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We can  draw 7  diaginals from every  vertex......and  we  need  to  divide  this  by 2  (since  diangonal  AH  =  diagonal  HA , for instance  ) 

So....the  formula  for  the number of  diagonals  =     ( n - 3) n  / 2  =   7 * 10  / 2   =   35

You can do this by trial and error. Since \(\sqrt{110 } \ is\ approximately\ 10.4880884817 \) with fractiona part equal to

                                                        \(10.4880884817 -10 = 0.4880884817<0.5\),

and \(\sqrt{111}\) is approximately \(10.5356537529 \)with fractional part equal to

                                                        \(10.5356537529 -10=0.5356537529>0.5\),

n = 111 must be the number you are looking for.

n / 16   will   be  reducible  when    n     is  even

We  have   [  100  - 2 ]  / 2  + 1 =   50   even  numbers...so

Prob   =   50   /100   =   1/2

thank you!

AD and BE are altitudes of triangle ABC.  If AC = 10, BC = 18, and AD = 5, then find BE.

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Angle A = sin^-1(5/10)

Altitude BE = sin(A) * BC

sand·wich

/ˈsanˌ(d)wiCH/

noun

an item of food consisting of two pieces of bread with meat, cheese, or other filling between them, eaten as a light meal.

a bread sandwhich, because a "stack" is too vauge and "or other filling between them" includes bread.

Hi, Techno! You misunderstood the question.

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A rectangular box has integer side length in the ratio 1:3:4. Which of 48, 56, 64, 96, 144 could be the volume of the box?

1 : 3 : 4 = 2 : 6 : 8 = 3 : 9 : 12

1 * 3 * 4 = 24    

2 * 6 * 8 = 96   Only the volume of 96 u<sup>3</sup> is possible with the given integer side length ratio!!!

3 * 9 * 12 = 324

This translates into mathematical language as follws:

the product of two numbers is found by multiplying them;

the two numbers are     '3'    and   'a number increased by 6';

'a number increased by 6' translates as 'x+6' or 'n + 6';

so the product is 3 times (x+6), which you write as 3(x+6);

'is' translates as '=', 'equal to';

so the final mathematical sentence for the given English sentence is:

                                                    3 (x+6)= - 24.

                      A

                      5                10

B                   D                                  C

                    18

Area of  triangle    =  (1/2)  ( AD) ( BC)  =  (1/2) ( 5) ( 18)   =   45

Also  ....

Area  of  triangle   =  (1/2)  ( AC) (BE

45  =   (1/2)  (10)  (BE)

90  =  10   BE

BE  =  90   / 10    =   9

See here  :    https://web2.0calc.com/questions/help-with-math_20

We  have

81 *  (2/9)   *  x^(2/7)  *  x^(3/7)   =

18x^(5/7)

ab =   18  ( 5/7)   =    90  / 7

the sugar number is 4        you are using   8    so eerything is doubled   to   2:12: 8      which sums to 22 cups total

floor  [ x^2 ]   =     3

Note  that   on  the interval   (-2  , - sqrt 3 ]     this will be  true

Also  on the interval     [sqrt 3 , 4 )      it will  be true

Directly proprtional means     x = k r     where 'k' is the proprtionality constant.

                   when x = 5           5 = k(25)    shows 'k' to = 1/5

when r = 40

    x = 1/5 (40) = 8    

x^2  =  5

x =  -sqrt 5   or   sqrt   5

Since  -sqrt 5   ≤   -2

Then  x = -sqrt 5  is one  solution

And

2 x  +  1  = 5         or        2x  + 1  =   -5

2x  =  4                             2x  =   -6

x = 2                                    x =  -3

Since  x  = 2 is on the  interval     -2< x < 3

Then  x =  2  is another solution 

And

3x + 8 =  5

3x   = -3

x  = -1

Not a solution since    x  = -1   not  on  the  defined  interval for this  function

So

f(-sqrt 5)   =  5

and

f(2)  =    5

See the  graph here  :   https://www.desmos.com/calculator/fcqghft5mb

The stick is 5 units long. Let the 3 pieces be x, y and 5 - (x + y)

Now this means that 

                  \( 0 ≤ x ≤ 5\)

                   \( x ≤ y \)   and 

                   \(0 ≤ y ≤ 5\)

This graph represents the sample space 

Area of sample space \(={1\over 2}× 5×5 = 12.5\) sq. units

Now the probability that all 3 resulting pieces are shorter than 2 units

                   \( x < 2\)

                   \(y<2\)  and 

                   \(5-(x+y)<2\)

Area of triangle \(={1\over 2}×\sqrt2×\sqrt5\)  \(={\sqrt{10}\over 2}\) \(=1.6\) sq. units 

∴ P(all 3 pieces are shorter than 2 units) \(={1.6\over 12.5} = 0.128\)

BD = 8*sin(37º)

Angle X = sin<sup>-1</sup>(BD / 11)

THX, catmg   and  amy     !!!!!

your question has been answered, I have attached a like below.

https://web2.0calc.com/questions/i-m-confused-about-this

explanation please?

The  equation is

y = (-3/7)x  +   15

To find the   x intercept   set   y  =  0    and solve   for  x

0  = (-3/7)x  +  15

-15  =  (-3/7)x

x = -15  ( -7/3)   =    35  =  x intercept

We  can set up this system

B + G  =  26                 (1)

B + (1/2)G  =   16       ⇒  -2B  - G  =  -32       (2)

Add (1)  and (2)     and we have

-B  =  -6

B =  6

P (Heads  ≥ 8 flips)  =  P( Tails ≤ 2 flips )  =

C(10,0)(1/2)^10   + C(10,1) (1/2)^10  + C(10,2)(1/2)^10  =  7 / 128
 

Techno the p*g.

n = 2 and s = 1, so n*s = 2.