geno3141

An example:  f(x)  =  3x² + 1         g(x)  =  2x + 5

f( g(x)  )  =  3( g(x) )² + 1  

               =  3( 2x + 5 )² + 1  =  3(4x² + 20x + 25) + 1  =  12x² + 60x + 75 + 1  

               =  12x²  + 60x + 76

g( f(x) )  =  2( f(x) ) + 5

              =  2( 3x²  + 1 ) + 5  =  6x² + 2 + 5

              =  6x²  + 7

Can you be more specific?

Do you mean:  How do I graph an equation that is in slope-intercept form?

Or:  How do I take a graph and find an equation that is in slope-intercept form?

Or:  I have an equation that isn't in slope-intercept form, how can I turn that equation into slope-intercept form?

Or:  ...

-5n - 6x  <  8 - 8n - n

Simplify each side:

-11n  <  8 - 9n

Add 9n to both sides:

-2n < 8

Divide both sides by -2 -- when you multiply or divide both sides of an inequation by a negative number you need to change the direction of the inequality (you don't change the direction if you multiply or divide by a positive number or if you add or subtract any values):

n  >  -4

(4x + 3) - (2x - 3)

=  4x + 3 - (2x - 3)

=  4x + 3 - 2x + 3               (because - -3  =  + 3)

=  2x + 6

What rectangular prism? What cube?

sin(65°)  =  483/x

Multiply both sides by x:

--->   x · sin(65°)  =  483

Divide both sides by sin(65°)

--->   x  =  483 / sin(65°)

Now, use your calculator ...

One way is to plot points.

Choose three values for x; so they are easy to calculate, choose multiples of 3 (the denominator).

If x = 0, then y = (4/3)(0) + 2  =  0 + 2  =  2   --->   (0, 2)

If x = 3, then y = (4/3)(3) + 2  =  4 + 2  =  6   --->   (3, 6)

If x = 6, then y = (4/3)(6) + 2  =  8 + 2  =  10   --->   (6, 10)

You now have three points, plot them and draw the straight line that passes through those three points.

The reason that I choose three points and not just two is that if I make a mistake, then the points (most likely) will not be on a straight line, so I'll be able to check my work.

The value will be:  30000 · 8.0 · 10⁵  =  (240000) · 10⁵  =  (2.4 · 10⁵) · 10⁵

   =  $2.4 · 10¹⁰  

g(x)  =  6(0.5)^x

g(2)  =  6(0.5)²  =  6(0.25)  =  1.5

(1/4)^-2  =  (4^-1)^-2  =  4²  =  16

(6x/7)^-2  =  6^-2 · x^-2 / 7^-2  =  7² / ( 6² · x²  =  49 / (36x²)

16 · 49 / (36x²)  =  784 / (36x²)  =  196 / (9x²)