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Take all 5 = 1 set

Include  5  and  select any 3 of the other  4 elements =  C(4,3)   = 4 sets

Include  5  and   select  any  2 of the other 4 elements  = C(4,2)   = 6 sets

Include  5  and  select any 1  of  the other  4 elements  =  C(4,1)  =  4 sets

Include  5 only =  1 set

So

1  +  4  +  6   +  4   +   1    =   16 sets

x(x+6) - 16 >0

x^2 +6x -16 > 0

(x+8)(x-2) > 0

roots are -8 and +2  

    this is a bowl shaped parabola .....between -8 an +2  it is below zero (or = to zero) ....above zero elsewhere

(-∞, -8) U ( 2 , +∞)

1. The roots are -8 and 2, so the solution is (-8,2).

2. First, we can divide both sides by x to get x^2 + 4 > 5x, so x^2 - 5x + 4 > 0.  The roots are 1 and 4, so the solution is (1,4).

As follows:

Like so:

I'll let you turn the Amps into milliamps.

(2y + 1)(4y¹⁰ + 2y⁹ + 4y⁸ + 2y⁷ + 2y⁶ + 4y⁵)

= 8y¹¹ + 4y¹⁰ + 4y¹⁰ + 8y⁹ + 2y⁹ + 4y⁸ + 4y⁸ + 4y⁷ + 2y⁷ + 8y⁶ + 2y⁶ + 4y⁵

= 8y¹¹ + 8y¹⁰ + 10y⁹ + 8y⁸ + 6y⁷ + 10y⁶ + 4y⁵

This problem is fairly simple, you just need to assign values to \(x\) and \(y\), then solve the equation.
 

Using the equation \(4x=3y\), we can assign \(x=3\) and \(y = 4.\)

\(\frac{2x+y}{3x+4y} \)

\(\frac{2(3)+4}{3(3)+4(4)}\)

\(\frac{6+4}{9+16}\)

\(\frac{10}{25}\)

\(\boxed{\frac{2}{5}}\)

Diana ate pizza for dinner and had 19 of the pizza left over. On Friday night, she ate 57 of what was left. How much pizza did Diana eat on Friday    

I'm going to go the other way, and assume you meant percents, i.e., 19% and 57%.  

Friday night, Diana ate 57% of the 19% that was left over.  0.57 • 0.19 = 0.1083  

The amount of pizza she ate Friday was 10.83% of the whole pizza she started with. 

_.

I'm assuming you made a typo and the numbers are supposed to be fractions.

The first sentence says she has 1/19 of the pizza left. Then she ate 1/57 of that. 

This means she ate 1/19 * 1/57 of the entire pizza, giving you the answer of 1/1083 of the pizza :)

It's false... if a line has a slope of 0, this means it's a horizontal line. It will intersect with another line..

Mine agreed with your book too.   

I am a bit confused.  Do you have a question?

I thought you already showed that it was a maximum.

"If a snowball melts so that its surface area decreases at a rate of 4 cm ^ 2 / min. find the rate at which the diameter decreases when the diameter is 39 ."

Do you mean 39cm?  A big snowball!!

Can you take it from here?

Hi Melody...so I had another look at the question (thanks to your feedback) and tried to keep it simple. 

So could the question be saying that the derivative of main function  is a maximum and is equal to square root of same function (ie  +/- values apply)...and therefore this is given and no need to prove it??!!

In that case I get the following for x (Word is terrible for writing power/equations so I hope there are no typos) - which agrees with book. Regards & thanks again

Using the web2.0 calculator on the home page here, enter:  asin(-0.3148)+180, making sure the calculator is in degree mode (adding 180 ensures the result will be in the third quadrant).  Then round the result to the nearest tenth of a degree.  (Use the 2nd button to make asin appear)

Find the value of d such that the system of equations
-10x + 15y = -17
dx +12y = 8
have a solution.

Hello Guest!

If  

x = 1.7,  y = 0,  d = 4.7058823529411765

is the system correctly.

  !

It is not different from my answer, they are exactly the same.  I'll show you.

\(x=\left(\frac{n+1}{2}\right)^{\frac{n}{1-n}} \\~\\ x=\left(\frac{n+1}{2}\right)^{\frac{-n}{n-1}} \\~\\ x=\left(\frac{2}{n+1}\right)^{\frac{n}{n-1}} \\~\\\)

And you are always welcome :)

Hi Melody....thanks for your prompt  reply.

This is the answer (no 10)  offered in the book which also differs from your solution......heck (2nd time I met this circumstance)!

re 'do more to show it is a Max value' : I extracted 2 nd derivative which is a negative...thus pointing to a maximum value.

Thanks for your feedback & knowledge!

Solve for x:
(x + 1)/x = -7/(x - 12)

Hello Guest!

\( \dfrac{x+1}{x}=-\dfrac{7}{x-12}\)

if  \(x\notin\{0,12\}\) then

\(-7x=x^2-12x+x-12\\ x^2-4x-12=0\)

\(x\in\{-2,6\}\)

  !

sinC = 13/85

If 2x = 5y and 7y = 10z, then z/x = 5/2*7/10 = 35/20 = 7/4.

did you find the answer

See here  :  https://www.desmos.com/calculator/w1uepv2ebv

The  range  is  [ .75, infinity  )

The  common difference is   -3/4

We  can  solve  this  for  n

20  -  (3/4)(n - 1)  <  0

20  - (3/4) n + 3/4   <   0        multiply  through by  4

80  - 3n + 3   <   0

83  - 3n <  0

83  < 3n      divide  both sides  by 3

83/3 < n

n > 83/3

n > ( 27  + 2/3 )

The 28th term  will  be  the first negative one

x - y =  12    →   y   =  x -  12      

So

y^2  =  5 ( x - 2)

(x  -12)^2   =  5x  -  10

x^2  -24x  + 144   =  5x  -10

x^2  - 24x - 5x  + 144 + 10   =  0

x^2  - 29x  +  154  =   0        factor

(x - 22) ( x - 7)   =  0

Set  both  factors  to  0   and solve  for  x

x = 22      or     x  =   7