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The  sum  of  the roots  =   3

So

a + b  =  3      square both sides

a^2 + 2ab + b^2   =  9        (1)

The product of the roots  =  1

So  ab  = 1        (2)

Sub (2)  into (1)

a^2  + 2(1)  + b^2  =  9

a^2  + 2  +  b^2  =  9

a^2 + b^2   =  7

thanks, hugo for explaining, I really appreciate it:)

Just to expalin

The quadratic formula is

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

So we have

\(x = {7 \pm \sqrt{-7^2-4*(-9)} \over 2} = {7 \pm \sqrt{49-36} \over 2} = {7 \pm \sqrt{13} \over 2}\)

That's then +/- sqrt(13), so the difference is (7+sqrt(13))/2 - (7-sqrt(13))/2 =

(7 - 7 + sqrt(13) - ( - sqrt(13))/2 = 2(sqrt(13))/2 = sqrt(13)

So I believe the answer is sqrt(13)

So I don't understand where the sqrt(85) came from.

x +  y =  k

y  =  -x +  k

x^2  + ( -x + k)^2  =  k

x^2  + x^2 - 2xk  + k^2   =  k   

2x^2 - 2kx  + k^2 - k  =  0 

If  this has a   unique solution for k   then

(-2k)^2  - 4 (2) ( k^2 - k )  =  0

4k^2  -  8 k^2  + 8k   =   0

8k - 4k^2  =   0

4k ( 2 - k)  =  0

k  =  0   (trivial)

k  = 2

When  k  =  2

x + y  =  2      ⇒   y  =  2 - x

x^2 + y^2  = 2

x^2 + (2 -x)^2  =  2

x^2 + x^2 - 4x + 4  =  2

2x^2  - 4x + 2  =  0

x^2 - 2x + 1  =  0

(x - 1)^2  =  0

x =  1

And

x + y  =  2

1 + y  =  2

y = 1

So....the solution point is  (1,1)    when k  =  2

answer=sqrt85

Feel free to ask how I got this answer, and tell me if this is correct or not:)

So I graphed the line, in red. The x intercept is -4 and the y intercept is 2. SO we have a triangle of base 4 and height 2. The triangle is 4*2/2 = 4 units.

Read CPhill's.

However I got 19 as my answer.

Top triangle 6*1, left 1*2, center rectangle 2*5 and bottom triangle 5*2, so we have

3+1+10+5 = 19.

To find coterminal angles, add (or subtract) multiply of 2·pi

Therefore, angles coterminal with 2·pi/3 are  

           2·pi/3 + 2·pi,  2·pi/3 + 4·pi,  2·pi/3 + 6·pi,, ...

and     2·pi/3 - 2·pi,  2·pi/3 - 4·pi,  2·pi/3 - 6·pi,, ...

[you should reduce each answer]

Similarly, for  -11·pi/7

Hint: use an equilateral triangle with a side length of 7 

The surface area is pi*r(r+sqrt(r^2+h^2))so the surface area is 96pi

See the following image  :

Let    B  =(-sqrt (3) , 0)   A  = (0, 1)   C = ( sqrt (3), 0  )

The  centroid occurs at the intersection of the medians = G

Let BE  be  the median drawn to  AC

cot (EBC)  =    (sqrt (3)  + sqrt (3)/2 )   / (1/2)     =  [ 3sqrt (3) / 2]  / (1/2)  = 3sqrt(3) =  BD/DG

can you please explain?

I feel like this is is an easy problem.

y  =  x² + 8x + 4  will have the same roots as  y  =  ¼ x² + 2x + 1

A + B  =  ¼ + 2

GG geno3141! im rlly proud of u.. 

well dude, at least i got him the answer in only 2 mins not like yall take forever!

i dont understand what u said, cphill, its complicated.. 

mine is way more clear! heron's formula is tough.. 
how did u memorize it all cphill? tell meeeeeeeeee!

From straight up being 0⁰     the minut hand moves   6 degrees per minute    6 x 15 = 90 degrees

    the hour hand moves 1/2 degree per minute  and 30 degrees per hour    .5 x 15 = 7.5 degree  + 30 x 2 = 67.5^o

90- 67.5 = 22.5^o

For the product not to equal 0, each of the three dice must not be a 1.

So, the probability that a isn't a 1 is 5/6

the probability that b isn't a 1 is 5/6

and the probability that c isn't a 1 is 5/6.

Since these are independent, the final probability is 5/6 x 5/6 x 5/6  =  125/216.

the square base has area 64 and then we use the Pythagorean theorem to solve for the height. 4sqrt3^2=h^2+4^2, so 48=h^2+16, and h^=32, or 4sqrt2. 4sqrt2*64/3, which is approximately 120.7 cubic feet.

You are right, that does work out.

y = (sqrt3/3)x