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I wasn't through.  I was previewing the text and then clumsily clicked Publish instead of Edit. 

To finish: 

There are 5 seating positions, in the straight row. 

The girls can be arranged in 6 ways in each position.

So there would be 30 ways the girls could be seated. 

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Yes, but he was also cursed by the devil, so it mostly balances out. 

LOL!!!!!

f(5)  =  3f(5-2) - 2f(5 - 1)

f(5)  = 3f(3) - 2f(4)

f(5)  = 3 [ 3f(3-2) - 2f(3 - 1) ] - 2 [ 3f(4-2) -2f(4 - 1)]

f(5)  = 3 [ 3f(1) - 2f(2)] - 2[ 3f(2) - 2f(3) ]

f(5)  =  3 [ 3(-1) - 2(3) ]  - 2 [ 3(3) - 2f(3) ]

f(5) = 3[ -9] - 2 [ 9 ] + 4f(3)

f(5) = -45 + 4 [3f(3 - 2) - 2f(3 - 1)]

f(5) = -45 + 4 [ 3f(1) - 2f(2) ] 

f(5)  = -45 + 4 [ 3(-1) - 2(3) ]

f(5)  = -45 +4 [ -3 - 6 ]

f(5)  = -45 + 4 (-9)

f(5)  = -45 - 36

f(5)  = -81

The Smith family has 4 sons and 3 daughters. In how many ways can they be seated in a row of 7 chairs such that all 3 girls sit next to each other?    

Number the chairs 1, 2, 3, 4, 5, 6, and 7

The girls will be seated together if they're in chairs  1, 2, 3

                                                                                 2, 3, 4

                                                                                 3, 4, 5

                                                                                 4, 5, 6

                                                                         or     5, 6, 7

unless you arrange the chairs in a circle

and then you can add to the above                          6, 7, 1

                                                                                 7, 1, 2

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ok believe it or not,,,, i had to do the same thing today LOL 


we had to read a book on our own, write an essay on it and present it.... 

the teacher told me my presentation was great but i'm scared lol i think i did bad ngl 

and oh my god shakespeare is SOOOOO annoying i don't understand a thing they say but uhhh this website really really helped me get through the shakespeare unit and let me tell you,,, after i discovered this website i kept getting 100s on my "mini essays" and quizzes 

they have really really helpful translations and like they have little annotations and translations in the margines which mainly helped me but yeah

its called 

myshakespeare.com

:D i hope it helps lol 

You have been blessed by God Cphill :D:D:D:D

also i am bad at thee and thy language. But no worries, I think I will get through our Shakespeare unit just fine.

Hamlet is a bit confusing though... just a bit 

Lol got a 4 page essay to memorize so I can present it.

Its called the dreaded ORAL>

Its due on Wednesday.

But my fate is fair! Compare to some unfortunate, thee will succeed with preparation!

Some people in my class haven't STARTED their essay, and they barely have finished the book their essay is on. Muchless memorize their entire speech. And... its due in two days.

Lesson: Don't procrastinate

thank you. 

We have the form  

ax^3 + bx^2 + cx +d

I think that we should have  f(-1)  = 15

Since (0,0)  is on the graph, then d  =  0

So  we have this system of equations

-a   +  b  -  c   = 15    (1)

a  +  b  +   c  = -5      (2)

8a  + 4b  + 2c   = 12    ⇒   4a + 2b + c  =  6  (3)

Add (1) and (2) and we get that  2b = 10  ⇒  b  = 5

Sub this into  (2) and (3) and we get that

a + 5 + c  =  -5  ⇒   a + c  =  -10   ⇒  -a - c  =  10   (4) 

4a + 2(5)  + c  = 6  →  4a + c  =  -4     (5)

Add (4)  and (5)  and we get that 

3a  = 6

a  = 2

And

-2 + 5 - c   = 15

-c  = 12

c  = -12

So....the function is

f(x)  = 2x^3  + 5x^2 - 12x

Factoring we have that

x (2x^2 + 5x - 12)  = 0

x (2x - 3)(x + 4)  = 0

So....settting  each factor to 0   and solving for x gives the  x intercepts  of  x  = 0 , x = 3/2 and x  = -4

Isosceles triangles?    I can find 12

I cant find the edit botton so ..

The function  \(f(n) = 3f(n-2) - 2f(n-1) \)  , where  \(f(2) = 3\)  and   \(f(1) = -1\)  . What is the value of   \(f(5)\) ?

Is this any better ?

Tell me if not.

We split it up into two cases, one where the first number is odd and one where the first number is even.

ODD: We have 3 choices for the first, 2 choices for the second, 3 choices for the third, and so on, giving us a number of 108 possible ways.

EVEN: We have 2 choices for the first, 3 choices for the second, 2 choices for the third, and so on, giving us a number of 72 possible ways.

108+72 = 180 possible combinations.

ah i see :D 

thanks for clarifying CPhill! 

thank you! 

i'd try to help but i am sort of confused in a way :( 

could you write the functions more spaces out please and i'll try to help! :) 

thank you >w<

Yes, I would definitely recommend what CPhill and heciticar said. Don't panic, you'll do just fine. Don't cram either, study at regular intervals. Good luck!

please help.ive been stuck on this for nearly 1 hr 

thanks a lot everybody! i really appreciate it :D

well i don't really know what you mean by that OP but you should think of f(x) and h(x) in terms of y! 

remember y=mx+b or in other words slope intercept form

you should use that method and graph normally 

for ex: ill do the first one f(x)=x 

remember!! we think in terms of y! 
so...... 
f(x)=x would be the same as y = x

now let's evalute our question: 

hmmm doesn't seem like it states the y intercept, so we are gonna plot our y intercept as (0,0) because when they don't "say" the y intercept so basically we are saying y=x+0

and now let's do our slope 
well it seems like you have a slope of wait wait!? x? no.....

note that when they say x it means 1/1x so you would have your rise as 1 and your run as 1 as well and once you have that! you can graph your line :D 


now.... what if they said y=-x? 

well no problem!! it would be -1/1x 

:)) 


im going to leave the other to you to solve now, and i hope this helped you in some way !! :))

A good night sleep can help tremendously.

If you did all the homework  and understood all the concepts.....no worries.....you'll do fine....