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Square root 90 is 3 * sqrt 10. It is irrational and therefore not rational.

It is real because it is not a letter, it is a number.

It is not whole obviously,

natural is whole except no 0s so not natural.

Not an integer= all negative and positive and 0 counting numbers.

It is only irrational and Real.

Hmmmmmmmmmmm well, we graph functions.

And when we shift things to the right we do positive of x. So it is the third choice.

Hi Pangolin.  I'm the guest from answer #1.  I didn't even notice the impossibility.  Good catch. 

_.

(3x + 47) + (x + 26) = (27 + x) + 10

3x = - 36

x = - 12

CE = x + 26

CE = - 12 + 26 = 14

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.

In a triangle, one side is twice as long as the shortest side and another is two inches less than four times the shortest side. If the perimeter of the triangle is 33 inches, what are the side lengths?    

Let's call the three sides of this triangle A, B, and C  

Let's let C be the shortest side.  No particular reason, I just picked one.  

Now "one side is twice as long as the shortest side" so let's let this side be A     thus  A  =  2C                   (1)

And "another is two inches less than four times the shortest side"                       thus  B  =  4C – 2             (2)

And finally "the perimeter of the triangle is 33 inches"                                          thus  A + B + C  =  33  

Can you solve it now, by the substitution method?  I'll get you started. 

Start with the A+B+C and substitute for A and B                                                     A  +      B      + C  =  33

Substitute terms from (1) and (2)                                                                           2C + (4C – 2) + C  =  33  

Add up all the C's                                                                                                   7C          – 2           =  33    

Add 2 to both sides of the equation                                                                        7C                          =  35  

Divide both sides by 7                                                                                                                       C  =  5    

Now go back up and substitute 5 for C in the equalities for A and B.                        A  =  10   and   B  =  18  

_.

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

Here is a description pic

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

You have blatently posted an AoPS question. 

I suggest you go and ask them for the help you need.

Find x and y so that both hangers balance.

Hello Guest!

\(4y+2x=3x+9\)

\(y=\frac{x+9}{4}\)

\(4y=2x\)

\(y=\frac{x}{2}\)

\(\frac{x}{2}=\frac{x+9}{4}\\ 4x=2x+18\\ 2x=18 \)

\(x=9\)

\(y=4.5\)

  !

Modular Multiplicative Inverse of 34^(-1) mod 47 == 18

Angle EBC = n / 6

It's False but nice try!

Suggested answers are ridiculous. Why not these numbers: 11, 12, 13, 14, 15...

Maybe should  also include 44,  55,  66

The above 8 + 3 = 11 / 6^2 = 11 / 36 

draw a perpendicular line from point B to line L₁

now we have a quadrillateral with 3 known angles: 135-90-60 degrees

angle x = 360 -135-90-60 = 75 degrees

The area of the picture in square inches is 44.