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A prime number is a natural number greater than one that cannot be formed by multiplying two smaller natural numbers.

The only way I can think of to approach this problem is to plug in some values and try. 

Three works because three squared is nine, and nine minus sixteen is negative seven. The absolute value of that is seven, which is a prime number. 

Since negative numbers are also integers, negative three must also work.

The two numbers are 3 and (-3)

The product of these two numbers is 3 * (-3) which is -9

I hope this helped, 

Supermanaccz

x² + y² - 4x + 2y  =  b        We need to get this into standard form. Rearrange the terms.

x² - 4x   + y² + 2y   =   b        Add  4  and  1  to both sides to complete the squares on the left side.

x² - 4x + 4  + y² + 2y + 1  =  b + 4 + 1          Factor each perfect square trinomial.

(x - 2)(x - 2) + (y + 1)(y + 1)  =  b + 4 + 1

(x - 2)² + (y + 1)²   =   b + 5

Now that this is in standard form, we can see that the  y  coordinate of the center is  -1 .

And     (the radius)²  =  b + 5       So

7²  =  b + 5

49  =  b + 5

44  = b

it only gave me one mark out of four and i wrote it all (the mark only came from writing point d)

We jhave the identity....

cos (A)  = sin (90- A)

So

cos (63)  = sin (90- 63)

cos (63)  = sin (27).....so....x  = 27  (degrees)

We  can write this in exponential form

[5^(1/3) ] ^x  =  125

(5)^(x/3)  = (5)^3

Since the bases are the same.....we can solve for the exponents

x/3  = 3         multiply both sides by 3

x  =

9        and that's the evaluation for the original expression

x = 180° - 27° + 360° n, x = 360° n + 27°

I'n just going to tell you the answer so I don't have to retype the whole thing :)

Oops, the LaTeX didn't show up :(

cos 63°  = sin x

After switching sides:

\sin \left(x\right)=\cos \left(63^{\circ \:}\right)

Using \cos \left(x\right)=\sin \left(90^{\circ \:}-x\right)

We have:

\sin \left(x\right)=\sin \left(90^{\circ \:}-63^{\circ \:}\right)

So x = 180^{\circ \:}-27^{\circ \:}+360^{\circ \:}n,\:x=360^{\circ \:}n+27^{\circ \:}\(180^{\circ \:}-27^{\circ \:}+360^{\circ \:}n,\:x=360^{\circ \:}n+27^{\circ \:}\)

Well...let's see....

15310 (1.2)*1   = 18372 ....nope....that's not correct  !!!!

Let's use the points

(0, 15310)  (1,18002)  (2, 21548)  ( 3, 25642)     and this utility to generate a quadratic function :

http://keisan.casio.com/exec/system/14059932254941

We get the function

y = 350.5x^2  + 2402.7x  + 15294.7

It appears that the last answer is pretty close to this....so...."D"

{4, 5, 6} | {4, 5, 4} | {4, 5, 5} | {4, 6, 5} | {4, 6, 4} | {4, 6, 6} | {4, 4, 5} | {4, 4, 6} | {4, 4, 4} | {5, 4, 6} | {5, 4, 4} | {5, 4, 5} | {5, 6, 4} | {5, 6, 5} | {5, 6, 6} | {5, 5, 4} | {5, 5, 6} | {5, 5, 5} | {6, 4, 5} | {6, 4, 4} | {6, 4, 6} | {6, 5, 4} | {6, 5, 5} | {6, 5, 6} | {6, 6, 4} | {6, 6, 5} | {6, 6, 6}

Probability = 6 / 216 = 1 / 36

point D  =  midpoint of AB  =  \((\frac{4+2}{2},\frac{6+-2}{2})\,=\,(\frac62,\frac42)\,=\,(3,2)\)

point E  =  midpoint of AC  =  \((\frac{4+-2}{2},\frac{6+-4}{2})\,=\,(\frac22,\frac22)\,=\,(1,1)\)

slope of DE  =  \(\frac{2-1}{3-1}\,=\,\frac12\)

slope of BC  =  \(\frac{-2--4}{2--2}\,=\,\frac24\,=\,\frac12\)

slope of DE  =  slope of BC

therefore  DE  is parallel to  BC .

Cheers 

I think you missed something, the number after "that both balls are red is..."

cos A  =   AC  / AB

And  AB  can be found as  √ [ 15^2 + 36^2 ] = √ [ 225 + 1296]  = √1521  = 39

So.....cos A  =    15 /39   =   5/13

Thank you so much!

This is a parabola.....In this form.....when the coefficient in  front of x is negative

y  = -ax^2  + bx  + c.....we have a parabola that opens downward  with the vertex the highest point on the graph

So......we have

y  = (-1)x^2  +  (-2)x  + 8

The  x coordinate of the vertex  is given by   -b/ [ 2a]

So  b = -2     and  a  = -1

So....the x coordinate of the vertex  =    - (-2) / [2 (-1)]  = 2/-2  = -1

Since this is the highest point on the graph of this parabola....the function will increase  on this interval :    (-inf, -1 )

However we must find out where the parabola is positive......we can  find the x intercepts by letting y  =0  and solving for x....so we have

0  = -x^2 -2x + 8        multiply through by  -1

0  =x^2 + 2x  - 8        factor

0 = (x - 2) ( x + 4)

Setting each factor to 0  and solving for x  produces the x intercepts of  x  = 2  and x  = -4

So......the graph will  be positive  and increasing from    -4 < x < -1  

See the graph here to get a feel for this :

https://www.desmos.com/calculator/bkyaq6zmzv

If  B  is the  x-intercept and  E  is the  y-intercept of  x + 3y  =  18 , then

point B  =  (18, 0)       and       point E  =  (0, 6)

Then...

point A  =  (-18, 6+6)  =  (-18, 12)

Line M  is perpendicular to line L.

slope of line L  =  -6/18  =  -1/3   so..

slope of line M  =  3

So line M passes through the point  (-18, 12)  with a slope of  3 . So the equation of line M is...

y - 12  =  3(x - -18)

y - 12  =  3(x + 18)

y - 12  =  3x + 54

y  =  3x + 66

LOL!

I need the answer soon as possible. Thank You

This is known as a cyclic quadrilateral.....the opposite angles sum to 180 degrees

So

J + L  =  180

68 + L  = 180     subtrct 68 from both sides

L  = 180  - 68  =  112°