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Solve the inequality \(x + 13 < 0. \) Give your answer in interval notation.

Hello CPhill!

\(x\in \mathbb R|\ x<-13\)

Is this a correct solution?

  !

If you mean QM's question then the answer would be 10 2/3

Do you mean How much water must be evaporated from 32 ounces of 4% salt solution to make a 6% salt solution?

Since CM  = MA,the  angle  CAM  = angle MCA.....call  these, x

And by the exterior angle theorem,  angle BMC =  2x

So    angle  CAM  +  BMC  =201

So        x  +   2x   =20

So       3x  =  201

So x  = 67

And  angle BMC  =2x  = 134

So....since  BM  =CM.....then angle  CBM  = angle BCM

So   angle   CBM =   ( 180  -134)   / 2  =     46   / 2  =    23°  = angle B

Thanks

what is the amount of water

x  +  13  <  0      subtract  13 from each side

x  <  -13              (this is in  interval form  )

3 miles  in 33 min  = 1 mile  in 11 minutes

Every  minute    Jeremy  runs  1/8  of a mile

Every muniute, Gerardo  runs  ( 1/11)  of a  mile

In 10 minutes, Gerardo runs   10 (1/11) miles =  10  / 11  miles

So....this is the is  the distance that  Jeremy needs to  close to  catch Gerardo....and  the  effective  distance he closes  every minute = ( 1/8   -1/11)  =  ( 3 /88)  miles

So      D  / effective  rate    =  Time

So       (10/11)  / ( 3/88)  =   (10/11)  * (88/3)  =  880 / 33  ≈  80/3  minutes  = 26 2/3 min =  26 min 40sec  

See  jugoslav's answer, here  :

https://web2.0calc.com/questions/help-please_90002

Thanks for trying to help tho... I just got it anyways. I got 8/3.

Idk rlly lol,

I just extended the line from  A to F and realizes it is a bit similar...

To solve this, we can make a few equations:

For the first triangle on the left

4y -18 + y + 14 + 6x - 11 = 180

5y + 6x  = 180 + 18 + 11 - 14

5y + 6x = 195

For the second triangle on the right

6x - 11 + x + 5  + 81 =  180

7x = 180 - 81 - 5 + 11

7x = 105

x = 15

5y + 90 = 105

5y = 15

y = 3

Therefore y is 3 and x is 15.

Hope that helps!!!!

🙃🙃👌

ok, but can you explain how you got it please

It may be 4, I am not 100% sure.

Let me know whether that's correct or not.

2 ( n+ 1) !   +  6n!   =  3 ( n + 1)!

Note  that  (  n + 1)! =    (n + 1) * n!

So

2 (n + 1) * n!    +  6n!  =  3 (n + 1) * n!            divide out  n!

2 ( n + 1)  +   6  =  3 ( n + 1)        simplify

2n + 2  +  6 =  3n  +  3

8 =  n +  3

8  - 3   = n  =   5

Cheating in AoPS??

I won't solve it, but I'll give you a helpful start.

Clearly, if we add up everything, then we would overcount, which we do not want. We want to count things once and only once. (Sound Familiar)

Now, make an expression where you add up everyone. The subtract that by two times the people who did all languages. (I technically gave you the answer.) 

Hope that helps!!!

🙃🙃👌

a   x +  y    = 58

     x = y +  14

b.   Substitute  the second equation into the first  for  x

(y + 14) + y  = 58     simplify

2y  +  14   = 58     subtract 14 from both sides

2y  =  44              divide  by  2  on both sides

y  =  44/2   = 22 

b.  You sell   y + 14  = 22  + 14  =    36

      Your friend sells   22

a)  1000(1 + .05) ²⁰

b)  9000 ( 1 + .1/4)¹²  = ..........     use this value in the second part

              value * (1 + .09/2)⁴ =  final amount

c )  this is really  four results that you add together

        500 ( 1 + .048/12)^12*18    +

            500 ( 1 + .048/12)^13*12    +

                500 (1 + .048/12)^8*12        +

                    500 ( 1+ .048/12)^3*12   =   total amount when 18 y/o

8 P 4 = 8! / 4! = 1680 ways

Point slope of a line would look like this:

(y-1) =  6/5 ( x-5)   

9 P 7 =   9!/(7!) = 181440 ways

x1(t)=3[u(t)−u(t−1,6)] x2(t)=5[u(t)−u(t−3,5)] Find z(t)=x1(t)∗x2(t).

\(x_1(t)=3[u(t)−u(t−1.6)] \\ x_2(t)=5[u(t)−u(t−3.5)]\\ Find\quad z(t)=x_1(t)∗x_2(t).\)

I still do no understand your question but is this what it is supposed to look like?

"What is the equation of the line that passes through the point (5,1) and has a slope of 6/5?"

Straight line equation:  y = (6/5)x + c

Find c by substituting the (x,y) vaues of the given point:  

1 = (6/5)*5 + c

I'm sure you can continue from here.