ethanyessir

we get 3x+3y=75. since we need to add 3x, we just make x=0, since the questions says "nonnegative". therefore, the minimum value is 75.

so, we can simplify the equation to be \(4x^2-8x+4y^2+14y=-12.\)

dividing the equation by 4, we get \(x^2-2x+y^2+7y/2=-3\)

completing the square, we get \((x-1)^2+(y+\frac{7}{4})^2=\frac{17}{16}\)

17/16 is the radius squared, so we take the square root and get \(\boxed{\frac{\sqrt{17}}{4}}\)

well, since they paint 1000 sq ft in 10 minutes, the individual work rate is 10 sq ft per minute.

plug that into the second equation, and you get 5(members)*10(work rate)*x(time)=1000. so x=20, 20 minutes.

I hope this is right, it seems simple enough .

Well there's two cubes, so the smallest possible configuration of them would be a rectangular prism...

So we have a rectangular prism with height 1, width 1, and length 2. 

Surface area would be 10.

Correct me if im wrong.

Use 3d pythagorean theorem,

3^2+5^2+11^2=x^2.

9+25+121=x^2

155=x^2

x=sqrt 155

So the distance between the two opposite corners is sqrt 155

OK so,

lets first rearrange the second equation: x^2-xy+y^2=64.

and we know that x+y=10.

we can rewrite the second equation like this

(x+y)^2-3xy=64

and since x+y=10,

100-3xy=64

which means that xy=12.

NOW

we solve x+y=10 and xy=12.

we can substitute x as 10-y

so we have

y(10-y)=12

10y-y^2=12

and we get the quadratic

y^2-10y+12=0.

this isnt easily factorable so i will use the quadratic formula.

we get that y=5+sqrt 13, 5-sqrt 13.

so that means 

(x,y)=(5+sqrt 13, 5-sqrt 13) and (5-sqrt 13, 5+sqrt 13).

:)

Hey,

I got the equation: x^3-3x^2+12x+10=0.

The problem is that this equation is not factorable with rational numbers and I don't think they want you to use the cubic formula.

Is there something wrong with the problem?