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1/2 r = y-2         y= 1/2r +2

1/2 r = 1/3 o      0=  3/2 r

1/2 r = 2 + w      w = 1/2 r -2

r                                r

Add right column    3.5 r     equals all of the marbles = 35

                                    r = 10

multiply first equation by   7 to get       14x = 35y

multiply second equation by 5 to get   35y=75z         use 1st equation in second equation

14x = 75z

z/x  14/75     

The equation of circle A is x^2 + y^2 = 1.

The equation of circle B is (x - 2)^2 + y^2 = 2

The equation of cirlce C is (x + 3)^2 + (y + 1)^2 = 4.

Question:  What is the square root of 16?

Answer:     √16 = 4

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~                                                                                                                        The fact is that  -4² = 4² = 16   but   sqrt(16) = 4

5 + sqrt(16) = 5 + 4 = 9

5 - sqrt(16) = 5 - 4 = 1

Thanks Alan!

If corners and crossings are allowed in the line, it goes like this:

$f(x) = 2x^2 - 3\ |\ if\ x <= 2\\ g(x) = ax - 7\ |\ if\ x > 2$

$x=2$

$f(2)=g(2)\\ 2\cdot 2^2-3=2a-7\\ a=\large \frac{2\cdot 2^2-3+7}{2}$

$a=6$

$g(x)=6x-7$

  !

Please proofread your Q

  with the parameters given     t = 1/2     meaning your pay = - 1/5 dollars per hour

If two (positive) prime numbers are roots of the equation x^2 - 19x + k = 0, what is the value of k?   

The only prime numbers I can think of that work are –2 and –17.  That would make K = 34.  

People sometimes forget that 2 is a prime number, they overlook it because it's even.  

_.

What is the square root of 16?   

It's +4.  Don't forget there are two roots, one positive and one negative. 

_.

t-27 = 4t       subtractt from both sides

-27 = 3t          divide both sides of the equation by 3

t = -9

Use the quadratic formula to find a, b:

x = 1/10 (11 - sqrt(41)) = a
x = 1/10 (11 + sqrt(41))= b

1 / [1/10 (11 + sqrt(41))] + 1 / [1/10 (11 - sqrt(41))] 

=11 / 4

The number of outcomes is 7.

I plugged into Wolfram Alpha, and got 19/3.

The smallest n = 9.

9 / 720 =0.0125

The diameter is 10 inches so the radius is 5 inches.

circumference of base   =   2π * (radius)   =   2π * (5 inches)   =   10π  inches

lateral area of cylinder   =   (circumference of base) * (height)   =  (10π  inches) * (21 inches)   =   210π  square inches

Assuming that the bottom of the pot is covered and the top of the pot is uncovered, we only need to add the area of one of the bases to the lateral area to find the total covered area. So let's find the area of the base and add one of those to the lateral area.

area of base   =   π * (radius)²   =   π * (5 inches)²   =   25π square inches

So...

total covered area   =   lateral area of cylinder  +  area of base

total covered area   =   210π  square inches   +   25π  square inches

total covered area   =   235π  square inches

total covered area   ≈   738.3  square inches

11^2005 =........... 9135081051 - These are the last 10 digits

OR:

11^1 =11

11^2 =121

11^3 =1331

11^4 =14,641

11^5 =161,051

11^6 =1,771,561

11^7 =19,487,171

11^8 =214,358,881

22^9 =2,357,947,691

Notice the pattern in ones digit = 1 and the tens digit = the last digit of the exponent = 5