geno3141

Let  J  represent the number of tickets in Japan.

Let  S  represent the number of tickets in Switzerland.

I'm going to modify the $79.663 to $79.63:

3J + 2S  =  79.63    --->     3J + 2S  =  79.63   (multiply by 2)  --->   6J + 4S  =    159.26

3S + 2J  =  75.57     --->     2J + 3S  =  75.57    (multiply by -3) -->  -6J  - 9S  =  -226.71  

                                                       Add down the columns:                    -5S  =  -67.45

                                                                                                                S  =  $13.49

When  S = 13.49 --->   3J + 2(13.49)  =  79.63   --->  3J + 26.98  =  79.63   --->  J  =  $17.55

Let  x  =  amount of pure acid                       Percent of pure acid = 100%  (1.00 as a decimal)

Then  81 - x  =  amount of the 10% acid solution

Formula:  (Percent)·(Amount)  +  (Percent)·(Amount)  =  (Final Percent)·(Final Amount)

               (100%)·(x)  +  (10%)·(81 - x)  =  (20%)·(81)

               (1.00)·(x)  +  (0.10)·(81 - x)  =  (0.20)·(81)

                          x    +  8.1 - 0.1x  =  16.2

                                           0.9x  =  8.1

                                               x  =  8 liters of pure acid

                                        81 - x  =  72 liters of 10% acid solution

Compound interest formula:      A  =  P(1 + r/n)^(n·t)

A = final amount                   P = amount invested = $5000.00                    t = number of years = 8

r = rate (as a decimal) =  0.05         n = number of times compounded per year = 12

A  =  5000(1 + 0.05/12)^(12·8)

If you enter this into a calculator, you will get the answer.  

(Hint:  your answer will be between $7000 and $7500.)

(1/5)x + (2/3)y  =  -(3 1/5)

Problems are usually easier if there are no fractions:

(1/5)x + (2/3)y  =  -16/5

Multiplying both sides by 15:

--->   3x + 10y  =  -48

Substitution can occur when one of the equations is solved for one of the variables.

Since the other equation is  3x - y  =  6 

this equation can be solved for y:  --->  -y  =  -3x + 6     --->     y  =  3x - 6

Substitute this value for  y  into the other equation:

--->   3x + 10y  =  -48    --->     3x + 10(3x - 6)  =  -48

                                    --->     3x + 30x - 60  =  -48

                                    --->     33x - 60  =  -48

                                    --->     33x  =  12

                                    --->     x  =  12/33     --->     x  =  4/11

If  x  =  4/11,  then  y  =  3x - 6     --->     3(4/11) - 6  =  -54/11

Tiddle is right!

Velocity is speed in a particular direction.

Velocity can change if the speed changes or if the direction changes.

happy7 has given the number of feet in 1000 miles.

To find the number of steps, divide this answer by the length of each step.

For instance, if each of your steps is 2.25 feet long, you would have 5280 x 1000 ÷ 2.25

2n + 12.5 = 150

25·a^(-5)·b^(-8) : 5·a^4·b

=   [ 25·a^(-5)·b^(-8) ] / [ 5·a^4·b ]             (ratios indicate division)

=   [ 25 / ( a^5 · b^8 ) ] / [ 5·a^4·b ]     (negative exponents become positive when placed in the denominator)

=   [ 25 / ( a^5 · b^8 ) ]  ·  [ 1 / ( 5·a^4·b ) ]    (division is replaced by multiplication of the reciprocal)

=   [ 25 · 1 ] / [ a^5 · b^8 · 5·a^4·b ]     (multiplying numerators times nums and denominators time denoms)

=   25 / [ 5 · a^9 ·  b^9 ]                                 (simplifying)

=   5 / [ a^9 · b^9 ]                                        (cancelling like factors)

3|x - 7| - 2  =  4

3|x - 7|  =  6

  |x - 7|  =  2

Either  x - 7  =  +2     or     x - 7  =  -2

                x  =  9                   x  =  5

6x² +7x - 3  =  0

To complete the square:

Step 1) Move the constant term to the other side (add 3 to both sides):

            6x² +7x     =  3

Step 2) Divide all the terms by the coefficient of the squared term:

             x² +(7/6)x     =  1/2

Step 3) Divide the coefficient of the x-term by 2, square that number, and add that number to both sides:

                       7/6 ÷ 2  =  7/12             (7/12)²  =  49/144

             x² +(7/6)x + 49/144  =  1/2 + 49/144

             x² +(7/6)x + 49/144  =  121/144

Step 4) Factor the left side:

            (x + 7/12)²  =  121/144

Step 5) Find the square root of both sides (don't forget the ± sign):

              x + 7/12  =  ± 11/12

Step 6) Finish:

              x  =  -7/12 ± 11/12

              x  =  1/3, -3/2