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x ( y + 4)  + 5 ( y + 4)  =  1 (x + 5) (y + 4)  = 1   and divide both sides by (y + 4) right

There is only way, as 1/15 + 1/15.

Solve  3x + y  =  15  for  y  to get  y = 15 - 3x

Let

z(x)  =  x² + y²  =  x² + (15 - 3x)²

So we want to find what value of  x  minimizes  z(x)

First let's find values of  x  which make  z'(x) = 0

z'(x)   =   2x + 2(15 - 3x)(-3)   =   2x - 90 + 18x   =   20x - 90  =  0  ⇒  x = 4.5

Now let's check whether the graph is concave up or down when  x = 4.5  using the second derivative test:

z''(x)  =  20   ⇒   z''(4.5)  =  20  >  0   so the graph is concave up

Since   z'(4.5)  =  0   and   z''(4.5) > 0  ,  we can say a min occurs when x = 4.5

When   x = 4.5,   y  =  15 - 3(4.5)  =  1.5

And   x² + y²   =   (4.5)² + (1.5)²   =   22.5

You are absolutely right, Phill! I don't know what happened but I didn't see this: "PQRS is a parallelogram of perimeter  26". My focus was on a triangle STR, and I assumed that that triangle was 3-4-5

Ok, I will find something else.

hello, thanks for the response. I still don't really get the concept and I've got a test in 5 minutes and this question is on the study guide so I really want an exact explanation

Sorry, nevermind. But I just want to say: everyone on here is so nice and kind. It is inspirational to see people who some cases don't know each other other than online, talk, and encourage other people. I feel safe on this website. So thank you!

Actually, I need help with all of it.

Given \DeltaΔABC with A(-7,-1) B(9,-5) C(-1,6), determine the equation of median AD in standard form. D is on segment BC.

Hello alinakapp!

\(D(\frac{-1+9}{2},\frac{-5+6}{2})\\ D(4,0.5)\)

\(m_{AD=}\frac{0.5-(-1)}{4-(-7)}\\ m_{AD}=\frac{4}{11}\)

\(f_{AD}(x)=y=m(x-x_A)+y_A\)

\(f_{AD}(x)=\frac{4}{11}(x-(-7))+(-1)=\frac{4}{11}x+\frac{28}{11}-1\)

\(f_{AD}(x)=y=\frac{4}{11}x+\frac{17}{11}\)

  !

All good! Thanks! Signing off for today! Have a good afternoon! Hope to see you around!

(side length)^3  = volume

Slight mistake  in (3)

It should be

2x - y - 4 ≥  0 

Sorry, MS!!!

Ok, man!!!

OK.....I'll see what I can do.....

3) We have the points (2,0)  and (3,2)...and a sloid line

This is easier

slope  [  2-0] / [ 3 -2] =  2/1  = 2

The equation is 

 y = 2 ( x -2)

y = 2x - 4

Rearrange  as

2x - y - 4   = 0

what is 8 divided by 1/4 simplified   

Think how many quarters there are in eight dollars. 

_.

Thanks! I think the glitch is patched! Thanks Chris!

Chris, can you ask the admins or if you could find why everything I'm posting is auto flagged?

2) We have two points on this   inequality  (-1,0)  and  (0,1)

Slope  [ 1 -0 ] / [ 0 - -1] =   1/1  = 1

If we had a solid line the equation would be

y= x + 1

But we have a dotted line

So

The equation is either

 y < x + 1                     or  y  >  x + 1

To see which one is correct, pick a point in the shaded area  and  test it  in  the equations  ..I'll pick (0,2)

2 < 0 + 1

Not true

So the equation is

y > x + 1

Rearrange  as

x - y + 1 <  0

See the graph here : https://www.desmos.com/calculator/arefq6sleo

The question was actually something like $(x+1)(x+2)(x+3)$. I solved that and didn't notice it was already in decreasing degree  But I noticed this 2.5 hours ago.