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Thanks for your answer! I appreciate it!

Marguerite drove 100 miles in 2.4 hours. If Sam drove for 3 hours at the same average rate as Marguerite, how many miles did he drive?

Hello Logic!

\(s=v\cdot t\\ s=\frac{100\ miles}{2.4\ hours}\cdot 3\ hours\\ \color{blue}s=125\ miles\)

  !

At constant temperature, the pressure of a sample of gas is inversely proportional to its volume. I have some oxygen in a 2.28 liter container with a pressure of 5 kPa. If I move all of it to a 5.7 liter container at the same temperature, what will the new pressure be in kPa?

Hello Logic!

\(\frac{p_1V_1}{T_1}=\frac{p_2V_2}{T_2}\\ \frac{5kPa\cdot 2.28l}{T}=\frac{p_2\cdot 5.7l}{T}\\ p_2=\frac{5kPa\cdot 2.28l}{5.7l} \)

\(p_2=2kPa\)

Greetings

  !

Oh i was looking at the older one -_- Thanks Melody :)

Solution #1

Jack picks 5/8 =0.625 pounds per minute.

Jill picks 6/10  =0.6 pounds per minute.

0.625 + 0.6       =1.225 pounds per minute - their combined rate per minute.

1.225 x 40          =49 pounds that Jack & Jill will pick in 40 minutes.

Solution #2

40/8 x 5 = 25 pounds that Jack will pick in 40 minutes.

40/10 x 6=24 pounds that Jill will pick in 40 minutes.

25 + 24    =49 pounds that both will pick in 40 minutes.

I think they lock automatically after a week. I really do not know why, it is something the site developer decided upon.

Maybe they lock under other condtions as well. I do not know.

If you want to continue an old thread you can write to a moderator ands ask them to unlock it for you. 

You would need to include the address of the thread in your message of course.

I certainly have done that for people. 

I am not sure how long a recently unlocked question would stay unlocked for though. 

Oh! Haha! It was my question!

Thanks for all of your solutions!

Thanks! Your right!

Excellent hectictar!

Here is another way:

1 lag = 7/4 ligs

7/4 ligs x 9 lags = 20 lugs

15.75 ligs = 20 lugs.       Multiply both sides by 4

63 ligs = 80 lugs.

This is one way to think of it:

We know...

9 lags  =  20 lugs      Multiply both sides of this equation by  4 .

36 lags  =  80 lugs

And we know...

7 ligs  =  4 lags         Multiply both sides of this equation by  9 .

63 ligs  =  36 lags

63 ligs  =  36 lags       and       36 lags  =  80 lugs    So...

63 ligs  =  80 lugs

This is given in the directions:

"If increasing one variable causes the other to increase, this is called a direct relation.

If increasing one variable causes the other to decrease, then this is called an inverse relation."

If you increase the height of the flagpole, the length of the shadow will increase. Relation is direct.

If you increase the weight of cut, the cost of the cut diamond will increase. Relation is direct.

If you increase the weight of runner, the time to run 2 miles will increase. Relation is direct.

If you increase speed of internet connection, time to load a large file will decrease. Relation is inverse.

(Even in this example, the time to load a large file depends on the speed of internet connection.)

If you increase the HP of a motorcycle engine, the acceleration of cycle will increase. Relation is ___.

If you increase the practice time, the ability to play a guitar will ____. Relation is ___.

Do you know the answer to the last ones?

b)

My CAS system gives the follwing values:
x = -4, y = 1, z = -3/2
x = -4, y = 9/5,  z = -5/6
x = 5/3, y = -12/5,  z = -3/2
x = 5/3,  y = 9/5,  z = 2
x = 3,  y = -12/5,  z = -5/6
x = 3,  y = 1,  z = 2

It was not unanswered. I answered this question just a couple of days ago.

Here is an even older answer.

Let's define \(z_0=1+i\). Then we want to find \(f(f(f(f(z_0))))\).

z is not real, so we have\( f(z_0)=z_0^2=(1+i)^2=1+2i+i^2=1+2i-1=2i\).

So \(f(z_0)=2i\) is not real either, and therefore \( f(f(z_0))=f(z_0)^2=(2i)^2=-4.\)

Now things change, because \(f(f(z_0))=-4\) is real and so \(f(f(f(z_0)))=-(-4)^2=-16\).

This is still real, so we have finally:

\(f(f(f(f(z_0))))=-(-16)^2=-256\)

I mean product of 5 and t is = to 5t and quotient is the answer to a division problem so I got 12/5t...

1 - above can have one additional arrangement: 8 + 7 + 1 + 3........19

4- above .............................................................: 8 + 6 + 2 + 3........20

10 - above............................................................: 7 + 7 + 2 + 3.........21

11- above..............................................................: 6+ 7 + 5 + 1.........22

12 - above.............................................................: 6 + 7 + 4 + 2........23

13-above................................................................: 6 + 7 + 3 + 3.......24

14- above................................................................: 5 + 7 + 5 + 2.......25

15- above.................................................................:5 + 7 + 4 + 3.......26

16-above..................................................................: 6 + 7 + 5 + 1...... 27

                                                                                    6 + 7 + 4 + 2.......28

                                                                                    6 + 7 + 3 + 3.......29

18-above...................................................................: 5 + 6 + 5 + 3.......30

So, it looks that in addition to the 18 listed above, you can have another 12 arrangements for a grand total =30

CPPhill: I think heureka's reasoning comes from this property of irregular quadrilateral:

"The line joining the mid-points of any two adjacent sides is parallel to the corresponding diagonal and equal to half of it."

Hey...it's like I always say..."Any port in a storm."

LOL!!!!!.....

MWAHAHA I knew it! I used guess and check during my test but honestly... at least I got it!

According the the  mid-point rule

[ sum of x coordinates of  both endpoints / 2  , sum of the y  coordinates of both endpoints / 2 ]  = midpoint

So

[ ( 6 + x / 2 ]  = 2    multiply both sides by 2

6 + x   = 4   subtract  6 from  both sides

x  = -2     

[ ( 5 + y ) / 2 ] =  -11    multiply both sides by 2

5 + y  = -22    subtract  5 from both sides

y  = - 27

So.... N  = (x , y )  =  ( -2,  -27)

Geometry is depressing... Anyways thank you!

Assumig the "y"  angles are vertical ...we have that

7y - 92  = y  - 3       add 92 to both sides....subtract y from  both sides

6y   = 89

y  =  89/6  =   ( 14 + 5/6  )°

So....each  of these vertcal angles measures  (14 + 5/6  - 3)°   =  (11 + 5/6)°  = (71/6)°

So....the measure of each of the  other two vertical  angles  =    [ 360  - 2* (71/6) ] / 2 = 

[ 360  -  (71/3) ] / 2  =     [ 1080 - 71 ] / 6  =  (168 + 1/6)°  =  (1009 / 6 )°

So...

3x - 1  = 1009/6

3x  =  1009/6 + 1

3x = 1009/6 + 6/6

3x  = 1015 / 6

x = (1015 / 18)°  = (56 + 7/18)°