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anybody?

that make sense! thank you

By integral calculus, the area is pi/4.

There are 36 possible triangles.

Uhhhh......yah......that is what was posted ......

4 by itself = 1 such number.

(12, 16, 24, 32, 36, 64)>>Total = 6 [These are 2-digit numbers that are divisible by 4]

(124, 132, 136, 164, 216, 236, 264, 312, 316, 324, 364, 412, 416, 432, 436, 612, 624, 632) >>Total = 18 [These are 3-digit numbers divisible by 4]

(1236, 1264, 1324, 1364, 1432, 1436, 1624, 1632, 2136, 2164, 2316, 2364, 2416, 2436, 3124, 3164, 3216, 3264, 3412, 3416, 3612, 3624, 4132, 4136, 4216, 4236, 4312, 4316, 4612, 4632, 6124, 6132, 6312, 6324, 6412, 6432) >>Total = 36 [These are 4-digit numbers divisible by 4]

(12364, 12436, 13264, 13624, 14236, 14632, 16324, 16432, 21364, 21436, 23164, 23416, 24136, 24316, 31264, 31624, 32164, 32416, 34216, 34612, 36124, 36412, 41236, 41632, 42136, 42316, 43216, 43612, 46132, 46312, 61324, 61432, 63124, 63412, 64132, 64312) >>Total = 36 [These are 5-digit numbers divisible by 4]

So, the total =1 + 6 + 18 + 36 + 36 =97 such permutations

I think you mean \(x^2-x\sqrt{5a^2-26a-8}+a^2-6a+12=0\)

See that 10^x button down next to the 'log' button?   ....   use that ......

Use casework. 

3,2,2 3 ways

3,4,1 6 ways

6,2,1 6 ways

In total there are 15 ways. 

6^3=216

15/216=5/36

:D

y=2+5/6x

4x-3(2+5/6x)=3

4x-6-2.5x=3

1.5x=9

x=6

y=2+5/6x

y=2+5/6*6

y=2+5

y=7

We can see pretty clearly that the input is the output subtracted by 3.

the function would be

$f(x)=x+3$

therefore if the input is n

the out put would ${n+3}$

Thank you, that's what I got. How do you calculate for depth?

We can let the parabola open upward......so we will  have the form

4a ( y - k)  =  (x - h)^2

The distance from the vertex to the focus =  20   = a

We can let the vertex be   ( 80, 30)

So we have the form

4(20) ( y- 30)  = (x - 80)^2   simplify

80 ( y - 30)  = ( x - 80)^2

Since the diameter  is 120 ft...the radius is 60 ft.....so we can let one point on the parabola be   ( 80 + 60 , a) =

(140 , a)......where a  is the height of the dish....so we have that

80 ( a - 30) = (140 - 80)^2

80 ( a - 30)  = (60)^2

80 ( a - 30) = 3600      divide both sides by  80

a -  30 =  45      add 30 to both sides

a = 75 ft  = the height of the dish

We can apply the quadratic formula:

 \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

$a=m$

$b=-(m-2)$

$c=(m-8)$

x =\({(m-2) \pm \sqrt{(-m+2)^2-4m(m-8)} \over 2m}\)

can you take it from here?

Given that all the comic book types must be grouped together, we can make each of these multiple comic books into 1 comic book. Therefore there are 3 comic books, how do we arrange it just 3! So that is 6 ways.

Now let us split each of these books into there only category

5!*2!*2!*6=$2880$ ways

U  R  welcome.....I hope you understand the solution !

Yes $guest_2$ I agree

7/9 percent    is      7/9  /100   fraction of the quantity=    7/900 ths of the quantity.

Try 7 divided by 9, that is 0.7777....

that is 77.7777777 repeating, if you were to round it it could be approximately 

77.8, 77.78 etc.

Did you perhaps leave off some parentheses in your question?

    .....because   2x+3-3 = 2x        2x+2-1 = 2x+1 

    all this does is shift the funtion graph UP by one

First change f(x) to y

$y=2x$

this is changed to

$y=2x+1$

however inside of the answers  I don't see 1 unit shifted up

here is the graph

https://www.desmos.com/calculator/z3osssy1ot

THANK YOU VERY MUCH

Rabbits : Sheep     is     6:2

Rabbits + 8  is to  6      as     R is to 2

(r+8)/6 = r/2

2r+16 = 6r

4r = 16

r = 4   

Now do it for rabbits and goats

rabbits : goats   is     6:3

4 rabbits is to 6     as     x goats is to 3

4/6 = x/3

x = goats = 3 * 4/6 = 2 goats

Thanks Grace