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What would I get if I get if I added powdered root of asphodel to an infusion of wormwood?

a sleeping potion "so powerful it is known as the Draught of Living Death"

Next time try  

Eye of newt and toe of frog,  

Wool of bat and tongue of dog  

_.

1)   you could also use Heron's formula

         semi perimeter =  s = (25 + 25 + 30)/2 = 40

             area = sqrt (s (s-JK)(s-JL)(s-KL) )

                area = sqrt ( 40(15)(15)(10)) = 300 units²

(2) In triangle ABC, we have AB = 5, AC = 12, BC = 13.  Find the circumradius.

This  is a right  triangle.......the  circumradius = (1/2)   (hypotenuse)  =  (1/2)(13)  =  6.5

(1) In triangle JKL, we have JK = JL = 25 and KL = 30. Find the area.

Let  J  be  the  apex

And the triangle  is isosceles

Let the  height  = JM

Then  we  have right triangle  JML   such  that

JM   =sqrt  ( JL^2  -  (KL/2)^2  )    =    sqrt ( 25^2  - 15^2)   =  sqrt (625 - 225)   = sqrt 400  = 20

So....the  area  =   (1/2)KL * JM =  (1/2)(30) (20)  =    300 units^2

magic.

Using  the  Law  of Sines

XY  /   sin Z  =  XZ /  sin Y

4 / sin 60   =  XZ / sin 45

4 / (sqrt (3/2))  = XZ / / ( sqrt (2) / 2)

4/sqrt 3  = XZ  / sqrt 2

4 sqrt 2 / sqrt 3     = XZ

4sqrt (6) / 3   =  XZ

not even that hard to factor:

\(4x^4+12x^3-9x^2-27x\\=x(4x^3+12x^2-9x-27)\\=x(4x^2(x+3)-9(x+3))\\=x(4x^2-9)(x+3)\\=\boxed{x(2x+3)(2x-3)(x+3)}\)

btw if you didn't do it by hand then how did you do it?

Be careful with that stuff.....

... According to Snape, if you did combine Powdered Root of Asphodel and an infusion of Wormwood, you'd brew a sleeping potion 'so powerful it is known as the Draught of Living Death.

" Kai had 75% of the total number of marbles the boy left in the end. "

What  does  this sentence mean  ????

So Kai and Jordan had 300 marbles together.

Since Kai gave away 25% less marbles than Jordan, I'm guessing that Jordan gave away 75% of the total marbles.

Half of 300 is 150

Jordan has 150 marbles left

A quarter of 150 is 37

Kai gave away 37 marbles

150-37=113

I confused myself throughout this problem but I think this is correct.

Yay!

The ratio is 3/8.

This is a divisibility rule for 11. Here's more information about divisibility rules:

https://en.wikipedia.org/wiki/Divisibility_rule#:~:text=If%20the%20number%20of%20digits,must%20be%20divisible%20by%2011.&text=If%20the%20number%20of%20digits%20is%20odd%2C%20subtract%20the%20first,must%20be%20divisible%20by%2011.

Welcome  back,  Varxaax   !!!!

23-6=17

11+13=24

24-17=7

7/23 = 0.30434782608

Yay!

(14x  + 22)  / ( x + 2)   =  -3x  - 1                   multiply  through  by  x + 2

(14x  + 22)  =  -(3x + 1) (  x + 2)

14x  +  22   =  - (3x^2  + 7x  + 2)

14x  + 22  =   -3x^2  - 7x   - 2          rearrange   as

3x^2 + 21x +  24   =   0

By  Vieta.....the  sum of  all  possible  solutions =   -21 / 3  =   -7

Hey, y'all, I'm back.

I found the same question here: https://web2.0calc.com/questions/2-problems_1

Yay!

Te other zero will be just as far from the vertex as the given one BUT on the OTHER side of the vertex

39,0

https://web2.0calc.com/questions/help_72524

Let's  look at  two simpler examples  and see if we can  find an   answer

Consider the  digits   2 , 4 , 6

We have :

246

264

426

462

624

642

Now....consider  the  digits  1,2,3 and  4

1234      2134     3124      4123

1243      2143     3142      4132       

1324      2314     3214      4213

1342      2341     3241      4231     

1423      2413     3412      4312    

1432      2431     3421      4321 

It appears  that  each  digit  will   appear   n! / n  times in each  column  where  n  is  the  number  of  digits  we  are considering

So   the   sum   of   any  column   of  the 5 digits  we  are  given  must  be

(  1   +  3   + 4  +  5  +  8)  ( 5! / 5)  =   (21) (24)   =  504

So......the  sum   must  be

504 ( 10^3  + 10^2  + 10  + 1)    =  559944  

The answer is B, C, D.

The sum of all the solution is 27.

sqrt  (3)    <   pi

So

h (sqrt 3)    =  floor  ( 4  * sqrt 3)    =    6

10001   isn't  divisible  by  11

If  we    assign  alternating  signs  to successive  digits  and  the  sum of the digits  =  0    (or 11), our  number  is divisible  by 11

For  example   

121   =   +1  - 2  + 1 =    0   =  divisible by 11

506  =  +5   - 0 +  6   =  11  = divisible by 11

The  smallest  I   can find is

10901  =   +1   - 0  +   9   - 0  +  1 =    11  =  divisible  by  11

x = -3    and   x  = 5        are roots.....and  ( 1, -6)   is  on the  graph.....so.......we  have  this

-6  =  a(1+3)  (1 - 5)      simplify

-6  = a   (4)  ( - 4)

-6  = (-16)a

a  = -6/-16 = 3/8

So......the  function  is

f(x)  =   (3/8)  ( x + 3) ( x - 5)

f(x)  = (3/8) ( x^2  -2x   - 15)

f(x)  = (3/8)x^2 - (3/4)x  - 45/8

See  the  graph here  :   https://www.desmos.com/calculator/aqoish07nx