Question

Debbie sells cookies and hotdogs. The daily cost of making cookies is $460 more than the difference between the square of the number of cookies sold and 20 times the number of cookies sold. The daily cost of making hotdogs is modeled by the following equation:

C(x) = 2x2 - 80x + 1,200

C(x) is the cost in dollars of selling x hotdogs.

Which statement best compares the minimum daily cost of making cookies and hotdogs?

It is greater for hotdogs than cookies because the approximate minimum cost is $300 for cookies and $392 for hotdogs.

It is greater for hotdogs than cookies because

Answer 1

Here are the answer choices: It is greater for hotdogs than cookies because the approximate minimum cost is $300 for cookies and $392 for hotdogs.

It is greater for hotdogs than cookies because the approximate minimum cost is $360 for cookies and $400 for hotdogs.

It is greater for cookies than hotdogs because the approximate minimum cost is $400 for cookies and $360 for hotdogs.

It is greater for cookies than hotdogs because the approximate minimum cost is $392 for cookies and $300 for hotdogs.

Answer 2

@jdoe0001

Answer 3

@sjada143

Answer 4

well... what do you think about the 1st equation? any ideas what it might look like? the cost of making cookies that is

Answer 5

If I had to go with one answer it would be "B"

Answer 6

in short.. you have 2 equations... ... so you'd want to find their vertex... then you can tell
which vertex is higher and from what ranges

Answer 7

Yea bro that's the problem I dont know how to make the equation

Answer 8

difference => minus -

so
"$460 more than "
+ 460

"the difference between "
( ? - ? ) + 460

"difference between the square of the number of cookies "
\((x^2 - ?)\)

"and 20 times the number of cookies"
20 * x = > 20x

"the difference between the square of the number of cookies sold and 20 times the number of cookies"
\(\bf (x^2 - 20x))\)

-----------------------------------------------------
"$460 more than the difference between the square of the number of cookies sold and 20 times the number of cookies"

\(\bf x^2-20x+460\)

Answer 9

Oh

Answer 10

Ok now what do I do

Answer 11

so you have 2 quadratic equtions, and thus 2 parabolas.. \(\large {
\textit{vertex of a parabola}\\ \quad \\

\begin{array}{llll}
f(x) = {\color{red}{ 1}}s^2{\color{blue}{ -20}}s{\color{green}{ +460}}\\
c(x) = {\color{red}{ 2}}s^2{\color{blue}{ -80}}s{\color{green}{ +1,200}}
\end{array}\ \quad
\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)
}\)

find their vertex... and then do a quick graph

once you know their vertex.... you can see where the price goes up and down
and where it makes a U-turn

Answer 12

hmmm should be "x" there anyhow
\(\large {
\textit{vertex of a parabola}\\ \quad \\

\begin{array}{llll}
f(x) = {\color{red}{ 1}}x^2{\color{blue}{ -20}}x{\color{green}{ +460}}\\
c(x) = {\color{red}{ 2}}x^2{\color{blue}{ -80}}x{\color{green}{ +1,200}}
\end{array}\ \quad
\left(-\cfrac{{\color{blue}{ b}}}{2{\color{red}{ a}}}\quad ,\quad {\color{green}{ c}}-\cfrac{{\color{blue}{ b}}^2}{4{\color{red}{ a}}}\right)
}\)

Answer 13

Ok, I found out that the vertex of the first equation is 20,400 and the second equation's vertex is 10,360

Answer 14

well... ok... so now we know where the costs DROPS and then goes back UP

Answer 15

so... what do you think?
keep in mind that the vertex....is an upward opening parabola, since the leading term is positive

the vertex is where the cost of making either cookies or hotdogs drops to its lowest
and if you're making them... of course you'd want the cost low

Answer 16

Ok so it is apparenly B when I graph it

Answer 17

@jdoe0001 ?

Answer 18

@jdoe0001 Are you there?

Answer 19

yes

Answer 20

@JuliusTheGreat @StudyGurl14

Answer 21

Anyone?

Answer 22

Oh thank god your back:D

Answer 23

@jdoe0001 I found out it is B, am I right?

Answer 24

you're correct

the cost of hotdogs at its minimum is 400
the cost of cookies at its minimum is 360

thus the cost for hotdogs is greater

Answer 25

sit is a bit lagged, also

Answer 26

Ok can you help with one more?

Answer 27

site that is, is a bit lagged =)

Answer 28

sure, post anew, if I dunno somene else may :)