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s is equal to 31 in base b.

There are 26 possible values of b.

If there's some way to prove that the three triangels in each row are equal, then there's three triangels in each row and one of them is blue.  Therefore the blue triangels are 1/3 of the large one.  Does that make sense? 

If n is an integer the denominator is odd, so the denominator can only be the odd factors of 20 so -5, -1, 1, 5. For each of these, n would be -2, 0, 1, and 3 respectively. The sum of these is 2

In one hour, pipe A fills up 1/6 of the tank and pipe B fills up 1/4 of the tank. Therefore pipe A and pipe B working together would fill up 1/6+1/4 = 5/12. Pipe C fills up the tank in the same time so it also fills up 5/12 of the tank. Therefore A+B+C = 5/6 in one hour.

x³  =  -4 + 4i

Step 1)  write  -4 + 4i  in  r·cs( theta ) form

         r  =  sqrt( (-4)² + (4²) )

         theta  =  tan^-1( 4 / -4)           

                                                        that your angle is in the second quadrant>

Step 2)  To get your first answer:

                  take the 3rd root of the r-value and divide the angle by 3

Step 3)  To find the other roots:  

              --  add 2pi/3 to the angle of the first answer (keep r the same)

              --  add 2pi/3 to the angle of the second answer (keep r the same)

The square root of 28 is 5.29150262213.

Therefore, the square root of 28 lies between 5 and 6.

You can use this formula to help you find the number of terms:  t_n  =  t₁ + (n - 1)d

t_n  is the last term of an arithmetic sequence.

t₁  is the first term of an arithemtic sequence

n   is the number of terms

d   is the common difference

This sequence contains two arithmetic sequences:

6, 10, 14, 18, ... 94, 98          and        7, 11, 15, ... 91, 95

In both of these sequences, d = 4.

For  6, 10, 14, 18, ... 94, 98                                   t_n  =  t₁ + (n - 1)d

t_n  =  98                                                                 98  =  6 + (n - 1)4

t₁  = 6                                                                    92  =  4n - 4

n   =  unknown                                                       96  =  4n

d    =  4                                                                   24  =  n

For  7, 11, 15, ... 91, 95                                         t_n  =  t₁ + (n - 1)d

t_n  =  95                                                                 95  =  7+ (n - 1)4

t₁  = 7                                                                    88  =  4n - 4

n   =  unknown                                                       92  =  4n

d    =  4                                                                   23  =  n

So, there will be a total of  24 + 23  =  47 terms

For this problem you can work backwards. If it is 6 years after Jacob is three times his age. First, subtract 6 from 39. 39 - 6 = 33. Then, divide by 3,     33÷3 = 11. So his age is 11.

a+b = 11/12    a = 11/12- b     sub into the following eq

ab = 1/6

(11/12 - b) b = 1/6

-b^2 + 11/12b -1/6 = 0     Quadratic fomula shows   2/3   an  1/4

g(2) = 2(2^2) + 2(2) - 1 which equals 11. g(11) = 2(11^2) + 2(11) - 1 which is 263.

the 2 fractions aer 1/4 and 2/3. If u check this 1/4 * 2/3 is 2/12 which equals 1/6. If u add the 2 1/4 plus 2/3 the sum is 11/12.

For the function:  f(x)  =  2x -5:

First, find the inverse:

step 1)  replace "f(x)" with "y":        y  =  2x -5

step 2)  interchange x and y:          x  =  2y - 5

step 3)  solve this equation for y :   x  =  2y - 5

                                                  x + 5  =  2y

                                             (x + 5)/2  =  y

                                                         y  =  (x + 5) / 2

step 4)  replace "y" with "f^-1(x)":  f^-1(x)  =  (x + 5)/2

This equation is the inverse.

Now, solve the problem:  For what value of x will f(x) = f^-1(x)?

Set  f(x)  =  f^-1(x)     --->     2x - 5  =  (x + 5)/2

                  4x - 10  =  x + 5

                       3x - 10  =  5

                                                  3x  =  15

                                                    x  =  5

Sorry I didn't take higher maths and didn't know the terminology, so I tried to learn it.  I learned that what I was trying to say was "sigma sum" and I found an online sigma sum calculator on the internet.  Using my numbers, the answer comes out to 0.3333··· in other words, the same as Electric Pavlov's answer.  So how come EP gets two positive hearts (so far) and I get a negative?  Can somebody explain that to me? 

listfor(n, 1,24, (4*n+2, 4*n+3))=(6, 7, 10, 11, 14, 15, 18, 19, 22, 23, 26, 27, 30, 31, 34, 35, 38, 39, 42, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 67, 70, 71, 74, 75, 78, 79, 82, 83, 86, 87, 90, 91, 94, 95, 98, 99)

If  g(x)  =  2x² + 2x -1,  find  g( g(2) ).

Work from the inside out; find the value of g(2).

    g(2)  =  2(2)² + 2(2) - 1  =  11

Now, replace the g(2)  of g( g(2) )  with 11,

so you now have  g( 11 )  =  2(11)² + 2(11) - 1  =  263.

To summarize:  g( g(2) )  =  g( 11 )  =  263

The graph of  y  =  x² + kx + 1  is a parabola with its minimum point at its vertex and rises, on both sides,  from there.

There is no way that this parabola will always be below zero; that is, will always be below the x-axis. So, the answer is the null set.

If the graph were:  y  =  - x² + kx + 1, which is a parabola with a maximum point and falling, it would be possible for the graph to be always below the x-axis.

Draw square MNPQ.

Find the midpoint of MN, call it "X".

Using X as the center, draw the semicirce inside the circle that starts at M and ends at N.

Choose a point Y on the semicircle. Angle(MYN) will be a right angle because it is inscribed

in a semicircle.

If you choose a point Y' inside the semicircle, angle(MY'N) will be an obtuse angle.

If the point that you choose is outside the semicircle, it will be an acute angle.

Now, to find the probability of its being acute.

We need to compare the area outside the semicircle to the area of the whole square.

Assume that the square has a side length of 2.

Then, the area of the square is 4.

The area inside the semicircle will be:  ½·pi·r2  =  ½·pi·(1)2​  =  ½·pi.

The area outside the semicircle will be:  4 - ½·pi.

The probability will be the area outside the semicircle divided by the area of the square:

   probability  =  ( 4 - ½·pi ) / 4   

[Because we're finding a ratio, we can assume whatever we wish for the side length of

the square. If you are in doubt, choose another number for this length, and recalculate.]

The S.A. of a cylinder is 2(πr^2) + h* 2πr, so we have 2πr^2 + 4πr^2 = 6πr^2.

The area of the 2 bases is 2(πr^2) so 2/6 = 1/3.

If you don't understand anything feel free to ask! :)

Thanks.  When I asked for an explanation, I hadn't seen that the other guest had already provided one.  Sorry . 

This question or one nearly like it has been asked several times in recent time....try a search....

See above....was working on explanation

That is correct, but wouldn't it help the student if you explained how you found the numbers?