All Answers 358142 Answers

I.  direct

II. inverse

III. joint

Let M  =   [ ( a + c) / 2  , (b + d) / 2  ]    = (m, n)

A'  =  (a +14  , b + 20)       B'  =  (c - 2, d - 4)

So  M'  =    [ ( [a + c]  + 12) / 2   ,  ( [b + d]  + 16)/ 2 ]  =   ( m + 6, n + 8)

So..... the distance between M  and M'   is

√ [ (m + 6 - m)^2  + ( n + 8 - n)^2 ]  =  √ [  6^2 + 8^2]  = √ [36 + 64]  = √100  =

10 units

Thanks but, you mean 63?  Haha!

'x' distance       2/3 x ( 15-(-6) ) = 14        14 + -6 = 8 = x

'y' distance       2/3 x (-5-19)  =  -16        19 - 16 = 3 = y

F=   P (1=i)^n     Where F = future value  P = initial value (50000)   i= periodic interest   n = number of periods

Jose :   F = 50, 000 (1+ .04)^2  = 54,080

Patricia  i = periodic interest where the period is 3 mos (4 times a year)  .04/4 = .01   and periods = 2 yrs x 4/yr = 8

             F= 50,000 (1 +.01)^8 = 54142.84

Difference =62.84   to the nearest dollar , Patricia earned $64 more than Jose.

Slope = rise/run  =   y1-y2  /  x1-x2

-3/2 = (y-7)  / (4-(-2))

-3/2 = (y-7) / 6

6 (-3/2) = y-7

-9 = y-7

y= -2

The  distance between these points is  =

√ [ (7 - 3)^2  + (10 - 5) ^2 )  = 

√[ 4^2  + 5^2]  =

√ [16  + 25 ]  =

√ 41    and this is the diameter......so the radius  =  √41/2

So....the area is 

pi * (radius)^2  =

pi *( √41 / 2)^2   =

(41/4)pi  units^2

Amount  accumulated after 6 months  =

1000 ( 1 + .04/2) =  $1020

Amt  at the end  =

1020 ( 1 + .05/2)  =  $1045.50

It is 59 now!

:D:D

Thanx, Melody !    

I wanted to see how Chris got the EXACT answer with a radical ....I got an equivalent numerical answer using the Law of Cosines (twice)   See handwritten diagram:

Not sure what "interest rate" is being accounted for, here.....maybe we should leave that for the "bean counters"......however....as to the "bean growers" like Alice, we can proceed as follows :

2 weeks = 14 days....so

452  = H ( 1.05)^14    wher H is the original height

Divide both sides by   (1.05)^14

452 / (1.05)^14   = H  ≈  228.3  cm  

Call the points  A, B, C, D , E, F

Let A= (0,0)   B = (3,0) C  = (8,0)  D  = (14,0) E = (21,0)  F  = (23,0)

Choosing any 2, we have C(6, 2)   =  15  possibilities

EF  =  2     CD  = 6    DF  = 9       CF  = 15    AE = 21  

AB  = 3      DE =  7    CE  = 13     BE = 18     AF = 23

BC  = 5      AC  = 8    AD = 14      BF =  20

BD  is the "Missing Link"  =  "n"  =  11  

However....some members might consider "Ginger Ale" to be the "Missing Link".....I'll have to let them decide that for themselves ........

Thanks so much!

I got 2x³-12x²+3x-21.5 when usuing long division to solve the equation:

(2x⁴-9x³+21x²-26x+12)/(2x-3)

Fisrt you need the value of x in (2x-3) to change from 2 to one, and you obviously get that from dividing by 2 which will give you (x-3/2). Then you use long division to do the rest.

yes that is very funny!

ha ha thats funny

thanks so much!

A  = k/ B

4  = k / 9  

k  =  36

A  =  36 /  -72   =    -  1/2

(1)  I believe the answer to this is 11

The circles can intersect  at 2 points

Each line can intersect each circle twice  = 8 points

And as long as the lines do not intersect at any of the other points, they can intersect at 1 additional point    

(2) Primes between 40 and 60  are

41  , 43 ,  47,  53 , 59

And  adding 12 to these  =

53 , 55 , 59, 65 , 71

And  3 out of the 5 are prime  [ 53, 59, 71 ]  

So....the probability that p + 12 is prime is   3 / 5

It's correct! Thanks!

ABC is a Pythagorean right triangle

AB  =  15

BC  = 8

And the hypotenuse, AC  = 17

So.....the perimeter  is     15 + 8 + 17   =  40  units

Thanks so much, CPhill! It's correct!

Area  =  100 *  (150 - k)      where k is the amount of the length broken off  in cm