Pangolin14

Simplifying these inequalities, we have x>12 and y>0. Therefore the minimum value=12+0=12.

Call the sides x,y,and z.

Writing equations, just random, 2z=x, 4z-2=y, and x+y+z=33.

z=shortest side.

So x=10, y=18, and z=5.

BUT WAIT!

By the triangle inequality, x+z>y

and it isn't

so that question is WRONG.

This is an intersection problem.

Call CD y. 

Then 10+y=x+26

and

3x+47+y=27+x

solving

we get for x and y

respectively

-12 

and 

4

therefore 

y

is 

4

.

I think you mean best deal to worst deal, but I'll infer!

Let's say the small size has 100 gallons of detergent (I know right?!), and costs 100 dollars.

Then medium costs 150 dollars and has 80 gallons of detergent.

It should, to be a fair deal, cost 150 dollars with 150 gallons.

Obviously medium is worse than small.

M

where < means worse.

Large has 200 gallons of detergent, and costs 195 dollars!

It should cost, to be a fair deal, 200 dollars!

It is 5 dollars cheaper!

Therefore, Large, Small, Medium from best to worst. Unless the detergent has short shelf life...

I don't know what you mean by An equilateral triangle is circumscribed about a circle of radius - 'r' but I will try to interpret it.

Just set a variable, calculate the area of each figure, and get (3 sqrt 3) /2.

I am assuming these beans are the only beans in the soup. Therefore 1/8+3/8+2/8(1/4)= 6/8. Therefore 1/4 of the mix is 8, and the whole mix is 32 ounces.

a)32

b)4

c)12

d)8

This is just simple algebra: Let n,d,and p be the number of nickels, dimes and pennies Anurak has, respectively. Then the cost will be:

5n+10d+p=75.

And number of coins:

d+3=n

5d=p

So, solving we get 3 dimes, 6 nickels, and 15 pennies!

3x=7y

xy=189

Are the equations. Solving, y=9 and x=21 so 9 is the answer.

I remember two years ago when I learned what the angle of elevation is xD!

The following picture is drawn with sketchometry:

The angle of elevation is essentially how much two lines intersecting are elevated when moved north/up. Overlap your two hands. Now bring one up. The angle they form is the angle of elevation!

Assume ABCD is the 2D building, and point E is the point from the ground in the question. Using SOH-CAH-TOA (Sine=opposite/hypotensuse-Cosine=adjacent/hypotenuse-Tangent=Opposite/adjacent) we get with some trig rules: 20.7

Use the RATIONAL ROOT THEOREM to find solutions for these. factors of the lead constant=96/factors of the lead coefficient=1= 1 x 96, 2 x 48, 3 x 32, 4 x 24, 6 x 16, or 8 x 12. The possible roots are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. 2 is a solution, so we can factor out an x+2. (x-2)*{x^4+6x^3-12x^2-56x+96}/{x-2}, and that equals (x^3+8x^2+4x-48)(x+2). Now simplifying this actually \(=x^3+\frac{8x^3-12x^2-56x+96}{x-2}\), and keep dividing this way until you get \(x^3+8x^2+4x-48\) . So now this is easily factorable, \(=\left(x-2\right)^2\left(x+4\right)\left(x+6\right)\)I am pretty sure D is right but look out for a graph that intersects x in 3 places: 2, -4, and -6!

-Pangolin14 :D