geno3141

20%  = 0.20

of  =  times

20 percent of 100 cm

0.20 x 100  =  20 cm

If a 16 foot tall giraffe casts an 8 foot tall shadow, then, by the same ratio, a 6 foot tall stump casts a 3 foot tall shadow. 

16/8  =  6/x

Cross multiply:  16·x  =  6·8          --->         16x  =  48         --->         x  =  3

Paul Erdös (1913-1996) wrote, and co-authored, a great many math papers. He was noted for the quality of his work and that he collaborated with more than 500 other mathematicians.

Erdös has Erdös number 0.

Any person who co-authored a paper with Paul Erdös has Erdös number 1.

Any person (who does not have an Erdös number smaller than 2) who co-authored a paper with a person who has Erdös number 1 has Erdös number 2.

Any person (who does not have an Erdös number smaller than 3) who co-authored a paper with a person who has Erdös number 2 has Erdös number 3.

Etc. 

Person C has Erdös number 1.

Person B has Erdös number 2.

Person C has Erdös number 3.

1 + 78h  =  157

Subtract 1 from both sides:

      78h  =  156

Divide both sides by 78:

          h  =  2

x(6 + 5)  =  3 + (x - 13)

=>  x(11)  = 3 + x - 13

=>  11x  = x - 10

=>  10x  =  -10

=>  x  =  -1

Distribute the -4 to each term:

(-4)(2m) - (-4)(7x) + (-4)(9)

=  -8m + 28x - 36

3x/4 - x/2  =  6

Equations are easier to work if there are no fractions; multiply each term by 4:

4(3x/4) - 4(x/2)  =  4(6)

=  3x - 2x  =  24

=          x   =  24

x^0  =  1

Y^-1  =  1/y

5x^-1  =  5/x

5^-1  =  1/5

25*x^0 ((y^-1 )/ (5x^-1)) * 5^-1y^2

= (25)*(1) ( (1/y) / (5/x) )*(1/5)y^2

    (1/y) / (5/x)  =  (1/y) * (x/5)  =  x/(5y)

= (25)*(1) ( x/(5y) )*(1/5)y^2

= 25 * ( x/(5y) )*(1/5)y^2

= [25xy^2] / [25y]

= xy

The last digit of 7^x rotates among 1, 7, 9, and 3 because:

7^0  =    1     7^4 = 7^4 x 7^0 = 2401           7^8 = 7^4 x 7^4 x 7^0 = 5764801      ...

7^1  =    7     7^5 = 7^4 x 7^1 = 16707         7^9 = 7^4 x 7^4 x 7^1 = 40353607    ...

7^2  =  49     7^6 = 7^4 x 7^2 = 117649        ...

7^3 = 343     7^7 = 7^4 x 7^3 = 823543        ...

What I'm trying to show is extra factors of 7^4 doesn't change the last digit of the answer.

So divide the exponent by 4,

if the remainder is 0, the last digit will be a 1

if the remainder is 1, the last digit will be a 7

if the remainder is 2, the last digit will be a 9

if the remainder is 3, the last digit will be a 3

Dividing the exponent of 2800 by 4, gives a remainder of 0, so the last digit will be a 1.

If you multiply both sides by a positive number, there are no restrictions.

However, if you multiply both sides by a negative number, you must reverse the direction of the inequality.

That is, if you have  -2x > 4, then you answer becomes x < -2.