All Answers 358184 Answers

a.) x^3 + 3x^2 - x = 3 

Subtract 3 from both sides

x^3 + 3x^2 - x - 3  = 0

Factor by grouping

x^2 (x + 3) - 1(x + 3) = 0

(x^2 - 1) ( x + 3) = 0

(x + 1) ( x - 1) ( x + 3) = 0

Setting each factor to 0 and solving for x produces

x = -1    or    x = 1    or     x = -3

b.) b^3 - 4b^2 -21b = 0

Factor as

b ( b^2  - 4b - 21) = 0

b (b - 7) ( b + 3) = 0

Setting each factor to 0  and solving for b produces

b = 0  or  b  = 7    or    b = -3

What is the area???

The perimeter is all solved using the distance formula, RP

The formula for the distance between two points is given by

√ [ (subtract the x coordinates of the two points)^2 + (subtract the y coordinates)^2 ]

So....for instance....the distance between A and B is

√ [ ( -2 - 2)^2 + ( -1 -1)^2 ] = √ [ (-4)^2 + (-2)^2] = √ [16 + 4] = √20 = 2√5

Now..using this example..compute the distances between

A and D

D and C

C and B

Add these four distances....this will be the perimeter

Do this part first....then....I will show you how to calculate the area

Let me know if you run into trouble......

I think you want the dimensions of the fence

Let the two sides perpendicular to the river be = x

The side parallel to the river is then [ 1000 - 2x] 

So, the area A is given by:

A = x [1000 - 2x]  =  -2x^2 + 1000x

The x value that maximizes this is =     - (-1000) / [ 2 * -2] = 1000/4 =  250 

So....the dimesions of the fence are    250 [1000 - 2*250] = 250 x 500

And the max area is  250 ft x 500 ft =   125000 ft^2

Yes on a,b,c if you are going to use the quadratic formula....or you may be ble to 'see' that it factors in to:

(x+5)(x+4) = 0     then x = -5 or -4

Yes, that is pretty odd, my answer looked weird.

I'm fine, thanks

yes yes yes yes yes

HAHAHA!!!!......me too, Synth......

[ This probably wasn't a "real" question ]

17,755,477,825,681,042,807,338

17 sextillion 755 quintillion 477 quadrillion 825 trillion 681 billion 42 million 807 thousand 338

And that's a mouthful....!!!

I think your calculation is incorrect, the answer I got is \(\frac{1}{\lfloor \sqrt[4]{2016} \rfloor}\)

We got bored with just staring at a calculator all the time....so.....it just seemed like the thing to do.....

Correct, NSS    ....

8 < 4x + 4 < 2(x + 10)

We have two inequalities to consider

8 < 4x+ 4                                                   4x +4  < 2(x + 10)

Subtract 4 from both sides                        divide through by 2

4 < 4x                                                         2x + 2 < x + 10

Divide both sides by 4                               Subtract 2, x from both sides

1 < x    (1)                                                           x  < 8   (2)

Combining (1) and (2) we have

1 < x < 8

is it C?

Could you give an example????

 How  can you do a fraction  that is involved in the equation 

Whoa!!!......very well done......that was a difficult one!!!

Nice, heureka !!!

We want all the sets of any 3 elements chosen from 8....and then we want alll the possible orderings of those sets....so

P (8,3)  =   336

Yes, ....it is.   And so is 'x' .

Look under the heading 'Possible Outcomes'.....and COUNT them.