.19

Answer 16

i got 0.44 and 4.56..

Answer 17

you have -5 for "b" (using the quadratic formula)

and [ -b±√(b²-4ac) ] / [ 2a ]

the second minus (next to the b) makes -5 into positive 5,
so it is not
( -5 ± 4.12 ) ½
but it is,
(5 ± 4.12) ½

Answer 18

yea i did get (5 ± 4.12) ½

Answer 19

i'll retype it into my calculator

Answer 20

which one's extraneous..?

Answer 21

extraneous is the one that doesn't work when you check. (if it is not approximately equivalent when you plug it in)

Check by plugging each one into the original equation.
(Sorry for a late reply, I disconnected 3 times -:( )

Answer 22

its fine. Ive plugged them in and i can't find any extraneous ones

Answer 23

if all of them work, then none of them are :)

Answer 24

alright thanks

Answer 25

Anytime... next time, I'll try not to reply so late.

Answer 26

sorry but i have a question... wouldn't 4.56 be extraneous because the side of the box is 4'' so how could 4.56 work...

Answer 27

@SolomonZelman