hectictar

Assuming that 3x + 12y  ≠  0 , simplify

     \(\dfrac{12x^3 + 48x^2y}{3x+12y}\)                   Factor  4x²  out of the numerator.

\(=\,\dfrac{4x^2(3x + 12y)}{3x+12y}\)                 Divide the numerator and denominator by  3x + 12y .

\(=\,4x^2\)

Is this your problem?

( ^³√( x + 1 )  -  ^³√( x ) )( ^³√( x + 1 )²  +  ^³√( x + 1 )^³√( x )  +  ^³√( x )² )

Since         (a - b)(a² + ab + b²)   =   a³ - b³

so does...

( ^³√( x + 1 )  -  ^³√( x ) )( ^³√( x + 1 )²  +  ^³√( x + 1 )^³√( x )  +  ^³√( x )² )     =    ^³√( x + 1 )³  -  ^³√( x )³

=   x + 1  -  x   =   1

Wow! You baked that cake so fast you ought to work at a bakery!!!

It tastes super good too!!

Thank you, I really really appreciate it!!! 

The inside is yellow too! Yummy!!! 

LOL!!! 

What does your teacher say is a "whole number" ?

I am pretty sure that 0.84 is not a whole number!

0.84  ≠  84

It can be written as a fraction, though.

0.84 cannot be expressed as a whole number.

When the equation of the parabola is in this form:

y  =  ax² + bx + c

The  x-coordinate  of the turning point   =   - \(\frac{b}{2a}\)

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For example, if the equation of the parabola is

y  =  3x² + 4x + 1

The  x-coordinate  of the turning point   =   - \(\frac{4}{2(3)}\)   =   - \(\frac{2}{3}\)

Plug this in for  x  to find the value of the  y-coordinate.

y   =   3( - \(\frac{2}{3}\) )² + 4( - \(\frac{2}{3}\) ) + 1   =   - \(\frac13\)

So the turning point is  ( - \(\frac{2}{3}\),  - \(\frac{1}{3}\) )

Multiplying a number by  10  moves the decimal point to the right one place.

For example...      2 * 10  =  20     and     0.7 * 10  =  7

When we multiply  2.56  by  1,000,000,000 , we are multiplying  2.56  by  10 , 9 times.

So we need to move the decimal point to the right  9  places.

2.56 * 1,000,000,000  =  2,560,000,000.0

The decimal point goes at the very end of  2,560,000,000 , but it isn't necessary to write it since only zeros follow it.

Well thank you!  

I did have a little hint after I saw what the answer was supposed to be from WolframAlpha though!!!

First factor this.

x⁴ + x³ - 11x² + x - 12     Rearrange.

x³ + x + x⁴ - 11x² - 12       Factor  x  out of the first two terms and split the  -11x² .

x(x² + 1) + x⁴ + x² - 12x² - 12    Factor  x² out of  x⁴ + x²     and  -12  out of  -12x² - 12 .

x(x² + 1) + x²(x² + 1) - 12(x² + 1)     Factor  (x² + 1)  out of all the terms. 

(x² + 1)(x² + x - 12)    Factor the  x² + x - 12 .

(x² + 1)(x² + 4x - 3x - 12)

(x² + 1)(x(x + 4) - 3(x + 4))

(x² + 1)(x + 4)(x - 3)

To find out the  x  values that make this equal to zero, set each factor equal to zero and solve for  x .

x² + 1  =  0           x - 3  =  0           x + 4  =  0

x²  =  -1                 x  = 3                   x  =  -4

not real