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Find the equation of the line passing through the points (-3, -16) and (4,5). Enter your answer in "y=mx+b" form.

1895

1)   The circumradius is given by

[ Product of the sides ] / [ 4 * Area ]

The area is given by  (1/2) Base * Height

This ttriangle is isosceles....let the base  = 2 units

The height [altitude ]  is given  by   √ [  (√ 10)^2   - 1^2 ] =  √ [  10 - 1 ]  = √  [9]  =  3 units

So...the area is   (1/2) 2  (3)   =   3   units^2

So....the circumradius is      [ √10 * √10 * 2 ]  [ 4 * 3] =   [ 20/12] =  5/3  units  ≈  1.67 units  

I'm not sure I understand. 2*0.5 is NOT sqrt(2).

t is total m is money paid per month 

T=25+14m

m would be six so

T=25+14*6

(-1) ^ 1.5 is 1.

2^0.5 is basically just multiplying 2 0.5 times, which is square root. 

a)      Avg Cost of producing/selling  a shirt is         C(x)  / x  =    [ 120 + 2.5x - 0.0002x ]  /  x

b)    Avg Cost producing/selling 1200   shirts  =     [ 120  +  2.5 (1200) - .0002 (1200 ]  / 1200  =  3119.76 / 1200  ≈ $2.60

c)     Profit  at $7.98 =   1200  [7.98  - 2.60 ]  ≈ $ 6456

d) Let P be the price......so we want to solve this ;

7368  =  1200  [ P - 2.60 ]        divide both sides by 1200

[7368  / 1200]  =  P  -  2.60       add 2.60 to both sides

[ 7368 / 1200 ]  + 2.60  =  P ≈  $8.74

I changed my answer now...sorry about that!  

2)

Since , we know that  is a right triangle with hypotenuse  by the converse of the Pythagorean Theorem. The circumcenter of a right triangle is the midpoint of its hypotenuse, so the circumradius is .

We have that

< -8, 2>  =   [  <8, 2> - <4,2> ] * F   +  < 4,2>         where F is the scale factor

  ( < -8 , 2 >  - < 4, 2 >  )  =   <4,0 > * F

< - 12,  0  >   = < 4 , 0 > * F

So  F  = - 3    = the scale factor

Midpoint "formula"

(  add x coordinates / 2 , add y coordinates / 2 )   .....so we have

( [ 9 + 2 ] / 2 , [ -8 + -5 ] / 2 )  =

(  11/2 , -13/2 )

Can you tell me what the answer is as a decimal?

hey, at least he's being considerate and KIND *cough* OfficialBubbleTanks

Thank you Promagna, Guest, XSquaredFactor

Upon further review, there appears to be ambiguity because the interpretations of 2/x+4=5/3x+5 are different.

ProMagma solved the equation \(\frac{2}{x}+4=\frac{5}{3}x+5\)

Guest solved the equation \(\frac{2}{x}+4=\frac{5}{3x}+5\)

This discrepancy occurs at the right side of the equation. That division symbol causes interpretations to differ; there really should be parentheses to clarify. This would not be the first time this forum has seen this issue. Strictly speaking, I believe that ProMagma's interpretation to be correct, but ManuelBautista2019 could have meant the other interpretation.

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Wow... That's really nice to look at though.