geno3141

First, collect all the variables to one side; since the right side has only one term, which is the variable, get rid of the 3y from the left side by subtracting 3y from both sides:

3y + 6 - 3y < 2y - 3y

Simplify:

6 < -1y

Remove the -1 by dividing both sides by -1; however if you multiply or divide an inequality by a negative number you must change the direction of the inequality (you don't change the direction if you add or subtract a negative -- only if you multiply or divide):

6 / -1 > -1y / -1

-6 > y     --->   y < -6

To solve an equation do the opposite to the number that you want to remove.

You want to remove the 2; since it represents division, multiply both sides by 2:

2 · 24 = 2 · -r / 2

48 = - r

Now, to remove the negative sign, which represents multiplying by -1, divide by -1:

48 / -1 = -r / -1

-48 = r 

11 = 10 + 1 = 10^1 + 1

101 = 10^2 + 1

11 x 101 = (10^1 + 1)(10^2 + 1)= 10^3 + 10^2 + 10^1 + 1

(The problem starts with 11 -- which is 10^1 + 1 -- Now mutiplying by 10^2 results in new terms -- 10^3 + 10^2 -- which are just larger than the old terms (which are saved by multiplying by 1) )

10001 = 10^4 + 1

11 x 101 x 1001 = (10^3 + 10^2 + 10^1 + 1) x (10^4 + 1) = 10^7 + 10^6 + 10^5 + 10^4 + 10^3 + 10^2 + 10^1 + 1

(The old answer was 1111 = 10^3 + 10^2 + 10^1 + 1 -- Now multiplying by 10^4 results in the new terms -- 10^7 + 10^6 + 10^5 + 10^4 -- which are just larger than the old terms 10^3 + 10^2 + 10^1 + 1 (which are saved by multiplying by 1) )

So, if we multiply by a number -- a power of ten that results in sufficiently new terms -- we will get an answer that begins with only 1s and if we then append to that the old terms by multiplying the old terms by 1, we will get an answer that has only 1s.

The necessary power of ten in the new factor is detemined by your requirement for the number of zeroes.

a^-2 = 1 / a²

( 1 / a² ) / ( a² b² )

    = ( 1 / a² )  · ( 1 / ( a² b² ) )

    = (1  ·  1  ) / ( a² · a² b² )

    = 1 / (a^4 b²)

In other words, with an "a to the power of minus 2" move the factor to the denominator and make the exponent positive two.

Then combine that with what is already in the denominator (another a² and a b²) to end with an a^4 b² in the denominator.

It is a fraction; as a decimal it is approximately -0.088 235 294 12

On the left side you have a 4 in the numerator (as a multiplier) and a 4 in the denominator. 

I would cancel these two numbers.

Then you have: 2x - 5 = 11                       Add 5 to both sides.

     ----->   2x = 16                                  Divide by 2.

     ----->     x = 8

Check:    4( 2(8) - 5 ) / 4

              4( 16 - 5 ) / 4

              4( 11 ) / 4

                   44 / 4

                    11 

f(x) = 9

9 = 12.57 / (1 + 4.11 e^( -.026t) )

9(1 + 4.11e^(-.026t) )= 12.57                         Cross multiply

1 + 4.11e^(-.026t) = 12.57 / 9                 Divide by 9. Feel free to calculate and use decimals from here.

4.11e^(-.026t)  = 12.57 / 9  - 1                        Subtract 1.

e^(-.026t) = ( 12.57 / 9  - 1 ) / 4.11                  Divide by 4.11.

ln( e^(-.026t) ) = ln(  (12.57 / 9  - 1) / 4.11 )     Since the variable is in the exponent, find the ln of both                                                                             sides; also, use log instead, if you wish.

-.026t x ln( e ) = ln(  (12.57 / 9  - 1 ) / 4.11 )     The exponent comes out as a multiplier.

-.026t  = ln(  (12.57 / 9  - 1) / 4.11 )                  The ln(e) = 1; it will disappear in multiplication.       

t = ( ln(  ( 12.57 / 9  - 1 ) / 4.11 ) ) / -.026            Divide by -.026.

Add this answer to 1970.

5 = 2L + 2(.64L)                            (First simplify by multiplying 2 and .64)

5 = 2L + 1.28L                               (Next, simplify by adding 2L and 1.28L)

5 = 3.28L                                       (Finally divide both sides by 3.28)

L = 1.52 (approx)

I = k / R   (where k is the proportionality constant for this situation.

Given that I = 5 and R = 7:     5 = k / 7    --->     k = 35      (cross multiply)

So this formula is:     I = 35 / R  

                    --->     I · R = 35                    (cross multiply)

                    --->      R = 35 / I                    (divide)

For a right triangle, the tangent of the two acute angles is defined to the length of the opposite side divided by the length of the adjacent side.

tan = opp / adj

If tan A = 3/4, the opposite side is the 3 ft side, the adjacent side is the 4 ft side. The angle that fits this criterion is angle 1.