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we are given $f(\sqrt{x + 1}) = \frac{1}{x}$, but we know that $\sqrt{x + 1} \equiv 2$ which gives you $x+1=4 \ \ \  \therefore \ \ \  x=3 $

knowing that we can put that x on the other hand and for the first side we can either plug in $3$ for x, or just use $f(2)$ for the whole thing (which ill be using as its... easier.):

so you get:

$\boxed{ f(2)=\frac{1}{3}}  $

For each of them, you want to multiply the numerator and denominator by the conjugate of the denominator.

1/(2 + √3) * (2 - √3)/(2 - √3) = (2 - √3)/(2^2 - sqrt(3)^2) = (2-sqrt(3))/1 = 2-sqrt(3)

Try the other ones. :))

=^._.^=

thanks chris :)

Let  p  be  the original  price per cookie  and  c  the  number bought

So

cp  =  35   ⇒  p   =  35 / c

And

(c + 4)) ( p -1)     = 35

(c + 4)  (  35/c - 1)  =  35

35  +  140/c  - c  -  4  =  35

-c +  140/c   +  31  =  35

-c + 140/c   -  4  =  0                        multipy  through  by  -c

c^2  + 4c   - 140    =   0                   factor

(c  + 14)  ( c - 10)  =  0

The  second factor set to  0  and solved  for c  =  10

He originally  bought  10 cookies    and  their  cost  was  $3.50  each  =   $35

So  4 more  at  a  $1  price  reduction per coookie  gives.......

14  (2.50)  =  $35    

thanks! !

Here's  the  graph of  the first  :   https://www.desmos.com/calculator/bwde1tjhsh

The second has the same shape, except  shifted  down  by  2  units

b)The  second  equation  gives  his  height when opening the  chute =   188  m

a)   The  time from jumping to opening the  chute  can be found as

188  = -4.9t^2   +  2t  + 500

4.9t^2  - 2t   +  188  - 500   = 0

4.9t^2  -  2t  - 312   =  0

The time =         ( 2 + sqrt (4  + 4 * 4.9 *312) ) /  (2* 4.9)   ≈  8.186  sec  ≈  8.2 sec

There are six available colors. find the number of ways to color the unit cells of a 2 x 2 grid such that no two adjacent cells are of the same color. solve the problem in two ways: by considering the number of colors used and by coloring the squares one after another.    

You have 4 cells.

You have 6 colors. 

Just put a different color in each cell. 

See  hectictar's answer here   :  https://web2.0calc.com/questions/i-know-gfb-is-similar-to-chb-but-how-do-you-find-gf

Did you look under your first post?

G  /  D  = 5/2

G  =  (5/2)D

(G - 36)   / D  =  1/2

(5/2 D  - 36)   / D  = 1/2         cross-multiply

2 ( 5/2 D  - 36)   =  D

5D  -  72    =   D

5D  - D  =   72

4D  = 72

D =  72 / 4    =    18

G  = (5/2) D   =  (5/2)(18)   =   45

Since  both  started  with  the same  number, let  this  =  E

So

(E  - 37)  = 2 ( E - 57)      simplify

E - 37  =  2E  - 114

114 - 37   =   2E  - E

77  =  E

Each started with  77

If  the  6.8%   is  the monthly interest rate

241488  (  1 + .068)^16     =    $691888

If  the  6.8%  is the  yearly interest rate   (more probable)

24148 ( 1 +  .068 / 12)^16   = $264338

Let the initial number of flowers that Willie set out with be x.

When he sneezed, he knocked off the petals of 2/3 of x and he threw away the petal-less ones. So the remaining number of flowers with him now is x-2/3x = 1/3x

He then added 4 more to the remaining. So the number of flowers with him now is 1/3x + 4 = (x+12)/3

On his way, he dropped 4/5th of what he had into a mud puddle. Which is 4/5((x+12)/3)

= (4x + 48)/15

The number of flowers left with him will be 

(x+12)/3 - (4x+48)/15 = (x + 12)/15

He then picked up 3 flowers from Suzabelle's mother's garden. The number of flowers he now has 

= (x + 12)/15 + 3

Suzabelle said she will now have a dozen (12) flowers, before she only had 5. So now she got 12-5=7 flowers from Willie.

Which implies  :

(x + 12)/15 + 3 = 7

On solving for x, we get x = 48.

Thus, Willie set out with 48 flowers the first time. 

Welcome to the forum 

ThAnks for checking my error you are right

(4-5i)(5+5i)=20+20i-25i-25(-1)

=20-5i+25

=45-5i

(11-5i)(3-2i)(2i)=(33-15i-22i+(-10))(2i)

=(33-37i-10)(2i)

=46i-74(-1)

=46i+74

https://www.wolframalpha.com/input/?i=%2811-5i%29%283-2i%29%282i%29

D) can be any real number but not both zero

We  have  a right triangle  with    legs AB  and BC   and  hypotenuse  AC

The area  of  this triangle =   (1/2)(10) (24)  =  120

The  shortest altitude   is  drawn  from the  vertex opposite  the  longest side  to the longest side ( B  to AC )

This  altitude  can be  found as

Area  = (1/2) ( AC)  (altitude)

120  =  (1/2) (26) ( altitude )

120  =  13    (altitude)

120  / 13   =  altitude

nvm i already got it

!

https://web2.0calc.com/questions/water-pressure

1 - Divisors of 20^20 ==2^40  x  5^20==861 divisors 

2 - Divisors of 10^10==2^10  x   5^10==121 divisors

3 - Divide (1) by (2) as follows: [2^40 x 5^20] / [2^10 x 5^10] =2^30 x 5^10.

4 - The divisors of the answer in (3) are: [30+1] x [10+1] ==31 x 11 ==341 divisors that are multiples of 10^10.

5 - Since 20^20 has 861 divisors, the probability that a randomly chosen divisor is a multiple of 10^10 is:

341 / 861 ==39.60511034 %

help

@MathProblemSolver101 i think ur wrong...why should you subtract 7 choose 4 times 5 choose 1? I understand you if the question says that you cant go to (4, 3), but the question says there is a frog there. He will get eaten if he goes there so no more journey!!! Maybe check again?

P.S. CPhill can you check?

You can also use waterfall/waterflow if you learn/already know about it.