All Answers 358232 Answers

Cross-multiplying, we have 8(n+3)=5n, 8n+24=5n, 8n-5n=-24, 3n=-24, n=-8.

This is the same  as counting the number of  identifiable"words" that can be formed with  four "T's"  and six "F's"

So

[ Total Letters ! ] / [ Repeats of T !    x    Repeats of F  ! ]  =

10!  / [ 4! *  6! [  =  

210 distinct answer keys

Thank you, CPhill!

Well, that is correct. Read here, for more info: https://cs.uwaterloo.ca/journals/JIS/sommars/newtriangle.html

We have N choose 3, in this case, 12 choose 3, which is 12!/9!*3!=12*11*10/3*2*1=220 triangles. You can add 108 triangles to that.

Nice, tertre  !!!!!

Yes, you should make an account and become known to us.  :)

We want to solve this inequality

Total cost of 1st company < Total cost of second company

.029 N +  4  < .034N      where N is the number of minutes we are looking for

subtract  ,029N from both sides

4 < .005N    divide each side by .005N

4 / .005  < N

800 < N

The first company will be cheaper after 800  minutes

We have 2x+1=7x-14. Solving, we attain 5x=15, x=3. So, with 2 rows: 2(3)+1=7. Or, with 7 rows: 7(3)-14=21-14, x=7.

[ Total trees  ! ]   /  [ Number of Goldn De;icious trees! * Number of Bartlett trees ! ]  = 

7! / [ 5! * 2! ]   =   

21 disitnct arrangements

Combos that don't add to  7  are

[ 1. 2 ]  [1,3 ] [1, 4 ] [1,5 ]

[ 2, 3 ]   [ 2, 4 ]

6 ways

If the number ends in 3

We have three choices for the first digit  and two for the second  = 6 numbers

The same logic would apply if the number ended in a "5"

So...   12 

The numer of disitnguishable arrangements  =

4!  / [ 2!  * 2!  ]  =    24 / 4   =    6

XY  = 28

Y = 196

So

X (196)   =  28     divide both sides by 196

X  = 28 / 196   =  1 / 7

The number of distinguishable "words"  that can be made is

5!  /  2!   =    120  / 2   =  60

Is the answer 20?

thank you.

THAT is the equation of a line in the form   y = mx + b     where m = slope = -2/3

Sin = opp/hypot          opp = 4   hyp = 9

adjacent leg using pythagorean theorem

  4^2 = ADJ^2 = 9^2

ADJ^2 = 65

ADJ = SQRT 65   

 TAN = OPP/ADJ =  4/ SQRT65    WHICH EQUALS    4 SQRT65 / 65   IF YOU MULTIPLY BY SQRT65/SQRT65

Thanks!It's not the answer i was looking for but this help me! 

I replaced your "eta" with "a". Look here and see if it is meaningful:

https://www.wolframalpha.com/input/?i=(a+%2F+2)+%3C++sin(%CF%80%2F(3v)),+solve+for+v

Thank you so much Chris

Thank you for the answer. Still a little confused though sorry but do I have to plug in the numbers in the equation you gave me. I know the number for (f)x but do i have to put the number like -3 for all of the missing x's

oh I missed the "4 letters or less" 

2(x-4) / ( x-4)(x-2)

2/(x-2)        when x = 0        2/-2 = -1

Substitute '0' for x in the original equation

-8/8 = -1                                                           Yup, they are equal  

It is helpful because it 'simplifies' the calculation(s) involved.....there are less chance for errors.

\(x+1 = 4 \Rightarrow x=3\\ \text{however 3 is not in the domain of either side of the equation (no division by 0)}\)

\(\text{again the point is no dividing by 0}\\ x^2-6x+8 = (x-4)(x-2) = 0 \text{ when }x=4, \text{ or }x=2\\ \text{Thus neither 4 nor 2 are included in the domain}\)

Another method:

2(x-4) /( (x-2)(x-4) )

= 2 / (x-2)      NOT   2/(x-6)