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The answer was sqrt10/2 which is basically the same, but I guess the teacher wanted it to be more simplified

Thank you so much for taking time to respond tho :D

10 c 3 = 120 subsets with 3 elements

   each element has a   3 out of 10 chance of being in teh subset    3/10 * 120 = 36   substes with the number '5'

That is impressive logic catmg.         

I think you have it!

n ==1  and

n == 4

Both of them satisfy the equation.

I  get  the  same result    .....

Let  the  point we  are looking for  be    ( x ,        (x^2 - 3) /  sqrt 2   )

We can  use  the  square of  the distance  formula

D^2  =   x^2   +  (x^2 - 3)^2  / 2         simplify

D^2  = x^2  +  (1/2)(x^4 - 6x^2 + 9)

D^2  =  x^2  + (1/2) x^4  -  3x^2  +  9/2         

D^2  =   (1/2)x^4  - 2x^2  + 9/2   take  the  derivative of  the  function  and set to  0

2x^3   -  4x   =  0

x^3  -  2x  =  0        factor

x( x^2  - 2)   =   0

Setting  the  second factor to  0   and solving for  x  we  get  x =  sqrt 2   or  x  =  -sqrt 2

Either  value  minimizes the  distance....so.....one  point  is  (sqrt 2 , -1/ sqrt 2)

And  the  distance =   sqrt ( 2  + (1/2)   =   sqrt  ( 2.5)   =  sqrt (5/2)    ≈   1.58

Here's  a graph :  https://www.desmos.com/calculator/3zo8v8cxyz

After answering 1, it said it was incorrect and that the actual answer is -2.  Thanks for answering though!

x - 41 / x - 51 = 3 / 1

3(x - 51) = x - 41

x = 56

Peter and Blake had $56 each.

By Vieta

p + q  =   -5/1 =   - 5

pq  =  3/1   =   3

Note  that

1/p  +  1/q  =     (p + q)  / (pq)  =       -5 / 3

Since  5   is already member  of the set.....we  just  want to choose  any 2  of  the remaining 9 elements for the other two members  of  the set.....

So

C( 9,2)   =   36    subsets

There are 27 subsets.

By Demoivre's Theorem, z^2010 + 1/z^2010 = 1.

The solutions are (4,6), (6,4).

https://web2.0calc.com/questions/asap-please-math

Points A(0,0), B(9,6) and C(6,12) are vertices of triangle ABC. Point D is on segment AB such that 3(AD) = DB, point E is on segment BC such that 3(BE) = EC, and point F is on segment CA such that 4(CF) = FA. What is the ratio of the area of triangle DEF to the area of triangle ABC? Express your answer as a common fraction.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using the shoelace method we find that [ABC] = 36, and [DEF] = 16.65.

[DEF] / [ABC] = 37 / 80

Here is a long discussion of this question from a while back :

https://web2.0calc.com/questions/how-many-ways-are-there-to-put-6-balls-in-3-boxes-if-the-balls-are-distinguishable-and-the-boxes-are-distinguishable

e = 7 o      This is given

Then

e-12 = o + 12      sub in the red equation

7 o - 12 = o + 12

6 o = 24

o = 4             then   pee = 7 * poo =  28        total = 32 coins

Answer:

15 6/7

Explanation:

The roots of 7x^2 + x - 5 = 0 are a and b.

Compute (a - 4)(b - 4).

Use of this information:

For the quadratic equation ax^2+bx+c=0, the sum of its roots = –b/a and the product of its roots = c/a.

In given case:

sum of roots=a+b= - 1/7

product of roots=ab= -5/7

Now let's find the value of (a-4)(b-4)

(a-4)(b-4)=

ab-4(a+b)+16=

-5/7-4(-1/7)+16=

-1/7+16=

15 6/7

The answer is 15 6/7

👍🏻👍🏻👍🏻

ur Welcome :D

deleted

1/36 ?

according to what I found with google, it will create a powerful sleeping potion.   I gave a more complete answer the first time, and it was removed, presumably by a moderator.  I don't know why, they never give you a reason.  

_.

The  length  of  the  hypotenuse  =

  [ 3/sin 30  ] * sin 60    +  [3/sin 60 ] * sin 30   =

3sqrt (3)   +  sqrt  (3)   =  

4sqrt (3)