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See if the following helps :

1)  Standard Form

Adele Acres  -  x^2 + y^2  =  16

Brown Lake  -  (x - 5)^2 + (y - 4)^2  = 9

Cady City  -   (x - 4)^2  + (y + 4)^2  = 25 

2)  General Form

Adele Acres -  x^2 + y^2  - 16  = 0

Brown Lake   -  x^2 + y^2 - 10x  - 8y + 32  = 0

Cady City -  x^2 + y^2  - 8x + 8y + 7  = 0

3)  See the graph :

I assume we aren't counting that the total of two odd numbers is an even number. 

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Excellent, EP  and TOP    !!!!!!

Thank you so much!

Probability of an even number on green=3/6 x probability of even number on red 3/6 x 6^2 =9 ways.

Center  =  (5, -2)

4x^2  + 3y^2 -16x + 9y + 16  = 0       rearrange as

4x^2 - 16x  + 3y^2 + 9y =  -16          complete the square on x and y

4(x^2 - 4x  + 4)  +  3(y^2 + 3y + 9/4)  =  -16 + 16  + 27/4

4 (x - 2)^2  + 3(y + 3/2)^2  =  27/4         multiply through by  4/27

(16/27)(x - 2)^2  + (12/27)(y + 3/2)^2  =  1

16(x - 2)^2          12 (y + 3/2)^2

_______   +         _________  =     1

  27                            27

16 ( x - 2)^2           4(y + 3/2)^2

__________  +     __________    =    1

      27                          9

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(Red, Green) : (2,2) (2,4) (2,6) (4,2) (4,4) (4,6) (6,2) (6,4) (6,6) - 9 ways.

Each hour, Rowena paints  1/14  of the room

And each hour, Ruby paints 1/6 of  the room

So.....we have that

(1/14)(x)  + ( 1/6)(y)  = 1/2

(1/14)(y)  + (1/6)(x)  =  1   

(1/14)x  + (1/6)y  =  1/2

(1/6)x + (1/14)y  =  1  

Multiply both equations through by  42

3x  + 7y   =  21     ⇒   21x + 49y  =  147       (1)

7x +  3y  =   42     ⇒   -21x -  9y  =  -126       (2)

Add (1)  and (2)  and we have that

40y  = 21

y = 21/40

And 

3x + 7(21/40)  = 21

3x  + 147/40  = 21

3x  =  21  - 147/40

3x  =  693/40

x = (693/3)/40  =  231/40

So  (x, y)  =  (231/40, 21/40)

Correct, so B.

Here is a very similar question ....can you see the method to solve this problem?

https://web2.0calc.com/questions/a-challenging-rate-problem-please-help-asap#r1

Assuming that you want us to answer in terms of n, the first few numbers of this sequence are 1,3,6,10... those are the triangular numbers. We know that the formula for finding the sum of the first n triangular numbers is n(n+1)/2, so that's your answer.

The center  is  ( 2, -3)

The major axis is horizontal and the minor axis is vertical

a^2  =  36

a  =  12

Length of the major axis  =  2a  = 2(6)  = 12

b^2  =  12

b = √12  =   2√3

Endpoints of major axis  =  (2,  -3 ± 6)  =  (2,  -3 + 6)  and  (2,  -3-6)   =     (2, 3) and ( 2, -9)

Endpoints of minor axis  = ( 2 ±2√3, -3)  

The center  is  (1, -2)

The major axis is  vertical  so  a^2  = 9   

The minor axis is horizontal so b^2  = 4

The focal distance  =  c  = √[a^2 - b^2 ]  =  √  (9 - 4)  =  √ (5)

So....the foci are located at

( 1, -2 ±√5 )

The equation form we need is

(x + 9)^2              (y + 3)^2  

________   +      _________   =  1

    a^2                      b^2

a  = the length of the major axis / 2  =  14/2   = 7   ⇒  a^2  =  49   

c  = the distance from the center to the focii  = 3 ⇒  c^2  =  9

b^2  =   a^2  - c^2   =  49 - 9   = 40

So we have

(x+ 9)^2               (y + 3)^2

_______     +    _________  =     1

   49                       40

The product of 6 and n   is   6n        now subtract 4  ....which answer do you think it is?

substitute 2 in for a    5 in for b and 4 in for c

(2)(5) - 4 = ??

x = 1

y = 1

z =-1

2 + sqrt(6) + sqrt(2) =~5.864

The same answer as "TOP"

1. We can rewrite is an algebraic equation, 50 = 1/4 * x. Multiplying both sides by 4 gets us x = $200, or C.

2. Five more than x is just 5 + x, or C.

I will attempt this problem, but I'm not sure whether or not my answer is right or not. I set x, y, and z all equal and I got sqrt(2) + 2 + sqrt(6).

Well, why don't you start now that you are very young. By the time you are 21, you will be an expert coder and will make life a lot easier for you.