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Note that the points  (5, - 2)  and  (4, -3)  would be on the graph  if we had a solid line

So....the slope would  be    [ -3 - -2 ] [ 4 -5]  = -1 /  -1     =  1

So...using   the point (5 , -2)  we can write the equation of this  "line"

We have

y  = 1 ( x -5)  - 2

y = x - 5  - 2

y = x - 7      or     x - 7   = y     subtract  y from both sides

x - y  - 7   = 0

However  ...we have a dashed line so we must have  a  >   or  <  insted of an  =

Note that the point  (0, 0)  is in the shaded region...so....testing this point in

x - y  - 7 >  0

0  - 0  - 7  >  0 

-7  > 0      not true

So...the equation must be

x - y  - 7  <  0

Here's the graph :  https://www.desmos.com/calculator/9jof1vd4lq

That is very fucking astute of you, EP!

Average  rate of change  (per year) =

[ 46.6  - 45.1 ]  / [ 1920  - 1970 ] =

1.5 / -50  =

-.03   crimes  per year

Thankyou!

Put everything in terms of powers on 2

A  =  2^(1/2)  / 4^(1/6)  =  2^(1/2)  / (2^2)^(1/6)  = 2^(1/2) / 2^(2/6)  = 2^(3/6) / 2^(2/6)  =

2^(1/6)  = 2^(2/12)

B   =   (128)^(1/12)  =   (2^7)^(1/12)  = 2^(7/12)

C =  [ 8^(-1/5)] ^2  =  [ (2^3)^(-1/5) ]^2  = [ 2^(-3/5) ]^2  = 2^(-6/5)

D  =  √  [  (2)^1 * 8^(1) /   4^(1) ]  =  √  [16 / 4 ]  = √ 4  =  2  = 2^(1)

E   =  [ 2^(1/2)  *  (2^2)^(-1/4) ] ^(1/3)  = [ 2^(1/2) * 2^(-2/4) ]^(1/3)  =

[ 2^(1/2) * 2^(-1/2) ]^(1/3)  = [ 2^0]^(1/3)  = 2^0

So..in order, we have

2^(-6/5) < 2^(0) < 2^(2/12) < 2^(7/12) < 2^(1)

So

C   E   A   B   D

Thank You So Much!

ah thank you so much! i think you're right

-2 ( s - 7)  >  4s  + 8

-2s + 14  > 4s + 8       subtract 4s , 14 from both sides

-6s > -6      divide both sides by  -6   and reverse the inequality sign

s <  1   

( -infinity , 1 )      [ in interval notation ]

Thankyou!!

L1   =  5x + 8y  = -9

In the form  Ax + By  = C....the slope of this line  is  -A / B

So...the slope of this line  =  -5/8

And the slope of a line perpendicular to this   =  8/5   = slope of L2

So....we have this equation of L2  that passes through (10, 10)

y  = (8/5)(x -10) + 10

y  = (8/5)x - 16 + 10

y  = (8/5)x  - 6

m  = 8/5     b  = -6      and their sum is   8/5 + (-6)  =  8/5 + (-30/5)  = -22/5

Let S  be the  the total sales per month

So...we have these equations

B  =  900 +  .15( S - 6000)

A = 500 + .10 ( S)

And we want to know when  B > A  ...so...

900 + .15(S - 6000)  >  500 + .10(S)      simplify

900 + .15S  - 900  > 500 + .10S

.15S  > 500 + .10S        subtract  .10S  from both sides

.05S  > 500      divide both sides by .05

S > 10000  ⇒  "B"  is better whenever his monthly sales are greater than $10000

Wow ok, a bit crude and I prefer to not clog my toilet.

This is the best answer

Thank you

Quadratic  trinomial  is correct

Quadratic = 2nd degree polynomial

Trinomial =  3 terms     [ tri  = 3 ]

Quartic trinomial  [ 4th degree polynomial  with three terms]

Ex :  x^4  + 3x^2 + 1

Cubic trinomial  [ 3rd degree polynomial with three terms ]

Ex :  x^3  + 2x  - 8

Cubic binomial  [ 3rd degree polynomial with two terms ]  [ bi  = 2]

Ex :   x^3  - 8

Set up direct proportion: \(\frac{20*5}{60}=\frac{100}{60}=\frac{10}{6}=\boxed{\frac{5}{3}}\)

Let's assume that 220.000  is supposed to be  220,000

Let  salesperson C  earn  E  during this period

Then  B  has earned  50% more than C  =  1.5C  = 1.5E

And A has earned  twice B  =   2B  = 2(1.5)C  =  3C  = 3E

So

A + B + C  = 220000

3E + 1.5E  + E   =  220000

5.5E  = 220000     [ divide both sides by 5.5 ] 

E  = 40000  =  amt  C  earned in the period

And B  earned   1.5C  = 1.5 (40000)    = 60000

So...in any one year, B's average earnings  = 60000 / 3  = 20000

Yes, when it goes upstream you have to subtract, but, if it is heading downstream, then you have to add!

Thank you, CPhill!

 You can easily eliminate the months: January, April, June, August, September, October, and December.

And, 2007 was not a leap year, February-9 dates, March-11 dates, May-11 dates, July-11 dates, November-10 dates.

If you add all the number together, you get an answer of \(\boxed{52}.\)

Nice,  tertre  !!!

She is stationary  between  3 PM and 3:30 PM  = 1/2 hr

She is also stationary between 4 PM and 5 PM  = 1 hr

She is also  stationary between 6:30 PM  and 7:30 PM  = 1 hr

Total time  for  the journey  =   6 hrs  [ 8 PM  -  2PM]

So  she is stationary  for  [ 1/2 + 1 + 1/2 ]  =  2 hrs

And she travels   [ 6 hrs  -  2 hrs  ]  =  4 hrs

5 minutes  =  1/12 hr

So

20 km / hr  x   1 / 12 hr   =    [ cancel   hr  ]

20/ 12  km  =

5 /3  km

Use exactly the same reasoning as in the answer to your question after this one. Make sure you change the numbers!. If you don't make any mistakes, you should get 4 3/7 hours, or about 4 hours and 26 minutes.