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If you want an answer/explanation, you need to tell us what the perimeter is.

You might have copied in LaTeX formatted numbers, so please either edit the question or provide the perimeter.

Thanks!

All the sides of a triangle are integers, and the perimeter is    . How many different possible triangles are there? (Assume that the triangle is non-degenerate. Two triangles are considered the same if they are congruent.)

the perimeter is?

Here's  what I get

2,2,2

2,4,4

4,4,4

4,4,6

4,6,6

6,6,6

Can someone check this  ???

a = log 80

b = log 45 

log  80   =   log  (8 * 10 )   =  log 8  + log 10       =   log ( 8 )    +  1   =  a

log 45  = log  ( 4.5 * 10 )  =  log 4.5  +  log 10  =    log ( 4.5) +  1      =  b

So

a - 1 =   log  8

b - 1  =  log  4.5

(a - 1)  +  (b - 1)  =   log 8  +  log 4.5

(a + b)  -  2 =   log (8 * 4.5)

(a + b) - 2  =  log 36

See here, also  :

https://web2.0calc.com/questions/i-have-different-geography-textbooks-and-different

sin A  = 24/25

cos A  =    - sqrt  ( 1 - sin^2 A)  =   -sqrt  ( 1 - 576/625)  =  - sqrt ( 625  - 576) / 25  = - sqrt ( 49) / 25  =

- 7/25

sin (A/ 2)   =  sqrt   [ ( 1 - cos A) / 2 ]  =   √ ( 1  + 7/25)/ 2  ]   =  √ [ 32 / 50 ] = √ [ 16/25 ] =   4 / 5

f(x)=1000-0.01x^2

I think  g(x)   is supposed to be   g(x)  = 150 -  0.001x^2

So

C(x)   =  f(x)  +  g(x)   

C(x)  =     ( 1000 - 0.01x^2  )  +  ( 150  - 0.001 x^2  )

C(x)   =  (1000 + 150)  -   (0.01 + 0.001)x^2

C(x)  =  1150   - 0.011 x^2

Inverse   of   [  - 1   4          =      1                  [3     -4          =       

                         2    3  ]            ______  *        -2     -1 ]    

                                                  -3 - 8     

      1        [  3      -4                 This goes in the first blank  and in the third blank

-____        -2     -1  ]       

     11     

  [ 8         Goes in the second blank

   -5 ] 

  1           [   3    -4     *  [  8         =       1         [44            This goes in the fourth blank

- ___          -2    -1 ]        -5 ]            - ___        -11]

   11                                                    11

[ -4             This goes in the last blank

   1 ] 

FV = future value = 85000    (given)

PV = present value = 40000  (given)

i = interest (in decimal) = .055  (given)

t = years   what you are looking for to answer this Q

FV = PV (1+i)^t

FV/PV = (1.055)^t

85000/40000 = (1.055)^t      Solve for the exponent 't' ....you should already know how to do this......

                      A

                    1

                D       sqrt (3) 

           sqrt (3)       F

                                  1

       B      1   E    sqrt (3)   C

DE =  EF  =  DF.....so  triangle   DEF  is also  equilateral

And  we can find   DE    using the Law of Cosines

DE^2     =   (sqrt (3))^2  +  1^2  -  2 (sqrt(3) * 1 *  cos (60°)

DE^2   =  3  +  1  -   2 sqrt (3)( 1/2)  

DE^2   =   4  -  sqrt(3)

So....the area of triangle  DEF    =   (1/2) (DE)^2 *  sin (60°)  =    (1/2) ( 4 - sqrt (3) )  ( √3/2)  =

( √3 / 4)  (4 - √3)   =

[  √[3  - 3/4 ]  units^2

a=1;b=0;p=0; cycle:d=a*10+b;if((sqrt(3x + 1) + sqrt(2 - x)) + (sqrt(3x + 1) + sqrt(2 - x))^2 + (sqrt(3x + 1) + sqrt(2 - x))^3 = 14, goto loop, goto next); loop:printd,", ",;p=p+1; next:b++;if(b<10, goto cycle, 0);b=0;a++;if(a<10, goto cycle, 0);print"Total = ",p

OUTPUT: x = - 1 / 4    [That is all I could find !!].

You do not state an initial velocity, so let's assume it is 0.

vf = vo + at        vo = original velocity = 0

vf = at       a is in seconds   75m/s^2      t is in weeks and one or the other has to match 

     convert weeks to seconds    3600 sec/hr x 24 hr/day x 21 day = t

        multiply this by a to find the final velocity (divide by 1000 m/km to get km/sec)

Then for the distance , starting at xo = 0

xf = xo + vot + 1/2 a t^2        vo and xo = 0       make sure a and t are in the same time units..... Done !

(5 P 2)  / 5!  = 20 / 120 = 1/6 

thanks again!!

log(1/2) + log(2/3) + log(3/4) + .... + log(99/100)

Note that we can write

log   (1/2   *  2/3    *  3/4   *   4/5   *  .......  *   98 / 99  *   99 / 100)    =

log  (  1  *  2/2   *  3/3   *  4/4 *  5/5 *  ........*   98/98  *   99/99  *   1 /100)  =

log  (  1   *   1   *   1      *   1    *  1 *  ........ *    1     *       1     *      1/ 100)  =

log  (1/100)  =    

log 10^(-2)  =

-2 log 10   =

-2

Yep....simplified  completely....

We have this

P  =  40 *  2^(t/15)      where  P   is the population after   t  hours

We want to find out the population after 40  hours  ....... so....

P  = 40 * 2^ (40/15)  

P = 40 * 2^(8/3)    ≈   254

Is this simplified completely?

Note that  :

1^3  -  (³√3)^3 =   (  1 - ³√3)  ( 1  + ³√3  + (³√3)^2  )  =  ( 1 - ³√3)  ( 1 + ³√3 + ³√9 )  = ( 1 - 3)

So

 2³√9

_______________           multiply  top/bottom by   (  1 - ³√3) 

( 1 + ³√3 + ³√9 )

2³√9 (  1 - ³√3) 

____________________________   =

 (  1 - ³√3)  ( 1  + ³√3  + (³√3)^2  )

2³√9  -  2³√27

_____________   =

    1  -  3

2³√27  - 2³√9

____________    =

    3    -    1   

2 * 3 - 2³√9

__________   =

          2

2  ( 3  - ³√9 )  

___________  = 

          2

3 - ³√9  =

3  - 3^2/3

I have this problem too, could someone please help?

sumfor(n, 1, 99, log(n / (n+1)) = -2

Sum of GP =1, 2, 4, 8, 16, 32 =63
Sum of AP =[F + L] / 2 * N
     63         =[1 + L] / 2 * 6, solve for L
L = 20 - Last term (6th term) of the AP 

\(x=15(0.89)^{19}=15(0.10924715256)=1.63870728841\)

So the answer = 1.64.

We have the form

y = ab^x

And we know that

27 = ab^1   ⇒  27 = ab   ⇒  27/b  =  a     (1)

2187  = ab^5        (2)

Sub  (1)  into (2)  for  a

2187  =  (27/b) * b^5     divide both sides by 27  and simplify

2187/ 27  =  b^4

81  =  b^4       take the positive 4th root

81^(1/4) =  b   =   3

And    27/b = a =    27/3   =  9

So....the function  is

y =  9 * 3^x