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I assume this is a division involving combinations???....if so, we have

C(44, 19)  / C (46, 19)   ≈  .339

"Worked out"  we have

(44! / [ (44 - 19)! (19)!] )  /  (46! / [46 - 19)! (19!] )  =

[44! / (44 - 19)!  ] / [ 46!  / (46 - 19)! ]  =

[44 !  (46 - 19) ! ] /  [46 ! ( 44 - 19) ! ]  =

 ([ 44 ! ] /[ 27 ! ]) / ( [ 46 ! ] [ 25 ! ] )   =

[27 * 26] / [ 46 * 45]  =  39 / 115  ≈  .339

Thank you! That was an excellent explanation, it really helped.

To answer your question, let's see, the basic shape is a parabola because of the x^2 (wavering on a graph), in other words, it's not a simple line.

So I'll try to do these two exercises on my own, please correct me if they're wrong:

f(x)=x^2+5x+6

y=0^2+5*0+6

y=0+0+6

y=6  or  (0,6)

f(x)=2x^2+10x+12

y=2*0^2+10*0+12

y=0+0+12

y=12  or  (0,12)

1. Determine where f(x) intersects the x-axis.

f(x)=x^2+9x+18

Mmmmm.....that's quite a different question from what we assumed your original was.....!!!!!

We can write this as

y = x^2 + 9x + 18   

And where it crosses the x axis, "y" will = 0     ... so we have

x^2 + 9x + 18 = 0      factor

(x + 6) ( x +3)  =  0     and setting each factor to 0, we have that  x = - 6 and x = -3

And those are the two points of intersection on the x axis.

No, I don't think there is "Google plus for Math". Have you tried the Khan Academy? They have hundreds of videos explaining all kinds of things in Math, and other subjects. 
 

There's a bit of a dilemma here, although I basically agree with Rom. Where, possible, I will try to point someone in the direction of some resource that can help them. The trouble with trying to "teach" is that, if there are a lot of questions to be answered, you can't spend five [or more] minutes on one single question while others are waiting. If the others dont see their questions being answered in a reasonable amount of time, they will just go somewhere else.

What to do ????

My turn to try:

f(x)=x^2+9x+18

y=0^2+9*0+18

y=0+0+18

y=18

You confused me with a new question.  LOL

YES    If   f(x)= x^2 +9x+18 then the y [really f(x) ] intercept is 18  

 SO  (0,18)  would be one point on the graph.  :))

y=x^2+9x+18 is a polynomial function

This is because the y is out the front by itself and There are a list of terms with x^(some integer) aded or subtracted together after the equal sign.

That is a VERY lay explanation but it will do for the moment.  :))

The number that is tacked on the end, the constant, will always be the y intercept!

Now the highest power of x gives the number of directions that the graph will take (sort of anyway).  This is called the degree of the polynomial.

Lets look at thes polynomial functions.

y=3x+7

y=3x^1 +7

the y intercept is 7

the highest power(degree) is 1 so it only has one direction.   Bingo...It has to be a line!

y=7x^2+12x+5

The y intercept is 5

the degree is 2 so it has 2 directions.   Bingo... It has to be a parabola

y=-6x^3-5x^2+12x

The y intercept is 0   (there is no constant...well there is it is an invisable 0)

The degree is 3 so it has 3 directions so it is (probably) like a sideways S

   I say probably because occassionally the directions are not clear and they look more like little kinks in the graph.  But don't worry about that.

Yours is y=x^2+5x+6

Tell me about its basic shape please.    :))

if n=0 then quiz:=0 else if n=1 then quiz:=1 else quiz:=quiz(n-1)+quiz(n-2) end;

This is code for the Fibonacci sequence     

Yes, I used 'Desmos' as recommended by Rom earlier this week in a previous post, but it didn't show me the steps so I am still stuck. I want to learn :( Thank you for taking the time.

Ok, if f(x)=y, and y=0, then this should be simpler than I have made it out to be, oops. 

My turn to try:

f(x)=x^2+9x+18

y=0^2+9*0+18

y=0+0+18

y=18

So is this all I have to do? Where does the factoring come in to play like you showed me like so:

"I will do a similar one and you see if you can copy the method for your one.

x^2+6x+8

I need to find two numbers that multiply to give +8 and add to give +6

Since they multiply to give a positive they must both have the same sign.

Since they add to give a positive as well, they must both be positive numbers.

ok so what multiply to give 8

1*8

2*4

that is it.  

2+4 =6 so that is the pair we need,  2 and 4

so 

x^2+6x+8=(x+2)(x+4)"

y= x^2+5x+6

The y intercept is NOT around 6.

It is where x=0

Put x=0 into the equation.

y=0^2+5*0+6

y=0+0+6

y=6

The y intercept is EXACTLY 6

NOTE:  I wrote all this BEFORE i saw your last answer.

Is it reasonable for me to assume you used a graphing program to make that graph?

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To make it a little quicker, you also need to be able to factor  

x^2+5x+6

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I will do a similar one and you see if you can copy the method for your one.

x^2+6x+8

I need to find two numbers that multiply to give +8 and add to give +6

Since they multiply to give a positive they must both have the same sign.

Since they add to give a positive as well, they must both be positive numbers.

ok so what multiply to give 8

1*8

2*4

that is it.  

2+4 =6 so that is the pair we need,  2 and 4

so 

x^2+6x+8=(x+2)(x+4)

now it is definitely your turn to give some input :))

I'm not sure, is it a parabola or a slope maybe? The y intercept should be approx around 6?

Ok that is a vey good point.

There is no y in the equations.

Here f(x) has been used instead of y so technically the vertical axis should be labelled as f(x) instead of y.

Just to make it less confusing I will change the equation from  

f(x)=x^2+5x+6

to

y= x^2+5x+6

Now can you tell me anything about this?    Hint:  it is not a line.

Can you tell me what the y intercept is now?  That is where x=0.

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This may be a slow process but you may get a lot more out of it if we interact with each other like this.

Do you know what this will be?  ..a slope?

Can you tell me why? ..because I don't see a 'y' in the equation to intersect the points.

Can you tell me anything else you know about this? I have tried to factor it out and it resulted in 0, I'm assuming I'm taking the wrong steps.

Thank you very much.

Hi, thank you for responding, I'm stuck here and I can't get ahold of my math teacher at this time. so, it is actually this:

1. Determine where f(x) intersects the x-axis.

f(x)=x^2+9x+18

(I tried just factoring it out but it resulted in '0')

Well, you should have put it on a new post but I can certainly try to help you learn.

f(x)=x^2+5x+6

You only just posted so I am assuming that you can answer straight away and I will try to talk you through this question.  That is the best way to learn.  :)

First you really need to recognise the basic shape.  

Do you know what this will be?  

Can you tell me why?

Can you tell me anything else that you already know about this?

 Like maybe the y intercept?

Can you teach me how to graph this linear equation?

f(x)=x^2+5x+6

My math teacher needs me to show my work every step of the way for this problem. Please help (I have the graph alrdy from online calculator, but it doesn't show the math steps in order to achieve it).

x^2+9x+18 =

This is not something that can be graphed.  It is just a queadratic expression.

You most likely mean

y=x^2+9x+18

Now there are different ways to takle this but I will assume that you have not done calculus.

Method:

1. You should rcognise instantly that this is a parabola.  It is concave up because the number in front of X^2 is an invisable +1    A positive x^2 coefficient means it is concave up.

2. Find the y intercept.  That is very easy.  It is where x=0

*Now look for the roots and the axis of symmetry.

3.Factorize the Right hand side.

4. Find the roots (or zeros) That means find the x values when y=0

5. Plot these 2 points.

6. The axis of symmetry is the vertical line half way between the roots.

7. Find the y value for the vertex and plot it.

8. Sketch the graph.

Now give it a go for yourself and ask if you have problems.

4/3 

An easy way to think about this is  by breaking 1.33 into 2 parts.

First start by taking away the whole number.

Now find the corresponding decimal to fraction. I know 0.33=1/3

Next take 1/3 and add the second factor you had which was the whole number.
1/3+1=4/3. I know this because 3/3=1 so 3/3+1/3=4/3

0.333333=1/3 so if i take 1/3+1=4/3.

If you mean -2^2=4 this is also the same as writing -2*-2=4

This is because if you multiply a negative by a negative you get a positive. As well as 2*2=4

Any number to an even amount of exponents(power) it is always positive

Any negative number to an odd amount of exponents(power) it is always negative

hmmm, I don't know.. it doesn't sound right and it is incomplete. :(

5+5=10

10 duh

\(\mbox{what do you know about the relationship between }f^\prime(x) \mbox{ and }(f^{-1})^\prime(x) ?\)

Factor it out:

x^2 + 5x + 6  = (x+3) (x+2) = f(x)  so the function equals 0  at x= -3 and x = -2 it will have a minumum exactly between them at -2.5    where f(x) = 6.25 = 5(-2.5) + 6 = 12.25 - 12.5 = - .25   Then substitute some more 'x' values in to continue the graphical points   .....

I Know!