geno3141

My guess:  143547

The first two digits of the answer are formed by multiplying the first two digits of the problem.

The second two digits of the answer are formed by multiplying the first and last digits of the problem.

The last two digits of the answer are formed by adding the number represented by the first two digits of the answer to the number represented by the second two digits of the answer and subtracting the middle digit of the problem.

Awesome!  -- Thanks!

x - 3y  =  16

Solve the equation for y:  - 3y  =  -x + 16

                                             y  =  (1/3)x  - (16/3)

The slope is the coefficient of the x-term:  1/3

The y-intercept is the constant terM:  -16/3

To divide fractions, multiply by the multiplicative inverse:

(29/8) / (1/4)  =  (29/8) x (4/1)  =  116/8  =  29/2  =  14.5

Supplementary angles are two angles whose sum is 180^o.

If one angle is  x^o,  the other angle will be  (180 - x)^o.

One angle is three times the measure of the other (supplementary) angle:  x  =  3(180 - x)

Solve:                                                                                                             x  =  540 - 3x

                                                                                                                     4x  =  540

                                                                                                                       x  =  135

This makes the other angle:  180 - x=  180 - 135  = 45.

The two angles measure  45^o  abd  135^o.

If the children are Alan (=0.5) and Barb (=0.3):

  this means:  not Alan = 0.5  and  not Barb  = 0.7:

a) both Alan and Barb:  0.5 and 0.3  =  0.5 x 0.3  =  0.15

b) exactly one:  either Alan and not Barb  or  not Alan and Barb

                                =  0.5 x 0.7  +  0.5 x 0.3  =  0.35 + 0.15  =  0.50

c) neither one:  not Alan  and  not Barb  =  0.5 x 0.7  =  0.35

d) at least one:  both Alan and Barb  or  Alan and not Barb  or  not Alan and Barb

                         =  0.5 x 0.3  +  0.5 x 0.7  +  0.5 x 0.3  =  0.15  +  0.35  +  0.15  =  0.65

With "and", you multiply; with "or", you add.

0/0  is undefined because it has no particular value.

For example:  6/3  =  2  because 6  = 2 x 3

Using this idea:  0/0  =  4  because  0  = 4 x 0

Also:                  0/0  =  9  because  0  =  9 x 0

And:                   0/0  =  27  because  0  =  27 x 0

So, you can make  0/0  to be any number:  0/0  =  n  because  0  = n x 0  for every number that you replace for n.

Consider this example:

Many persons attended a conference. Doughnuts were served.

You were cleaning up aferwards and there were 5 doughnuts left on a plate and 3 unopened boxes of doughnuts, 12 to a box.

How many doughnuts were left?

3 boxes and 5 more:  3 boxes + 5:  3(12) + 5  =  36 + 5  =  41 doughnuts.

The multiplication tells you how many were in the boxes (there were 36 doughnuts in the 3 boxes); you shouldn't add the 5 to the number in each box, because there weren't 17 in each box!

The multiplication tells you how many individual elements there were in all the sets; the addition tells you how many individual items were left over.

So, if you have a problem like:  7 + 5(10),  you have 7 individual items and 5 sets of 10 items  -- there are 5 x 10  or 50 items in the sets plus the original 7, for 50 + 7  =  57.

An extensive explanation can be found at:

http://www.math.uakron.edu/amc/DataAnalysis_Statistics/Data%20Analysis/Notes/ScatterPlots&RegressioninstructionsTI_73.pdf

First, use the distributive property:  3(a + 4)  =  3(a) + 3(4)  =  3a + 12

3(a + 4) - 9  =  3a + 12 - 9  

Since 12 - 9  =  3:

3(a + 4) - 9  -  3a + 12 - 9  =  3a + 3