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(3x)^2-4y^2 if x = -2 and y = -3

(3(-2))^2 - 4(-3)^2

(-6)^2 + 12^2

36 + 144

= 180

#SpookySkeleton

CR

Here is your linear graph

You can use your graph paper. You could use  4cm represents 10^16 metres.  Then your number line will be 4*8=32cm long

Mercury through to Pluto are so close to the sun that the distance is not discernable.  They are all at 0 on top of the sun. The other 3 points are the stars. You can add the labels.

moderator

The standard form of the circle equation is:  (x - x0)² + (y - y0)² = r² , where the coordinates of the centre are (x0, y0) and the radius is r.

Adele Acres: Since this is at the origin x0 = 0 and y0 = 0 and we are told r = 4.

Brown Lake:  5 miles east of the origin means x0 = 5; 4 miles north means y0 = 4; we are told r = 3.

Cady City:  4 miles east means x0 = 4; 4 miles south means y0 = -4  (note that it is negative);  we are told r = 5.

Can you take it from  here?

take a hot bath and get a good night's sleep

you'll do fine

Ah,,, i see thanks melody :)

Put it into standard form,

you do this by completing the square for the y terms.

Then you isolate the constant, then square root it to find the radius.

2 y-intercepts

https://prnt.sc/pgpfqx 

The one on the right. 

Since the maximum compounding is continuous compounding, therefore 9% compounded continuously is equal to:e^0.09 =1.0941742837 - 1 =0.0941742837 - which is the effective annual rate.
But, in order to convert it to a monthly compound, we must take the 12th root of: 1.0941742837^(1/12) =1.0075281954 - 1 x 1200 =9.0338345334% compounded monthly =9.41742837 which is 9% compounded continuously.
FV = PMT x {[[1 + 0.090338345334/12]^(10*12) - 1] / (0.090338345334/12)}
FV =$1,700 x{[[ 1.0075281954 ]^120 - 1] / (0.0075281954)}
FV =$1,700 x                   193.88485999672
FV =$329,604.26 - FV of the income after 10 years.

Note: You could also use:0.09/12 =0.0075 =e^0.0075 =1.0075281954 - which is the same as above.

You use combination to find cases

And the ruel for probability is the number of selected cases OVER all possible cases. 

Then you can find the probability where one is hOpLeSsLY rOMaNTiC out of the two chosen. Then you can add that to the answer of the first question.

I will let you find that out

Chris just forgot the -g(x) portion of f(x)

so he got 9 fpr the first part...

9 - (2(3)-1)

9-6+1 = 4

13%,

So lets pretend that 13 people are hOpLeSsLY rOMaNTiC, and that there is 100 people.

To find the probability for the first question, we find the combination of 2 chosen out of 13 over the combinatino fo 2 chosen out of 100

So 

78    

4950

13/825

Yes you must be taking an AoPS class! How lucky of you Saketh :D

Just try the problems they give you first, and try your best. And maybe post your attempted solution with the question.

*You will get smarter (trust me)*

If (x+4) is a factor, then  x+4 = 0      so  x= -4

   if you put -4 into the origianl equation (this would be f(-4) ) and get any other number besides  0    , then (x+4) is not a factor.....

      can you figure this out now?

XDDDDDDD

Initial location   -4,9 

final location     -14, 2       (10 units left  7 units down)

Now you have two points on a line......let's see....do you remember how to find the slope between these two points?

Subtract   "  3x⁴ +2x-1 "   from both sides of the equation.....and the left side will be left with only  h(x) =...........

Since f(x) is multiplied by the x   fo  (x-1)   the degree will be raised by ONE.....so f(x) must be of 3rd degree  (it has an x³ term in it)

Jose's final amount will be   FV       FV = 50000(1.04)^2        .04 is the interest  2 is the years

Patricia will have     50000(1.01)^8        .01 is the periodic interst rate    each period (3mos)  total periods = quarterly x 2 yrs  =8

I'll let yu calc the diff...

Let g(x) = ax + b. Then g(f(x)) would be a(2x-3) + b

a(2x-3) + b = 2ax -3a + b = 5-4x

The x coefficients must match up, and the constants must match up as well, so 

2ax = -4x

a = -2

We can then plug it into 2ax - 3a + b

-4x +6 + b = 5-4x

6 + b = 5

b = -1

so g(x) = -2x-1

x=4

g(x)= -2(4) - 1 = -8 - 1 = -9

How long will the annuity last for?