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b+4 = a       then

b-a =

b   -   (b+4) = -4        so     (b-a)^2 = (-4)^2 = 16

Hey there, Guest!

There are five choices for each ball: \(5^4\) = 625

Among these 625 distributions, there are 5 cases where the four balls reside in the same box because there are five boxes. So from 625, subtract 5 to count the required.

625 – 5 = 620.

Hope this helped! :)

( ﾟдﾟ)つ Bye

also Is the symbol in promblem 8 multiplication? 

1.7345 degrees

Casework then use snake method or odedution 

45-45-90=x-x-xsqrt(2)
xsqrt(2)=14

x=14/sqrt(2)

x=14sqrt(2)/2

x=7sqrt(2)

area = x*x/2 = 7*7*2 / 2 = 7*7=49

Here is one way....I do not know if it is the BEST way:

2x^2 -18x+17 = 0    quadratic formula says roots are   9/2 +- sqrt (47)/2         can you take it from here ?

2x + 5y = -8

6x + 15y = a     Multiply top equation by 3 to get:

6x + 15y = -24                if a and -24 are equal the two equations are the same and there are infinite solutions 

a = -24

isosceles means each LEG is the same length

Use pythag theorem to find leg length

L^2 + L^2 = 14^2

2L^2 = 196

L^2 = 98

L = sqrt 98                 Now area = 1/2 * L * L = 49 units²

https://web2.0calc.com/questions/domain_100#r2

The probability of getting only one of the dice right is 5^4/6^5, and the probability of getting zero right is 5^5/6^5, so the answer is 671/1296.

f(x) = e^(2x) + 2e^(4x), g(x) = -2e^(2x) - 2e^(4x).

When x = 1/8, the expression is equa to -173/18.

f(2)   means   that  we  want  to  know  the   y coordinate  of  ( 2  , y)

Find  the  value of  y  when  x =  2......this  is   0

So  f ( 2)   =   0

Number is xy

x+y = 7     or y = 7-x

10x + y   +27 = 10y + x

10 x  + ( 7-x) + 27 = 10(7-x) + x

9x + 34= 70 -9x

18x = 36

x = 2    then y = 5    

25

By  Vieta

u  +  v  =     -5/3             square both sides

u^2  + 2uv  + v^2   =  25/9     (1)

and

uv =    11/3        (2)

And

u/v  +  v/u   =     ( u^2  + v^2 )  /   uv         (3)

Using (1)  and (2)

u^2  + 2uv  + v^2  =  25/9

u^2  + 2 (11/3) + v^2  = 25/9

u^2  + v^2    =    25/9   -   2 (11/3)

u^2  + v^2  =   25/9  - 22/3

u^2 + v^2  =  25/9  - 66/9  =   -41/9

So    (3)  becomes

(-41 / 9)   / (11/3)   =     (  -41 /9 )  * ( 3  /11 )   =  (-41/11) ( 3/9)   = ( -41/11) (1/3)  = -41/33    =  u/v + v/u  

s = 15 y/o    b = 1/5 (15) = 3 y/o     You can finish......

(x - 4)^2  + 8   =

x^2  -8x  + 16 + 8

x^2  - 8x  + 24   =  ax^2  + bx + c

3ax^2 + 3bx  + 3c  =

3 ( ax^2  + bx + c)  =

3  (    x^2  - 8x  + 24 )  =

3 [ (x - 4)^2  + 8 ]  =

3 (x -4)^2   +  24

h does not change......it  still  =   4

1. 

(a)  The  ride  completes  a loop  every  40 sec    and  3  complete loops in two  minutes

So......   15   mintues   =   900 sec

So the  number of  complete loops  in this time frame  =  floor  [ 900/40]   = 22 complete loops

(b)  When  the ride ends  we look at the position  at 15 min.....note that the height at this point  = 180 ft

At  6 min after the ride started note  that the height of the last passenger to board   = 15 ft

6min  =   360 sec

This  makes sense.....he'she will have  completed  =   floor  [ 360 / 40  ]   =  9  complete loops  at this point

He/she  will exit at its lowest point at the  6 minute mark....so.....no waiting  !!!

For each ball, you have 5 different options. 

First ball has 5 options, second ball has 5 options, third ball has 5 options, and fourth ball also has 5 options, 5*5*5*5 = 625.

=^._.^=

Let  k  be  the  number of balls    and  n  be  the  number of boxes

Assumig no restrictions  ( boxes may be  empty)  the  number of  ways   =

C   ( k + n - 1 , n - 1)   =

C  ( 8 , 3 )   =     56  ways

I think any multiple of 7 less than 7 would do the job because there seems to be no negative limit.

Ur  welcome   !!!!!

There is a good explanation here:

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

Thank you!