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Thank you for the help! I never thought of using Vieta's Thereom to solve this. :)

By Vieta's Theorem

The sum of  the roots =  -b / -2

So

(3 + sqrt 5) + (3 -sqrt 5)  =  -b/-2

6  = -b / -2       multiply both sides by  -2

-b=  -12

b =12

Also  the product of the  roots  =   c / -2

So

(3 + sqrt 5) (3 - sqrt 5)  =  c / -2

9  - 5  = c / -2

4 =  c  /-2     multiply both sides  by -2

-8 = c

The parabola is

y=  -2x^2  + 12x  - 8

The x coordinate of the  vertex =  -b /[2a]  =     -12/ [ 2 * -2]  = -12 / -4  =  3

And the y coordinate of the  vertex is   -2(3)^2  + 12 (3)  - 8   =    -18 + 36 - 8 =  10

So....the vertex  is   ( 3, 10)  

The answer to 1. is:

F: All of the below.

The answer to 2. is:
 

C: Contrapositive

Call the  monthly  salary, S

Amount  left after  depositing  (1/2) of his salary in the bank  = (1/2)S

So

(1/3) *(1/2)S    -  15 * 8  = 720    simplify

(1/6)S  - 120  = 720      add 120  to both sides

(1/6)S=  840     multiply both sides by 6

S = $5040

Rearrange as

2x^2 - 12x + 2y^2 + 4y =  20          divide through by  2

x^2 - 6x  + y^2  + 2y  = 10      complete the square on x and  y

x^2 -6x + 9  + y^2 + 2y + 1  = 10 + 9 + 1      factor

(x - 3)^2  + (y +1)^2   =  20

This is a circle  with a center of  (3, -1)  and a radius of  √20

The  side of the square = twice the radius of the circle  =   2√20  = √80

So....the area of the square   =  side^2  =  (√80)^2 =   80  units^2

How many ways are there to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among 4 people if each person must receive exactly 1 of the bracelets?

Find a+b+c.

Hello Guest!

\(f(x) =y= (x-2)*(x-2)+1\\ y=x^2-4x+4+1\\ y=x^2-4x+5\\ \)

\(a=1\\ b=-4\\ c=5\\ a+b+c=2 \)

  !      asinus

"Anchor" J  at any point on the  circumference

Proceeding in a clock-wise direction we could have the following possibilities for  the four points

JKLM

JKML

JLKM

JLMK

JMLK

JMKL

Note that the  two entries in red  are  the ones  where  chords JK  and LM  intersect

So.....the probability of intersecting chords  is   2 / 6    =     1 / 3

See here   : 

https://web2.0calc.com/questions/i-need-help_5754

thanks!

Thank you!!

The  vertex  is  ( 2,1)

The x coordinate  of the  vertex is given by

-b/ [2a] = 2

-b= 4a

b = -4a

And another point on the parabola  is   (0, 5)    so  c  =  5

So   we can solve this

a (2)^2  + b (2)^2 + c  = 1

a(2)^2   - 4a (2)  + 5  =1

4a  -8a  + 5  =1

-4a  = -4

a = 1

And b = -4(1)  =- 4

So....the function is

x^2  - 4x  + 5

So

a + b +  c  =

1  - 4  +  5  =

2

-27 is the answer

thank you for explaing the process with me and also thank you for helping me out i have been so confused on this problem for a few hours 

I = Prt

3940 = P * .06 * 5

3940  = P  *  .3       divide both sides by .3

13,133.33  =  P

This is impossible.....the  cosine only ranges between -1  and 1  inclusive.....so  63/10  = 6.3  which is outside that range

Yep....thanks, DragonLord....I realized my mistake later on.....16 is correct  !!!

CPhill, only a slight mistake. 15/9=5/3, other than that. Good!!! So, I'm pretty sure it would be 16. <3

Equation: y = -2 cos 4 x + 3

Is the 15% interest "simple interest" or "compound interest"? That will make a big difference !!

The way you have it stated in your question, it sounds like "simple interest". If that is indeed the case, then:

[0.15 x 20,000 x 3] + 20,000 = $29,000 - total principal + interest paid to the bank after 3 years.

I see, thank you for your help, Cphill and Guest!!! <3

Cos

amplitude   (14 -4 ft) /2 = 5

5 cos

period  10 hours     2pi/10 = pi/5

5 cos (pi/5  x) 

Shifted 7 hours right        -7 will shift it right

5  cos  (pi/5(x  - 7))   

Midline is at 9   ( the graph is shifted up 9)

5 cos (pi/5 (x-7)) +9 

(a)  The probability  is   5/16 * 3/16  =   15 / 256 ≈  .0586

(b)  The probability  is  5/16 * 3/15  =   5/16 * 1/5  =  1/16  = .0625

The  possible  rational  roots   is given by  

± All  the possible factors of  15   divided by  All the possible factors of  9

Factors  of  15 =   1, 3, 5, 15

Factors  of  9  =  1, 3 , 9

So...all  the possible rational roots  =    ± (  1 , 1/3 , 1/9 , 3,  5 , 5/3 , 5/9 , 15  )

So.....16  possible rational roots

Thanks to DragonLord for catching my earlier error   !!!!

Hi Melody: Believe or not, if you reverse gene3141's power expansion, he gets EXACTLY  the same answer  as Guest #3, or: 473 / 729. Here is geno3141's calculation with "reversed powers" of 2/3 and 1/3 as follows:

6nCr2*(2/3)^4*(1/3)^2 + 6nCr3*(2/3)^3*(1/3)^3 + 6nCr4*(2/3)^2*(1/3)^4 + 6nCr5*(2/3)^1*(1/3)^5 + 6nCr6*(2/3)^0*(1/3)^6  = 473 / 729