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That just means you're really good at math, CPhill...

LOL!!!

The problem is  that my "Saturday"  math largely  resembles  my "Other Days of the Week"  math.....

The roots you specfy  will not produce a polynomial  with real coefficients

I think  you must  mean that    f( 1 + i)    = f( 1 - i)  =  0 

So we  have

f(x)  =  (x - ( 1 + i) )   (x - ( 1 - i ) )   =

(x - 1   - i )   (  x - 1  + i)    =

x^2  -x  - ix  - x + 1  + i   + ix - i  - i^2   =

x^2  - 2x  + 2

Yah....well I made a mistake too!   Just edited it          It's Saturday math .....

forgot i could divide it.

Slope =   (-5-1) / (-3-6) = -6/-9   = 6/9    ( as varxaax found)

Point slope form    becomes     (y-1) =2/3 (x-6)

                                                     y = 2/3x -3

                                                      3y -2x = -9

RIP My mathematics career, Never-2021, Died by: EP.

From (-3, -5) to (6, 1), the line goes 9 right, and 6 up.

Then the the equation must be y=6/9x-3 

9y=6x-27

9y-6x=-27

Yeah umm. It's not very possible with a GCD of 1.

9-6-27=-24

Yay!

EDIT: RIP Varxaax, 2020-2021

I took your working and looked for integer answers.

\(\frac{1}{-35-2c} \begin{pmatrix} -7 & -2 \\ -c & 5 \end{pmatrix}\\\)

each of these elements must be an integer.  so

\(\frac{-2}{-35-2c}\)   must be an integer,    I only looked at -2 because the absolute value of it is the smallest one.

so    \( -2\le -35-2c \le 2\\ 33\le -2c \le 37\\ 16.5\le -c \le 18.5\\ -16.5\ge c \ge -18.5\\ -18.5\le c \le -16.5\\ \)

but c is an integer, so c might be   -18 or   -17

I checked both of these and they both worked.

thank you!

When are the two equations equal?

7x+10 = 8x+8

2 = x       at two hours the charges are equal

20 children total       8 boys       soooo    12 girls

5 boys with speaking parts         5 girls with speaking parts

  10 total speaking parts   out of 20    

10/20 = 1/2 probability

Try and imagine it.

   \(-1\le x\le1\\ -1\le y\le1\\ -1\le z\le1\\\)

this encloses a cube.  The centre is (0,0,0)  what is the side length,  What is the area?

Now

\(x^2+y^2+z^2\le 1\)

is the formula for a sphere with centre (0,0,0) and radius  ?    What is the area?

The sphere is inside the cube.  What fraction of the cube space does the sphere take up?  

That will be your answer.

Just as Alan has already said.

here is an answer

DOMAIN is just all of the 'x' values a graph can have ....this one only goes from x= -1 to x  = 3

-1 <=x<=3

Sorry, but I don't get why you are doing this. Could you please elaborate? Thanks!!!

Is that a test?

This constraints represent a sphere of radius 1 inside a cube of side length 2.

Volume of cube  \(Vc=2^3=8\)

Volume of sphere \(Vs=\frac{4}{3}\pi 1^3=\frac{4}{3}\pi\)

Probability \(p=\frac{Vs}{Vc}\)

I'll let you finish!

Late answer, bu hopefully still helpful.

If you take 90 and multiply it by 0.06, you get 5.4

You add 5.4 to 90 and get 95.4

That is 95 dollars and 40 cents.

Yay!

The surface area of a prism is the perimeter of the base times the height, plus two times the area of the base. In this case the base is a triangle so we have a triangular prism.

surface area   =   ( perimeter of base ) * ( height of prism )  +  2 * ( area of base )

surface area   =   ( 2 ft  +  1.5 ft  +  2.5 ft ) * ( 10 ft )  +  2 * ( 1/2  *  2 ft  *  1.5 ft )

surface area   =   ( 6 ft ) * ( 10 ft )  +  2 * ( 1.5 ft² )

surface area   =   60 ft²  +  3 ft²

surface area   =   63 ft²

Your result is correct.  I was too hasty!

I solved the de as you did and got exactly the same result.

You can check that it's correct by differentiating it and seeing that it takes you back to the original de.

So,

\(\displaystyle y = x \ln(x) +x, \\ y' = \ln(x) + x/x + 1 =\ln(x)+2, \\ xy'=x\ln(x)+2x =( x\ln(x)+x)+x=y+x,\\ y'=y/x+1,\)

which is the original de, so with you, I think that it's correct.

surface area:

(8m+5m+5m)*20m+2*1/2*8m*3m=18m*20m+8m*3m=360m²+24m²=384m²

volume:

1/2*8m*3m*20m=240m³

consider

I will leave you to finish it.

r =  d/2  =   6/2  = 3

SA  = 2pi r  ( r  + h)  =  2pi * 3   ( 3 + 8)   =  66 pi  in^2  ≈   207.345 in^2