Kitaer is a manager at a landscaping company. He has two workers to landscape an entire park, Cody and Kaitlyn. Cody can complete the project in 2 hours. Kaitlyn can complete the project in 1 hours. Kitaer wants to know how long it will take them to complete the project together.

- anonymous

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- anonymous

really confused on this?

- anonymous

@jim_thompson5910

- jim_thompson5910

x = time it takes for Cody to do the job alone
y = time it takes for Kaitlyn to do the job alone
z = time it take them to do the job together
we're given x = 8 and y = 6. Solve for z
\[\large \frac{1}{x}+\frac{1}{y}=\frac{1}{z}\]
\[\large \frac{1}{8}+\frac{1}{6}=\frac{1}{z}\]
\[\large \frac{3}{24}+\frac{4}{24}=\frac{1}{z}\]
\[\large \frac{3+4}{24}=\frac{1}{z}\]
I'll let you finish

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## More answers

- anonymous

so 5/24?

- jim_thompson5910

no

- anonymous

? Please explain

- jim_thompson5910

\[\large \frac{3+4}{24}=\frac{1}{z}\]
\[\large \frac{7}{24}=\frac{1}{z}\]
cross multiply or take the reciprocal of both sides

- anonymous

Oh! Okay :) Sorry, I didn't notice that

- anonymous

so 7z=24

- anonymous

yes?

- jim_thompson5910

now fully isolate z

- anonymous

so 24/7

- jim_thompson5910

yep 24/7

- anonymous

is that the answer?

- anonymous

Can I ask another please?

- jim_thompson5910

sure, go ahead

- anonymous

Thanks :)

- jim_thompson5910

what are some key features that you can think of? any at all?

- anonymous

Maybe some degrees?

- jim_thompson5910

you mean the degree of the polynomial?

- anonymous

yes

- jim_thompson5910

what does the degree tell us?

- anonymous

how many answers it would have

- anonymous

I mean roots

- jim_thompson5910

close, the degree tells us the maximum number of roots, or x-intercepts, possible
example: x^3 + 7x^2 + 9 has at most 3 roots. It could have 3 roots, or 2 roots, or just 1 root.

- anonymous

I understand. :)

- jim_thompson5910

the degree also tells us how many turning points there are
number of turning points = (degree) - 1
example: degree = 3 means we have 2 turning points
|dw:1437527865525:dw|

- jim_thompson5910

also, a degree 3 polynomial has 3 branches
|dw:1437527902361:dw|

- jim_thompson5910

other key features:
* y intercept
* end behavior

- jim_thompson5910

the end behavior is explained in these articles
http://www.purplemath.com/modules/polyends.htm
http://www.mathwords.com/e/end_behavior.htm

- anonymous

Ok! Thank-you<3 So the answer would be

- anonymous

basically we need degress, y-intercepts, and end behaviors

- jim_thompson5910

knowing the degrees helps us determine how many roots max are possible
it doesn't tell us the actual x-intercepts

- jim_thompson5910

you have to set the polynomial equal to 0 and solve for x

- jim_thompson5910

key features used to graph:
x-intercepts
y-intercept
number of turning points (equal to degree - 1)
end behavior
also, a couple of other points doesn't hurt either

- anonymous

Hahha :) Thanks !

- jim_thompson5910

np

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