All Answers 356085 Answers

A little hard to visualize this   (I did it with a piece of paper   - hope I didn't mess it up  !!!)

When we make the fold  EF = EA  = 9  and  EB = 6

And triangle EBF is right  so    BF  = sqrt  [ 9^2 - 6^2 ]  = sqrt  45  =  3sqrt 5

And FD =  BC

And triangle FDC is right  with   DC = 9    FC  = BC - BF =   BC - 3sqrt5  = BC - sqrt 45

So

FC =  sqrt  [ FD^2 -  DC^2 ]

(BC - sqrt 45)  =  sqrt  [ BC^2  - 81) 

(BC - sqrt 45)^2   = BC^2 - 81

BC^2 - 2*BC*sqrt45 + 45  = BC^2 - 81

-2sqrt (45) BC =  -81 -  45

-2 sqrt (45) BC =  -126

BC  =    126 / ( 2 sqrt 45)  =   126 / (2 * 3 * sqrt 5)  =   21 / sqrt 5  =  (21/5)sqrt 5

Look at the graph here :   https://www.desmos.com/calculator/em32xqiof4

We can split the area into two triangles....one with a base and  height of 4

Area =  (1/2)4*4  =  8

And the second one  with a base of 16 and a  height of 8

Area  = (1/2)(16)(8)  = 64

The area  we are interested in  =    64  - 8   =  56

I've been on here for 8+ years and Melody even longer....so, we have had plenty of time  to "gather" hearts.....I've actually taken several longish breaks......"gathering" hearts isn't our focus......helping people  is....

Since RP  = RQ.....then angles PQR  and RPQ  are equal

And by vertical angles , angle MPN  = angle RPQ =   58

And since MP = NP, then  triangle MPN is isosceles  and we  can figure angle PMN as

(180  - 58 )  / 2  = 

122 / 2   =

61°

We have the points

(1,8)

(2,6)

(3, 7)

(4,5)

(5,3)

(6,4)

(7,2)

(8,1)

(9,3)

There is a formula for this  but it's a little involved  !!!

Let's use some  technology to find  the best ft line : http://www.learningaboutelectronics.com/Articles/Regression-line-calculator.php#answer

The line is    y = -.77x + 8.2

Use Heron's Formula to find the area

s = the semi-perimeter  =   ( 8 + 12 + 14)  / 2  =    17

Area =  sqrt  [ 17 (17- 8) (17 - 12) ( 17 - 14) ]    =   3sqrt (255)

The longest altitudes will be drawn to the two shortest sides

So

3sqrt (255)   =(1/2)(8) * altitude 1              3sqrt (255)  =(1/2)(12) * altitude 2

(3/4)sqrt (255) = altitude 1                         (1/2)sqrt (255)  = altitude 2

Sum of altitudes   =    [3/4 + 1/2]sqrt (255)  =  1.5 sqrt (255)

Let the total number of  brochures given out by each volunteer =   x

So....the total brochures given out  = 38x 

6  volunteers  gave out only  1/3 of theirs......so the total number they gave out = 6 (1/3)x = 2x

So.....  38 - 6    = 32   gave out  x +  21

So

2x  + 32 ( x +  21 )  =   38x        simpify

2x + 32x +  672  =  38 x           rearrange as

34x  + 672  = 38x

672  =  38x -  34x

672  = 4x

672  / 4   = x  =  168

So.....the total  number given out =   38 (168)  = 6384

Modulus just means the length of the complex number from zero.

The values of  | m + n | = 3√10 would sit on a circle with radius 3√10

The best way to reach that radius whilst minimizing the length is to draw a straight line. That is if you represent m and n as vectors, they would have the same direction. 

This could be proven to be the minimum length by using theorems like the law of cosines or triangle inequality.

To illustrate my point, move around n and try to find the minimum length of the black line:

PV ==FV / [1 + R]^N, where PV==Present value, FV==Future value, R==Interest rate, N==Number of periods.

PV ==14,000 / [1  +  0.075/12]^(3*12)

      ==14,000 / [1  + 0.00625]^36]

      ==14,000 / [1.00625]^36

      ==14,000 / 1.2514461355

      ==$11,187.06 - what must be deposited now to grow to $14,000 in 3 years at 7.5% comp. monthly.

A certain integer has 4 digits when written in base 8.     Let the mumber be y

8^3=512      8^4=4096

In base 10                                  512 <= y < 4096

The same integer has d digits when written in base 3. What is the sum of all possible values of d?

3^5 = 243       4 digits

3^6 = 729        5 digits

3^7 = 2187      6 digits

3^8 = 6561      too big

so it could have 4, 5 or 6 digits in base 3 

What is the value of x and the length of DE?

Hello Guest!

I understand it like this:

\(f(x)=DE=11x+15\\ g(x)=FG=81\\ 11x+15=81\\ \color{blue}x=6 \)

\(DE=81\)

  !

(28.80 -  10.20)  / 6   =   $3.10

I believe this is a similar problem  :  https://web2.0calc.com/questions/help-plz_60366

See if you can follow it....if not...I'll try to help  !!!