geno3141

To divide common fractions, multiply by the reciprocal:

(16/165) ÷ (17/165)  =  (16/165) x (165/17)  =  16/17       (The 165's cancel.)

There are two equations, one for the number of jackets and one for the value of the jackets.

Let  x  represent the number of jackets that cost 350 crowns each and

let  y  represent the number of jackets that cost 650 crowns each.

Number of jackets:               x + y  = 20                   --->     y  =  -x + 20

Value of the jackets:  350x + 650y  =  9400              --->     y  =  -(350/650)x + 9400/650

Graph these on the same graph; the point where they intersect will tell you how many of each were bought.

There are many equations that can be used to find a decimal approximation of pi. Wikipedia has several.

It depends upon which log you use.

If you use common logs, which use the abbreviation 'log' and you use the log key on your calculator, you will get 10^6 = 1,000,000.

If you use natural logs, which use the abbreviation 'ln' and you use the ln key on your calculator, you will get e^6 = 403.42...

3^1  =  3

3^2  =  3 x 3  =  9

3^3  =  3 x 3 x 3  =  81

A parabola can have this form:  y - k  =  a(x - h)²

where (h,k) is the vertex and a is an expansion factor.

The points that you describe can be interpreted as (0, 7200), (8000, 10000) and (16000, 7200) with the vertex at (8000, 10000). I got the 8000 because it has to be halfway between the starting x-value (0) and the ending x-value (16000).

Thus, x = 8000 and y = 10000. Putting them into the equation to find the value of a:

      y - 10000 = a(x - 8000)²

I can use any point for the values of x and y, so I will choose (0, 7200):

    7200 - 10000  =  a(0 - 8000)²

               -2800  =  a(64000000)

              a  =  -2800 / 64000000  =  -7/160000

So, an equation of the parabola is:  y - 10000  =  (-7/160000)(x - 8000)²

Since you have a denominator of 3, multiply 3 times both sides:

3[y - 2]  =  3[ -5/3(x - 4) ]               When you multiply by 3, multiply only the first factor, not both of them.

3y - 6  =  -5(x - 4)                           Use distributive property.

3y - 6  =  -5x + 20                          Add 6 to both sides.

3y  =  -5x + 26                               Divide both sides by 3.

y  =  (-5/3)x + (26/3)

2d  =  d + 11 + 11

2d  =  d + 22

d  =  22                     (subtract d from both sides)

If my interpretation is correct:  2(x² + 3y) + x + y  =  2x² + 6y + x + y  =  2x² + x + 7y 

Or, possibly:  2x(x² + 3y) + x + y   =  2x^3 + 6xy + x + y

Inverse variation has the form:  y = k / x

For this problem:  pitch = k / wavelength

                          400  =  k / 2      --->     k  = 800

Formula for this problem:  pitch  =  800 / wavelength

                                         700  =  800 / wavelength

                      700 x wavelength  =  800

                               wavelength  =  8/7 m