geno3141

The formula for the sum of the first n terms of a geometric series is:  Sum  =  a(1 - rⁿ) / (1 - r)

where         a = first term = ¼         r = common ratio = ½          n = number of terms

--->     255/512  =  (¼)·( 1 - (½)ⁿ ) / ( 1 - ½ )

--->     255/512  =  (¼)·( 1 - (½)ⁿ ) / ( ½ )

--->     255/512  =  (½)·( 1 - (½)ⁿ )

--->     255/256  =  1 - (½)ⁿ 

--->           (½)ⁿ  =  1 - 255/256

--->           (½)ⁿ  =  1/256

--->           (½)ⁿ  =   (1/2)⁸

--->                n  =  8 

First one:

1)  Since AP = PB = 4 and triangle(APB) is a right triangle:  AB²  =  AP² + BP² 

               --->   AB²  =  4² + 4²   -->  AB  =  .......

2)  Since BP = PD and P is the midpoint of BD   --->   BD = 8

     Since triangle(BDC) is similar to triangle(BPA), DC = 8.

3)  Since(triangle(BDC) is a right triangle:  BC²  =  CD² + BD² 

               --->   BC²  =  8² + 8²   --->   BC  =  .......

4)  Now, add up the parts.

Second one:   (use Pythagorean triples)

-- try a 13 -13 -20 isosceles triangle.

To be a binomial, the answer can have only two terms.

It will have a t² term (because 7t·5t = 35t²) and it will have a constant term because, according to the

directions, you can't use zero in the box.

Therefore, the t-term must disappear.

Using an 'x' for the term in the box, we have:  (7t - 10)(5t + x)  =  35t² - 50t + 7xt - 50x.

We need to get  -50t + 7xt  to be zero:  -50t + 7xt  =  0

(dividing out the t)                                    -50 + 7x  =  0

                                                                          7x  =  50

                                                                            x  =  7 1/7

The lower left-hand corner angle of the triangle is 85^o because it is vertical to an 85^o angle.

Since the lines are parallel, the angle supplementary to the lower right-hand corner angle of the 

triangle is 98^o.

This makes the lower right-hand corner angle of the triangle 180^o - 98^o  =  82^o.

Now, we know two of the three angles of the triangle; all we need to do is find the size of the

third angle.  180^o - 85^o - 82^o  =  .......

There seems to be missing information -- are "6" and "-3" consecutive terms, or are there terms

between them that are missing? If so, how many?

1)  0 + 0  =  0     1 + 0  =  0             2 + 0  =  0                           etc.

     0 + 1  =  1     1 + 1  =  2             2 + 1  =  3

     0 + 2  =  2     1 + 2  =  3             2 + 2  =  4

     0 + 3  =  3     1 + 3  =  4             2 + 3  =  5

     0 + 4  =  4     1 + 4  =  5             2 + 4  =  6  =  0

     0 + 5  =  5     1 + 5  =  6  =  0     2 + 5  =  7  =  1

2)  The identity element is 0 because 0 + n  =  n + 0  =  n  for  n = 0, 1, 2, 3, 4, 5

3)  The inverse of 0 is 0 because 0 + 0  =  0

      The inverse of 1 is 5 because 1 + 5  =  5 + 1  =  0

      The inverse of 2 is 4 because 2 + 4 = 4 + 2  =  0

      The inverse of 3 is 3 because 3 + 3  =  0

3x² + 5x - 2  =  (3x - 1)(x + 2)

So, either  3x - 1  =  0     --->     x  =  ........

            or    x + 2  =  0     --->     x  =  .......

And, finish ...

1)  angle(NEA)  =  ½·( arc(NA) - arc(TA) )  =  ........

2)  angle(ENA)  =  ½·arc(TA)  =  ........

3)  angle(EAN)  =  180^o - angle(NEA) - angle(ENA)  =  .......

4)  angle(NAS)  =  180^o - angle(EAN)  =  ........

1)  Since Z is the center of the circle, arc(BC) = angle(BZC)   --->   arc(BC) = .......^o

2)  Since angle(BAC) cuts off arc(BC), angle(BAC) = ½·arc(BC)   --->   angle(BAC) = .......^o 

3)  Since AB || CD, angle(DCA) = angle(BAC)   --->   angle(DCA) = .......^o