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Sorry....correction made   !!!

From the Philagelphia frame of reference  :

7PM Saturday  = 17 hrs travel + 1 hr + 1hr   = 19 hrs  

19 hrs after 7PM Saturday =  2 PM  Sunday (Philadelphia time)

But Hong Kong is 14 hrs ahead of  Philadelphia time.....so

2 PM Sunday  +  13 hrs =   

3AM  Monday  (arrival time in Hong Kong )

She will get  4 hrs sleep  before she  has to get up at 7AM on Monday morning  [ it takes her 1 hour to get to her job at 8 AM ]

Yep, this certainly works as well. Kinda just reversing my steps and then finishing the problem. :)

Solve for x:
9 x^2 - 36 x - 720 = 0

Divide both sides by 9:
x^2 - 4 x - 80 = 0

Add 80 to both sides:
x^2 - 4 x = 80

Add 4 to both sides:
x^2 - 4 x + 4 = 84

Write the left hand side as a square:
(x - 2)^2 = 84

Take the square root of both sides:
x - 2 = 2 sqrt(21) or x - 2 = -2 sqrt(21)

Add 2 to both sides:
x = 2 + 2 sqrt(21) or x - 2 = -2 sqrt(21)

Add 2 to both sides:

x = 2 + 2 sqrt(21)      or      x = 2 - 2 sqrt(21)

[ (2+2sqrt(21))  +  (2 - 2sqrt(21))]^2 ==4^2 ==16

x = 42  and  y = 56

x + y = 42 + 56 =98 - smallest positive value.

880 acres / 4 = 220 acres - area of each quarter.

220 / 2  == 110 acres sold

880   -  110 ==770 acres left

Round trip fare to Ireland is $864. If kids can fly for ⅔ fare, determine the total fare for a family of 2 adults and 4 kids.

Adult fare =864

Kid's fare =864 x 2/3 =576

[2 adults x 864  +  4 kids x 576] =[1,728  +  2,304] =4,032 dollars - total fare for family of 2 adults + 4 kids.

See the detailed answer here:  https://web2.0calc.com/questions/i-pick-two-whole-numbers

Inscribed arc = 1/2 * arc measure

170 * 2 = 340

340/360 = 34/36 = 17/18 of the whole circle --> 18^2 * 17/18 * pi = 17*18 = 306 pi

We have: (x-4)(2y+1)-1 = xy

So xy + x - 8y - 5 = 0

The numbers are 2 and 7 so 14.

Divide by 9 on both sides

x^2 + 6x - 80 = 0

So x^2 + 6x = 80

(6/2)^2 = 9

s = 80 + 9 = 89

The sequence computed to 100 terms:

listfor(n, 1, 100, gcd((n^2 - 1),(n+1)^2 - 1))=(3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3, 1, 1, 3).

As you can see, the maximum GCD is 3.

Large circle radius R = ?        Small circle radius r = 1

Large circle area            A_l = R²pi           Small circle area      A_s = pi

Trapezoid area               A_t = R²/2 + R + 1/2

Annular ring area           A_r = R²pi - pi

R²pi - pi  / (R²/2 + R + 1/2) = 3/2

R = 1.62719711 units

So, the ratio is      1 : 1.62719711       or        0.614553697

Yes, she will most definetely get her good night of sleep, infact, she'll get 17 hours of sleep.

starting from 7 PM saturday, 17 hours later it will be 12 PM on sunday then 1 hour to get from the gate to her apartment which will bring us to 1 PM. 1 hour later used to get ready for bed it will be 2 PM. That leaves us 17 hours left until 7 AM, which is the latest time that she can wake up.

Are you asking for the equation? If so the answer is:
y>=1/2x+3/2

That post from Nauseated was funny! 

Do you know what the dyslexic rabbi said?  YO! 

I liked the troll post too. 

Goodnight, Gracie. 

_.

Very nice, ChattyChen  !!!!

Thank you very much for putting the time and effort to solve my problem!
 

(It's correct by the way!)

All    factors  of  7  =   1 , 7

All   factors of 18   =  1, 18     2, 9    3, 6

So we have

(x + 1) ( 7x + 18)      n  = 25

( x + 18) ( 7x + 1)   n  =  127

( x + 2) (7x + 9)       n = 23

( x + 9) ( 7x  + 2)    n  =  65

( x + 3) (7x + 6)    n   = 27

( x + 6) ( 7x + 3)   n  =  45

 a + b  =  24      so    b = 24 - a

Sub this into the other equation

2a (24 - a)  + 10a  = 3(24 - a) + 257 

48a - 2a^2  + 10a  = 72 - 3a  + 257

-2a^2 + 58a   = 329 - 3a 

2a^2 - 61a + 329  = 0 

(2a - 47)(a - 7)  =  0

only one of the solutions for a is an integer and it is 7

7 + b = 24

b = 17

(7)(17)=119

Hi Ron, the word you are looking for is Dyslexia.

thank u very much!

To do this question you need to find the least common factor of 8 and 14, which is 80 so 80 days pass before they do their chores on the same day

A pentagon has 5 sides, therefore its rotational symmetry is 72 degrees, but that is not an obtuse angle so 2*72 is 144, which is an obtuse angle so therefore the obtuse angle is 144 degrees