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I got tired of formatting LaTeX by clicking the button every time, so here's my solution:

To elaborate, start by noting that $m-20 \ne m-4 \ne m-100$ since the constants are different. Use the distributive property on the last $2$ equations, which gives $5(m-4)=5(m)+5(-4)=5m-20,$ which is not equivalent to $m-20,$ and $5(m-100)=5(m)+5(-100)=5m-500,$ which is also not equivalent to $m-20.$  Thus none of the expressions are equivalent to $m-20.$

_{Is there not a shortcut for LaTeX?}

what is the number in 234 and 312     

The largest common factor of 234 and 312 is 78 if that's what the omitted words would have asked.  

_.

Better check you calculations again....and OF COURSE it will be the shorter time !!!!!!!!!!!!!!!!!!!!!!!!

Have you written out the beginning of the sequence of yourself?

What did you do yourself before you asked for help?

So which solution would it be, 2, or 9/4

108 = -6t^2+ 51t

-6t^2+51t-108 = 0     Use Quadratic Formula    a = -6   b = 51   c = -108    

                                      you will get two values of t ....one is on the way up..... the other is on the way down....

3 * $ 2.45       +  $2.59      +   4 * $ .79 = amount

Let me correct myself: there are at least 2 ways to solve this...

Hello, asinus!    There are 2 ways to solve this:   1/   Pythagorean theorem (above)

                                                                                                or

                                                                              2/   AS² = PS * SN     

( N is a point on a circle opposite to point P )

 ∠A : ∠P :  ∠ASP are in ratio  1 : 2 : 3  =  30º : 60º : 90º

∠BSA = 60º

Need the diagram

If I understand your question:

There are: 1000 / 3 =333 numbers that are multiples of 3

First number =333 / 1000 x second number =332 /999 x third number =331 /998 x fourth number =330/997=[333 / 1000  x  332/999  x  331/998  x  330/997] =12,076,031,880/ 994,010,994,000==302203/24875150==1.215%

Circle O is a unit circle. Segment AS has length 14/5 and is tangent to circle O at A. If P is the intersection of OS with circle O, find length PS.

Hello Guest!

$(\overline{PS}+r)^2=2.8^2+r^2\\ $

$r=1\\ \overline{PS}=1.973$

  !

AO = PO

PS = [sqrt(AS² + AO²)] - PO

PS = 1.973213749

If you graph y = x - 1/x, then it clearly fails the Horizontal Line Test over all real numbers, so f is not invertible.  But if you restrict to positive real numbers, then it passes the Horizontal LIne Test, so g is invertible.

You can also verify it this way:

(10 nCr 8+10 nCr 9+10 nCr 10)/2^10= 7 / 128

10!/[8!*2!*2^10] + 10!/[9!*1!*2^10] + [10!/[10!*0!*2^10] ==[45 + 10 + 1] / 2^10==56 / 2^10==7 / 128

Which expression is equivalent to  m − 20? (4 points)

 (m − 4)

 (m − 100)

5(m − 4)

5(m − 100)             NONE of them are equivalent to m - 20

Thank you very much!

Slope of given line, m      m = 1/2    perpindicular slope is - 1/m  = -2

midpoint of AB   is   4 , 6

y-6  = -2(x-4)     is your new line      re-arrange

y-6 = -2x+8

y = -2x+14

By the Sine Law, YZ = 6*sqrt(2).

1/2x^2-(1/4x+3)

Just put in '8'  where 'x' is in the equation and compute the value  

Use law of sines

4 is to sin 45   as   XY is to sin 60

4/sin45   =   XY/sin60      solve for XY

a(50) = It is simply the 50th Fibonacci number =12586269025

b(50) = It is the 52nd Fibonacci number             =32951280099

a(50)  +  b(50) =[12586269025 + 32951280099] mod 5 == 4