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tan 60  =  opp/ 1     opp = left side = 1.732

Dashed line        = adj / hyp   = cos 60

                                1/ cos 60 = 2 = dashed line              

Then the L upper angle in the larger triangle is 60 degrees      cos 60 = 2/x      then  x = 4

3. https://web2.0calc.com/questions/find-all-values-of-x-such-that-frac-2x-x-2-frac-6 Hope this Helps!

2 * 105   +   2 * 120   +  2 * alpha = 720

alpha = 135 degrees

larger circle - smaller circle   =   8 * smaller circle      area

pi L²   -    pi S^{2              =}    8 pi  S²  

L^2 - S^2  = 8 S^2

L^2 = 9 S^2  

S/L = 1/3

Normal Force, Weight, Thrust, and Drag

We can convert the 10, 10, and 12 cm's to 2 miles, so that it is

$20, 20, 24$, we can find the area with $(a+b)/2*h$

$(20+24)/2*20=440$

that is 440 square miles, then we multiply by 640

our answer is $440*640$

too lazy to use calculator lol

Area =   (12+10) /2  X  10 = 110 cm^2

each cm^2 = 4 mi^2            110cm^2 * 4 mi²/cm2     * 640 acres/mi²  =281600 acres     (edited)

We can  find    DZ  thusly

150  = (1/2)  AB  * ( WC  +  DZ)

150  = (1/2) 12  *  ( 6  + DZ)

150  =  6  * ( 6 + DZ)

150/ 6  =  6 + DZ

25  - 6  =  DZ  =   19  =  BW

And triangles  DQZ  and BQW  are  congruent,,,,so  their  heights are  congruent =  12/ 2  =  6

So....the  area  of triangle BQW  = (1/2) BW  *  6    =   (1/2) (19) (6)  =   57

x = 8% grams   

500 -x = 6% grams

.08 ( x)     +    .06 ( 500-x)  =  .0752 (500)

.08x         +   30 - .06x   = 37.6

x = 380  gm    of 8%       120 gm of 6%

223 x 2 + 2 x 277 = 1,000

Let  the number   that   David  had at first =  D

Then Caleb  had  D + 37

Caleb  gave away  4G

David  gave  away  G

And  we  have  this sysyem

D - G  =  G  + 5      ⇒     D = 2G +5       (1)

(D + 37)  - 4G  =  2 (D - G)                   (2)

Sub ( 1)  into  (2)  for D

(2G+ 5 + 37)  - 4G  =  2 ( 2G + 5 - G)

-2G  +  42   =  2( G + 5)

-2G  + 42 =  2G + 10

42  - 10 =  2G + 2G

32  =  4G

32/4  =  G = 8

D=  2(8)  +  5   =  21

C  =  21  + 37  =  58

Proof

Caleb started  with  58  and gave away 4(8) =  32    he ended  up  with  26

David  started  with 21   gave away 8  and  ended up  with  13

And Caleb  had  twice  as many left as David

2 (223) + 2(277) = 1000 pages read

On the left side the numbers are multiplied   so  7 , 7  = 49

on the right side they are added together    so  12, 12 = 24

1 box - 3/8 - 1/4  =  9/24         of which   5/6   are yellow

                                           9/24  *  5/6  *  t = 20        t = total bands

                                              t = 64 rubber bands in the box

Sum of interior angles     (n-2)(180)

    then each interior angle      (n-2)(180) / n

       each exterior angle   is   180 - (n-2)(180)/n

Now to the question     (n-2)(180)/n     ={ 180 - (n-2)(180)/n  } *10

                                      (180n- 360)     ={ 180n - (n-2)(180) } * 10

                                       180n - 360      =  {180n - 180n + 360 } * 10

                                         180n -360   =  3600

                                          180 n = 3960

                                                n = 22                              interior angle = 163.636     exterior = 16.363

ANOTHER way:

10 n   + n = 180

n = 16.363   = exterior angle

10n = interior = 163.636

(n-2)(180)/n = 163.636

180n - 360 = 163.636 n

n = 22      

"

Let the side length of the octagon = S.....this = the hypotenuse of an isosceles triangle

So...the length of one of the legs of the isosceles triangles =   S/√2

And the side of the square = 

S + 2S/√2 =  S + S√2

So

S + S√2  = 10

S(1 + √2)  = 10    divide bot sides by ( 1 + √2)

S =     10   / ( 1 + √2 )   ≈    4.14  (inches)" 

WORDS FROM CPhill

Hope it helps~TinderWolf

Nevermind! I got it right

Blue -> 3/8 of the total 3/8

Red -> 1/4 of the total  1/4 = 2/8

Yellow -> 5/6 of the remainder 

Blue = 3/8

Red = 1/4 

the remainder 

1 - 3/8 - 1/4

1 - 3/8 - 2/8

Yellow = 5/6 * 3/8 = 5/16

5/16 -> 20

1/16 -> 20 / 5 = 4

16/16 = 4 * 16 = 64

Call  the number of $5  bills x

And the number of $2  bills  = (1/3)x

So

No of  $2 bills  x  value each  +  No  of $5  bills x  their value  each =  136

(1/3)x * 2   +  x * 5  =   136      simplify

(2/3)x   +  5x  =   136

(2/3)x  + (15/3)x  =  136

(17/3)x  = 136

x = 136 ( 3/17)  =  24  =  number of $5 bills

P = 6S       where  S  is  the  side  length

A =  6(1/2)(S^2)  (sqrt (3)  / 2 =     (3sqrt (3) /  2) S^2

But

If     6S  =  (3sqrt (3) / 2 ) S^2       what   is  x  supposed  to  be   ???

If the leading coefficient of the x² term is positive the parabola will be bowl shaped ...open upwards

   pick any positive number for  'a'     and the equation in your Q will open upwards

This is impossible...to see why

(2/5)J  = (3/4)K

J  = (5/2)(3/4)K

J =  (15/8)K

So...originally....Josh  has  more  money  than Ken   -  (15/8) ths  as  much

So...if Ken  gives  Josh   $28......they  can't possibly  have  the  same amount......

I didn't say anything about how many questions you can answer.

I said " please limit your social posts to maybe one a day. "

I am not trying to dampen your enthusiasm altogether.  

YHXB  is  a  quadrilateral

Angles HYB  and HXB  = 90

Angle YBX =  67

So angle  YHX  = 360  -67  - 90  - 90 =     180  - 67  =  113°

And angle AHC  is a vertical angle  to YHX  so it  has  the  same measure   = 113°

Number of diagonals of a polygon     n ( n-3)/2

n(n-3)/2 = 10n

n^2 -3n = 20n

n^2 -23n= 0

n ( n- 23)  = 0        n = 0  (throw out)     or     n = 23