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y  =  f(-3x)      The  x-intercepts of this function are the values of  x  when  y = 0

The  x-intercepts are the  x  values that make this equation true:

0  =  f(-3x)

                                    Since  f(x)  =  x² - x - 6  ,   f(-3x)  =  (-3x)² - (-3x) - 6

0  =  (-3x)² - (-3x) - 6

0  =  9x² + 3x - 6

                                    Divide through by  3 .

0  =  3x² + x - 2

                                    Factor the right side.

0  =  3x² + 3x - 2x - 2

0  =  3x(x + 1) - 2(x + 1)

0  =  (x + 1)(3x - 2)      Set each factor equal to zero.

x + 1  =  0       or       3x - 2  =  0

x  =  -1            or         x  =  2/3

The x-intercepts are  -1  and  2/3 .

√5  is an irrational number

Distance to entrance

 61 tan 48

Distance to friends

61 tan  10  

Diference = friends to entrance distance

61 tan 48   - 61 tan 10  =  61 (tan 48 - tan 10) = 56.99 =~ 57 ft

y tan 33  =  (y + 855) tan 25

                                                           Distribute  tan 25  to both terms in parenthesees.

y tan 33  =  y tan 25 + 855 tan 25

                                                           Subtract  y tan 25  from both sides of the equation.

y tan 33 - y tan 25   =   855 tan 25

                                                           Factor  y  out of both terms on the left side.

y( tan 33 - tan 25 )   =   855 tan 25

                                                           Divide both sides of the equation by  ( tan 33 - tan 25 ) .

y   =   855 tan 25 / ( tan 33 - tan 25 )

Divide both sides of the equation by tan 25 to get

y  tan33/tan25 = (y+855)      now divide both sides by y

tan 33/ tan 25 =   (  y+855)/y     simplify

tan 33 / tan 25  = 1 +855/y         subtract 1

tan 33 /tan 25 - 1 = 855/y        re-arrange

y = 855 / (tan 33/tan 25 -1)

This is a variation of Charle's law

V/T = k      k is a constant and T is degrees K  (MUST BE IN DEGREES K)

FIRST    -55 c  + 273.15 = 218.15 K

               30 c                  = 303.15 K

Now the original volume and temp    590 ml / 218.15 K  =  konstant = 2.70456

Now, assuming a constant pressure, the NEW volume     

x ml / 303.15 =2.70456

x= 819.89 ml

Since they BOTH equal the k onstant , you can set it up as a ratio:

590/218.15 = x / 303.15      x = 819.89 ml

=cubrt (27 x 2) - 8^3 sqrt(1/4)

= 3 sqrt(2) - 512 (1/2)

= 3 sqrt(2) - 256

Not sure I understand your question....can you clarify?

First prize =                  x dollars

second =                      x-50

third = x-50 - 50  =       x-100

fourth = x-100-50 =      x-150

fifth = x-150 -50 =        x- 200

Total money is all of these added together

x + (x-50) + (x-100) + (x-150) + (x-200)     simplfies to

Total Money = 5x - 500

This is an equation for a parbolic path that the rocket follows.

It is a parabola opened downward due to the  ' - ' sign in front of the x^2 term.

The MAXIMUM of this quadratic is given by   -b/2a  =  -12/2(-3) = -12/-6 = 2 seconds.

  If we use this value of 't' in the height equation, we will find the maximum height the rocket reaches.

-3(2^2) + 12(2) + 60 = max height = 72 feet

Here is a graph:

The graph shown is the graph of  y = 4/x  shifted  6  units left and  2  units up, so it has the equation

y  =  4 / (x + 6) + 2

y  varies directly with  x  and inversely with  z .

y  =  kx / z

                            And  y = 18  when  x = 15  and  z = 5 .

18  =  k(15) / 5

                            Multiply both sides by  5 .

90  =  k(15)

                            Divide both sides by  15 .

6  =  k                  So...

y  =  6x / z

Find  y  when  x = 21  and  z = 7 .

y  =  6(21) / 7

y  =  126 / 7

y  =  18

1)      w  and  t  vary inversely, so...

t  =  k / w

                               t = 1/5   when  w = 4  ,   so...

1/5  =  k / 4

                               Multiply both sides of the equation by  4

4 * (1/5)  =  k

4/5  =  k                  Now we can use this value of  k in the equation  w = k / t

t  =  (4/5) / w

                               Simplify.

t  =  (4/5) * (1/w)

t  =  4 / (5w)            To find t  when  w = 9 ,  plug in  9  for  w  in this equation.

t  =  4 / (5(9))

t  =  4 / 45

Hi Rosala,

Thanks for your feedback and for that answer.

Could you please try to explain what you don't understand about the 3rd one?

I am super busy over this time but I will try to get back to you. If not I do believe Chris understands perfectly and will be able to explain.

I hope I don't sound like I am taking you for granted Chris. It is just that you are here more than me and you are super generous with your time and knowledge:)

width   =   4  yards

length   =   5\(\frac23\)  yards

area   =   width  *  length

                                                      Plug in the given values for width and length.

area   =   4 yards  *  5\(\frac23\)  yards

area  =   (4 * 5\(\frac23\))  square yards

                                                      Convert  5\(\frac23\)  to  \(\frac{17}{3}\)

area  =   (4 * \(\frac{17}3\))  square yards

                                                      Multiply.

area   =   \(\frac{68}{3}\)   square yards

                                                      Convert  \(\frac{68}3\)  to  22\(\frac{2}{3}\)

area   =   22\(\frac23\)  square yards

I assume this is :

 (x * √ (3a) *  ³√b^2)³

Writing these in exponential form is easier, Manuel.....then we can just apply the rule that (a^m)^n  = a^(m * n)

So we have

[ x * ( 3a)^(1/2) * b^(2/3) ]  ^3  =

x^3  *  (3a)^(3/2) * b^2  =

x^3 * 3a √ [3a ] * b^2

ah okay haha thanks

No...1/8 is correct....I was just making a joke....LOL!!!

In the world of mor.onic stup.idity, a slug is the speed of thought.  The volume is brain size and it’s very small, which makes for a very dense and sluggish brain.

Don't you wish that ice cream worked that way  ??

Eat  (1/3) of a bowl....you get  "wider'

Eat 3 bowls.....you get  "narrower "

If   2 - 3sqrt (2)  is a root so is its conjugate, 2 + 3sqrt(2)

And if 1 - sqrt (3)  is a root then so is  1 + sqrt(3).....so we have

[ x - (2 - 3sqrt (2) ]  [ x -  (2 + 3sqrt(2) ] [ x - ( 1 - sqrt(3) ] [ x - ( 1 + sqrt (3) ]     simplify

[ x^2 - x(2 - 3sqrt (2) - x (2 + 3sqrt (2) + 4 - 18 ]  [ x - ( 1 - sqrt(3) ] [ x - ( 1 + sqrt (3) ]    

[ x^2 - 4x - 14 ]   [  x^2 - x(1 - sqrt (3) - x (1 + sqrt (3) + 1 - 3 ]

  [ x^2 - 4x - 14 ] [ x^2 -2x - 2 ] =

x^4  - 6x^3 - 8x^2 + 36x + 28

3C2 . 1/6 . 5/6 = 5/12

In a quadratic function, the domain   - the values of x covered by the graph  - is always going to be  "all real numbers"

This will not be true of the range .....[  the y values covered by the graph ].