geno3141

To find the image, take the x- and y-values of each corner point of the original figure and multiply it by the scale factor.

Therefore, corner point (-3,-2) becomes corner point (-6,-4), 

                  corner point (-1,1) becomes corner point (-2,2),

                  etc.

The order in which the figure is written is very important because this indicates which sides correspond and which angles correspond.

If quad( DXHW ) is similar to quad( LSCT ),

then side( DX ) is similar to side( LS ), side( XH ) is similar to side( SC ), side( HW ) is similar to side( CT ), and

        side( WD ) is similar to side( TL )

and angle( D ) is congruent to angle( L ), angle( X ) is congruent to angle( S ), angle( H ) is congruent to angle( C ),

       angle( W ) is congruent to angle( T )

The perimeter of the new photograph will be 2.25 times larger than the perimeter of the original photograph.

The area of the new photograph will be 2.25 x 2.25, or 5.0625, times larger than the area of the original photograph.

The "mod" value is the remainder after division.

To find N in the equation:  111,119 mod N = 954

     first, subtract 954 from 111,119     --->     111,119 - 954  =  110,165

     now, find the factors of 110,165     --->     110,165  =  5 x 11 x 2003

     we need a factor larger than 954     --->     N = 2003

To find M in the equation:  111,119 mod M = 82

     first, subtract 82 from 111,119     --->     111,119 - 82  =  111,037

     now, find the factors of 111,037      --->     111,037  =  37 x 3001

     we need a factor larger than 82     --->     M = 3001

The function  f(x)  =  3x + b  can be written as  y  =  3x + b.

To find the inverse of this function:

1)  interchange the x and y terms:  x  =  3y + b

2)  solve for y:                            x - b  =  3y     --->     3y  =  x - b     --->     y  =  (x - b) / 3

To find where they intersect, set the two functions equal to each other:  3x + b  =  (x - b) / 3

and, since they intersect at the point (-3, a), replace x by -3:               3(-3) + b  =  (-3 - b) / 3

                                                                                                                  -9 + b  =  (-3 - b) / 3

                                                                                                              -27 + 3b  =  -3 - b

                                                                                                                       4b  =  24

                                                                                                                         b  =  6

So, the original function is  y  =  3x + 6  while the inverse is  y  =  (x - 6) / 3

Replace the x in either function with -3 and you get that y = -3, so  a = -3.

I think that the answer is 73: 

98 97 96 95 94 93 92 91 87 86 85 84 83 82 81 76 75 74 73 72 71 65 64 63 62 61 54 53 52 51 43 42 41 32 31 21 9

Since TIP is an isosceles triangle, either TP matches TI, therefore TP = 5

                                                             or TP matches PI, therefore TP = 7.

Since TOP is an isoscels triangle, either TO matches PO, therefore TO = 11

                                                             or TO matches TP when TP = 5, therefore TO = 5

                                                             or TO matches TP when TP = 7, therefore TP = 7.

The sum of all possible lengths for TO = 11 + 5 + 7 = 23.

a)  Numerator:         (x²y)²·(xy)³·z²  = (x²y)·(x²y)·(xy)·(xy)·(xy)·z²  =  [x²·x²·x·x·x]·[y·y·y·y·y]·z²  =  x⁷·y⁵·z²

     Denominator:     (xy²)²·y·z  =  (xy²)·(xy²)·y·z  =  [x·x]·[y²·y²·y]·z  =  x²·y⁵·z

    Combining the numerator and denominator:     [x⁷·y⁵·z²] / [x²·y⁵·z]  =  x⁵·z

b)  Numerator:  (12)²·(6³)·5²  =  (2·2·3)²·(2³·3²)·5²  =  (2²·3)²·(2³·3²)·5²​  = 2⁴·3³·2³·3²·5²  =  2⁷·3⁵·5²

     Denominator:     (2·3·3)²·(3·5)  =  (2·3²)²·(3·5)  =  2²·3⁴·3·5  =  2²·3⁵·5

     Combining the numerator and denominator:  [2⁷·3⁵·5²] / [2²·3⁵·5]  =  2⁵·5  =  160

You'll need to answer part c.

To find the percent of discount:

1) calculate the amount of discount:  $17.00 - $13.00  =  $4.00

2) divide this answer by the original amount:  $4.00 / $17.00  =  0.2342941176,,,  --->   rounded:  0.234

3) turn this answer into a percentage:  0.234  --->   23.4%

The first prime larger than 10 is 11. The following products of two primes, one of which is 11, are less than 500:

11 x 13, 11 x 17, 11x 19, 11 x 23, 11 x 29, 11 x 31, 11 x 37, 11 x 41, 11 x 43

The next prime number is 17. The following products are less than 500:

13 x 17, 13 x 19, 13 x 23, 13 x 29, 13 x 31, 13 x 37

The next prime is 17:

17 x 19, 17 x 23, 17 x 29

Finally:

19 x 23