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Break even occurs when the profit is zero; so set P = 0:

                  0  =  -45(x - 9)² + 1125

           -1125  =  -45(x - 9)² 

                25  =  (x - 9)² 

Either:     - 5  =  x - 9     or       5  =  x - 9

                 4  =  x           or     14  =  x

Now, you need to choose the correct answer.

what doe you mean when you say then , for each....

Set the two equation equal to each other:  -3x² + 12x - 6  =  2x² - 4x + 3

Get all the terms to one side:                      -5x² + 16x - 9  =  0

Multiply by -1:                                               5x² - 16x + 9  =  0

Now, use the quadratic formula to get the two values for x.

Then, for each x-value, find the corresponding y-value by substituting each value

back into either of the original equations.

You will now have the two points of intersection.

:o wow that was great!!! Thx for ur explantion and answer!!!

Since GH || EF, arc(EH) = arc(GF)   --->   x² - 2x  =  56 - 3x

                                                            x² + x - 56  =  0

                                                         (x + 8)(x - 7)  =  0

Either  x = -8 (not allowed) or  x = 7.

arc(EH)  =  x² - 2x  =  (7)² - 2(7)  =  49 - 14  =  35

arc(GF)  =  56 - 3x  -  56 - 3(7)  =  56 - 21  =  35

arc(GH)  =  70

arc(EPF)  =  360 - arc(EH) - arc(GH) - arc(GF)  =  360 - 35 - 70 - 35  =  220

a) The meal deal consists of one sandwich, one drink, one dessert. There are 5 different choices of a sandwich, 5 choices of a desssert, and 6 choices of a drink so \(5\cdot4\cdot6=\boxed{120}\) different combinations.

b) Two of the four desserts are sugar free so there's a \(\frac{1}{2}\) chance that the dessert chosen is sugar free. 3 of the the 6 drinks are sugar free so there's also a \(\frac{1}{2}\) chance the drink chose is sugar free. Therefore the probability that both are sugarfree is \(\frac{1}{2}\cdot\frac{1}{2}=\boxed{\frac{1}{4}}\)

In a geometric progression:     n₁  =  7     and     n₆  =  7/32

Since  n₆  =  n₁ · r⁵      --->     7/32  =  7 · r⁵     

                                     --->     1/32  =  r⁵     (divide by 7)

                                     --->       1/2  =  r       (take the fifth root)

a  =  7 · (1/2)

b  =  7 · (1/2)²  

THIS IS ALSO FROM MBMT MATH TOURNAMENT!!!! You just changed the name of the person in the problem!!! You should actually do the problem like my team. We worked very hard to get the awnswer 2 and we got it correct.

Hi there! so lets break down this question, first we need to expand this into an equation we can solve!

When we expand 

x(x+1)(x+2)(x+3)=120

we get 

\(x^4+6x^3+11x^2+6x=120\)

Now that we have this equation we can start to break down into something we can simplify/factor

\(x^4+6x^3+11x^2+6x−120=120−120 ,\\ x^4+6x^3+11x^2+6x−120=0\)

fun! now we have something we can factor,

\(x^4+6x^3+11x^2-120=0,\\ (x−2)(x+5)(x^2+3x+12)=0 \)

Now we can just look for what value of x makes this new equation equal to zero. 

so we have to make it so that x equals a number that will turn the value into 0 or just set factors into 0. 

I hope that this helps because I dont want to just hand you your answer! If you are still stuck just come back to this thread!

Hope you understand

~ Wolf :D

Oh, oops! I see it now. I don't know where I got the -4x from. Thanks for helping me out!

I'm not sure how you went from \(y(2x-6)=rx+s\)  to  \(2xy-4x=6y+s\). 

You expanded this part wrong, so let's start from this point.

\(y(2x-6)=rx+s\)

\(2xy-6y=rx+s\)

\(2xy-rx=6y+s\)

\(x(2y-r)=6y+s\)

\(x=\frac{6y+s}{2y-r}\)

Using the horizontal asymptote of y = -4, we find that r = -8. 

Now use the point (1, 0) to find s. 

good job, Guest!!!  

Hour hand moves .5 degree per minute and starts at 270 degrees at nine o'clock

    So hour hand is at.   270 + (20*.5)= 280^o

       ^{Minute hand is at 120 degrees  at 20 after}

280-120=160^o  between the hands....

I put it off topic because I felt as if because I had already asked a question that it was unnecary to promote it under an math question... 

~ Wolf

incorrect but thx anyways

Try x = 416

This is as simple as this:   ()

a = 3         b = 4       c = 5

Area  A = (3 * 4)/2 = 6

h = 2A/c = 2.4

x = sqrt( a² - h²) = 1.8

y = 5 - 1.8 = 3.2

You can do the rest

don't ask because you are too lazy to do so, right>

if you can come to this site you can google it

Then use WIKIPEDIA and the WORLD WIDE WEB!

I'm sure you could go to google, or if *you are in a google banned place*, BING, and duckduckgo!!!

Search it up!

No place for history here!

90 million alcumus

That cracked me up

At 9:40, the minute hand is at 4 and the hour hand is between 9 and 10. 

There is \(30 ^\circ*5=150^\circ\)between the minute hand and 9 o'clock. 

The hour hand is \(\frac{20}{60}*30^\circ=10^\circ\) past 9 o'clock.

So our answer is \(150^\circ+10^\circ=160^\circ\)

dont ask

i'm an undercover agent from web2.0calc, and i will report you to the admins.

a - b = 150*pi - 16*pi = 134*pi.

Isn't that cheating?