geno3141

Since there are 60 minutes in an hour, 120 minutes will be two hours from now.

12:51 + 2:00  =  14:51  (or 2:51)

x² - 5x + 6

Since the last term (+6) is positive, the two signs will either be both positive or both negative.

Since the middle term (-5x) is negative, the two signs will be both negative.

The form of the answer is:  (x -    )(x -    )

The last term, 6, can be factored either as 1 and 6 or 2 and 3.

Trying  (x - 1)(x - 6), when foiled, becomes x² - 7x + 6, which isn't correct.

Trying  (x - 2)(x - 3), the answer becomes x² - 5x + 6 !!!!!!!!!!!!!!!!!!!

Working with the real term first:

     3(-2) - 4   =  -6 - 4  = -10

Now, the imaginary term:

     ( 1 - 2(-2) )  =  ( 1 + 4 )  =  5

Putting these toether:     -10 + 5i

The 4 represents amplitude.

The +5 represents a horizontal shift.     ***

The +3 represents a vertical shift.        ***

A change in period  would be represented by a multiplier of the x term, as in:  y  =  sin(3x), which Since this problem as simply x, or 1x, there is no increase or decrease in the period.

Hint:  the '+ π/4' give the graph a horizontal shift of π/4 to the left.

So, find the x-intercepts of the function  f(x) = sin(x) and subtract π/4 from each of these x-values.

The price is calculated by multiplying the price per pound times the number of pounds.

So:  p  =  3.99 · w

Let the number of dimes be:  d

Then, since the number of quarters is two less than the number of dimes:  q = d - 2

The number of nickels is twice the number of quarters:  n = 2·q  =  2(d - 2)  = 2d - 4

Since there are 40 coins,  p + n + d + q  =  40

                               or:   p + (2d - 4) + d + (d - 2)  = 40

               Solving for p:    p  + 4d - 6  =  40         --->      p  =  46 - 4d

 .01(46 - 4d) + .05(2d - 4) + .10(d) + .25(d - 2)  = 3.86

Multiply by 100:

       (46 - 4d)  +  (10d - 20)  +  (10d)  +  (25d - 50)  =  386

                       41d  -  24  =  386

                                41d   =  410

      --->  d = 10

Use this to find the other answers and check the work.

Use the distributive property on   x(1-3x)  to get  x·(1) - x·(3x)

      x·(1)  = 1x or just x

      x·(3x)  =  3·x·x  = 3x²

So   x(1-3x)  =  x - 3x²

Now: x(1-3x) + 3x - 1  =  x - 3x² + 3x -1

To simplify this:  x + 3x  = 4x

So, the answer is: - 3x² + 4x -1

Base three:  11

Base four:    10

Base five (or any base greater than five:  4

x + 1/3  =  5 + x/2

Oftentimes, equations are easier to solve if there are no fractions.

To get rid of fractions, multiply each side by a common denominator (a common denominator of 3 and 2 is 6).

6 · (x + 1/3)  =  6 · (5 + x/2)

6 · x  +  6 · 1/3     =     6 · 5  +  6 · x/2

6x  +  2    =    30 + 3x

Get all the x's to one side (subtract 3x from both sides);

6x - 3x + 2  =  30 + 3x - 3x

3x + 2  =  30

Subtract 2 from both sides:

3x + 2 - 2  =  30 - 2

3x  =  28

Divide by 3:

x  = 28/3   or   9 1/3