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Thank you for helping but that answer is incorrect, anyone can please help.

 If line $l_2$ represents the graph of y=mx +b, then find m+b.

Hello Guest!

P ( -5, -7)

\(f(x)=-\frac{3}{4}x-3.5\)

\(m_1=-\frac{3}{4}\\ m_2=\frac{4}{3}\)

\(g(x)=m(x-x_P)+y_P\)

\(g(x)=\frac{4}{3}(x+5)-7\)

\(g(x)=\frac{4}{3}x-\frac{1}{3}\)

     \(y=mx+b\)

\(m+b=1\)

  !

Hmm... I'm getting \(\frac{\pi\sqrt{2}}{2}\)...

Is anyone getting another answer?

Thanks so much! That is indeed a great solution!

An alternative that I thought of was:

f'(0)^2 = f(0)f''(0) --> Since f(0) = 1, we conclude that f''(0) = f'(0)^2. Now, we can differentiate both sides to get f'(x)f''(x)=f(x)f'''(x). Now, we can differentiate this equation once again! And use the product rule! --> f'(x)f'''(x) + f''(x)^2 = f(x)f''''(x) + f'(x)f'''(x) --> f''(x)^2 = f(x)f''''(x).

Plugging in x=0 simply gives us the answer, that is, f''(0)^4 = f'''(0) = 0. Therefore, f''(0) = \(\pm 3\) and further, since f'(0)^2 =f''(0), we get the end result, \(f'(0) = \pm \sqrt{3}\). Yayyyy!

0<= x <=4

If 4x = 3y, what is the value of (2x + y)/(3x - y)?

Hello Guest!

\(4x = 3y\\ y=\frac{4x}{3}\\ \color{blue}(2x + y)/(3x - y)\\ =(2x+\frac{4x}{3})/(3x-\frac{4x}{3})\\ =\dfrac{6x+4x}{9x-4x}\\ \color{blue}=2 \)

If 4x = 3y,  is  (2x + y) / (3x - y) = 2

  !

$\theta = \frac{2 \pi}{3}$

If you let x go infinity, then you get 0 = A + B.

If you let x = 0, then you get 7/2 = A/(-2) + B.

The solution to this system is then A = -7/3, B = 7/3, so (A,B) = (-7/3,7/3).

The probability is 3/32.

I think you are correct, at least I checked over! 

oh ok

'Guest ' accounts cannot do this....must have an account.

Place the 4 x 6 x 8 box on one of the 6x8 sides

   place the 2 x 3 x 5  box on top of it , on one of its 3x5 sides

2 x    4 x 6    +    2 x   4x8       +   2x   2 x 3   + 2x  2 x 5       +     3 x 5    +  ( 6x8 - 3x5)       total

This way she does not paint  a   6x8 face      and a   3x5   face     and  a   3x5 piece of the other 6x8 face

The only way the resulting product is a multiple of 3 is if 1 (or both) of the number(s) are multiples of threes. Continue with casework. 

I know this is late but a Merry Christmas to him too!

i think i agree with u

thank you now i can solve the problem :kekw:

(x-12)/7 = h'(x)

Thanks a lot to you both !!!

n     $1 $2 $5 $10

1  = (20, 0, 0, 0)
2  = (18, 1, 0, 0)
3  = (16, 2, 0, 0)
4  = (14, 3, 0, 0)
5  = (12, 4, 0, 0)
6  = (10, 5, 0, 0)
7  = (8, 6, 0, 0)
8  = (6, 7, 0, 0)
9  = (4, 8, 0, 0)
10  = (2, 9, 0, 0)
11  = (0, 10, 0, 0)
12  = (15, 0, 1, 0)
13  = (13, 1, 1, 0)
14  = (11, 2, 1, 0)
15  = (9, 3, 1, 0)
16  = (7, 4, 1, 0)
17  = (5, 5, 1, 0)
18  = (3, 6, 1, 0)
19  = (1, 7, 1, 0)
20  = (10, 0, 2, 0)
21  = (8, 1, 2, 0)
22  = (6, 2, 2, 0)
23  = (4, 3, 2, 0)
24  = (2, 4, 2, 0)
25  = (0, 5, 2, 0)
26  = (5, 0, 3, 0)
27  = (3, 1, 3, 0)
28  = (1, 2, 3, 0)
29  = (0, 0, 4, 0)
30  = (10, 0, 0, 1)
31  = (8, 1, 0, 1)
32  = (6, 2, 0, 1)
33  = (4, 3, 0, 1)
34  = (2, 4, 0, 1)
35  = (0, 5, 0, 1)
36  = (5, 0, 1, 1)
37  = (3, 1, 1, 1)
38  = (1, 2, 1, 1)
39  = (0, 0, 2, 1)
40  = (0, 0, 0, 2)

40 ways to make a change for a $20 bill.
 

Five

3/9 = .33

4/10 = 40 %

9 /15 = 60 %         from 10 to 15 is   5 more shots

In geometry, a space diagonal of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face as each other. Wikipedia

A diagonal through 'space' of a solid figure as opposed to a 2-dimensional diagonal ...

The answer is 20.