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question reposted: JD is repainting some of the walls in the classrooms at Golder. One wall has a width that is 4 feet less than its length. The wall has an area of 140 square feet. What is the length of the wall? 

Let the length be L. We can write an equation for the area:

L(L - 4) = 140

L^2 - 4L - 140 = 0

(L - 14)(L + 10) = 0

L = 14 or L = -10

Length can't be negative, so the wall's length is 14 feet.

For a), you could write about either the first cube or the second cube. 

example:

a) What is the volume of the first cube?

b) 7^3 = 343 cm^3.

first line: 3x + 4y = -14

4y = -3x - 14

y = -3x/4 - 7/2

second line: parallel to first line, so the slope is 4/3. this line also passes through (-5, 7) so we can write this line in point slope form first:

y - 7 = 4/3(x + 5)

y - 7 = 4x/3 + 20/3

y = 4x/3 + 41/3

m + b = 4/3 + 41/3 = 15

g(5) = g(f(x))

f(x) = 5

3x - 8 = 5

x = 13/3

g(f(x)) = 2(13/3)^2 - 5(13/3) + 3 = 170/9

A different route:

(a+b)³  = ( a^3 + b^3 )  + 3 a^2b + 3 b^2 a

   7³    =   (   44   )       + 3 ab ( a+b)          we know (a+b) = 7     .... sub that in to get:

   7^3 - 44 = 21 ab

    ab = 299/21

Now   1/a + 1/b =   (a+b) / ab   

                        =  (7)  / (299/21) = 147/299    

6 out of 10 match a marble in the second bag   so     6/10

now there are 6 x 6 possibles   with  6 being a match   6/36

6 / 10  x  6/36 = 1/10

This may get you started:

a + b  =  7     --->     b  =  7 - a

a³ + b³  =  a³ + (7 - a)³  =  44

Expanding  (7 - a)³  =  (7)³ - (3 7²·a) + (3·7·a²) - a³   =  343 - 147a + 21a² - a³  

Substituting:

a³ + b³  =   a³ +  343 - 147a + 21a² - a³  =  44

                                  343 - 147a + 21a²  =  44        

                                  21a² - 147a + 343  =  44

                                  21a² - 147a + 299  =  0

Use the quadratic equation to find a; use that answer to find b; and finish.

The numbers  1, 2, 3, and 4  are in the first bag but not the second bag.

So, if you draw any of these numbers from the first bag, you can't get a match from the second bag.

The probability of never getting a match is  4/10.

However, if you draw a  5, 6, 7, 8, 9, or 10  from the first bag, you can get a match from the second bag.

The probability that you will get one of these numbers from the first bag is  6/10.

After choosing one of these six numbers, there will be a  1  in  6  chance to draw the same number from the second bag.

So, the probability of success will be:  6/10 x 1/6  =  ........

I agree with the answers from guest; however, if you are to use geometric means:

The geometric mean of  a  and  b  is sqrt( a · b).

Therefore the geometric mean between  48  and  243/16  is:

     sqrt( 48 · 243/16 )  =  27      (the third term, or center term)

Then, the geometric mean between  48  and  27  is:

     sqrt( 48 · 27 )  =  36     (the second term)

and the geometric mean between  27  and  243/16  is:

    sqrt( 27 · 243/16 )  =  81/4     (the fourth term)

See below......  solve for 'x'

198 is found by    tan 68 = 80/d       then  d = 198

Start with this:

(x^2 + y^2 ) ²   = ( x^4  + y^4)    +   2 x^2 y^2        now remember    x^2 + y^2 = 1    so

       1              =   17/19          + 2 x^2 y^2            I think you should be able to finish from here, yah?

Note that   c  and  a   are the 'x' coordinates....

  All you need to do is equate the two given parabolic equations, simplify and then use the Quadratic Formula to solve for the x's  ( c and a )

-x^2 - x + 1     =     x^2 - 3x - 3    <====== take it away !

First, I think you are supposed to find out all the 5 terms of the GS between 48 and 243/16

[243/16] / 48 ==0.31640625

0.31640625^(1/4) ==3 /4 - this is the common ratio.

The 5 terms of your GS look like this:

48 , 36 , 27 , 81 / 4 , 243 / 16 , >>Number of terms = 5>>Total Sum == 2343 / 16

Note: I don't think you need "geometric means"!!

Gamemaster,

You need to start talking about the questions that you post.

I mean you need to discuss what you already think you know and what thoughts you have on the rest.

Just dumping questions is simply NOT cool.

I think you are capable of better.  

Have you tried drawing this.  You will not get it without a picture.

You will end up with a half a big circle and a quarter of 2 little circles.     the area of a circl is pi*r^2

Try if for yourself

Note that the other answer already given is incorrect.

Find a polynomial f(x) of degree 5 such that both of these properties hold: f(x) is divisible by x^3.

and   f(x)+2 is divisible by (x+1)^3

Write your answer in expanded form (that is, do not factor f(x)

\(f(x)=x^3(ax^2+bx+c)\\ g(x)=f(x)+2=x^3(ax^2+bx+c)+2\\ g(-1)=0\quad so\\ -1(a-b+c)+2=0\\ -a+b-c+2=0\\ \boxed {c=2+b-a}\\ g(x)=x^3(ax^2+bx+2+b-a)+2\\ g(x)=ax^5+bx^4+(2+b-a)^3+2\\ \)

Next I divided that by  x+1 and got

\(h(x)=ax^4+(b-a)x^3+2x^2-2x+2\)

I know h(x) must also be diviasable by (x+1)    so  h(-1)=0

h(-1)=a(1)+(b-a)(-1)+2(1)-2(-1)+2

h(-1)=a+(-b+a)+2+2+2

h(-1)=2a-b+6 =0

b=2a+6

\(h(x)=ax^4+(2a+6-a)x^3+2x^2-2x+2\\ h(x)=ax^4+(a+6)x^3+2x^2-2x+2\\\)

Now I divided that by   (x+1)^2 = x^2+2x+1

And put the remainder = 0 hence solving for a.

I will leave you do the grunt work and some of the finishing up.

Note: This method does work but there may be a quicker way.

Hi Frosty,

Welcome back to the forum. :)

Why have you included all that unrendered latex?

You should make it as easy as possible for people to read and interpret your questions. 

Beats me ... any ideas.

Please include the address of the original question.

Put the given equation into standard circle form by completing the square for x and y

(x+5)^2   +  (y-3)^2   =   24 + 25 + 9     

r^2 = 24+25+9 =58

Area = pi r^2    = 58 pi

Ok thanks, that makes sense :)

What figure.

If you are going to copy stuff then cite where it comes from and include everything that is needed.

If they add the same number of numbers, this is an interesting problem:

(finding the sum of the smallest n positive numbers minus the sum of the largest n

negative numbers:

1 number:                                                           (2) - (-1)  =    3

2 numbers:                                            (2 + 4) - (-1 + -3)  =  10

3 numbers:                               (2 + 4 + 6) - (-1 + -3 + -5)  =  21

4 numbers:                  (2 + 4 + 6 + 8) - (-1 + -3 + -5 + -7)  =  36

5 numbers:  (2 + 4 + 6 + 8 + 10) = (-1 + -3 + -5 + -7 + -9)  =  55

For a pattern:  3  =  1 · (2·1 + 1)

                      10  =  2 · (2·2 + 1)

                      21  =  3 · (2·3 + 1)

                      30  =  4 · (2·4 + 1)

                      55  =  5 · (2·5 + 1)

n^th sum:  Sum  =  n · (2·n + 1)