All Answers 356735 Answers

Point-slope form of a line is written in the following form:
 

\(y-y_1=m(x-x_1)\)

\((x_1,y_1)\) is a Cartesian coordinate located on the said line.

\(m\) is the slope of the line.

Based on the information given, we already have this information. Just put the information together into a coherent equation.

\(y-1=-4(x-4)\)

Let the portion of the job that Alice can complete in one hr  = 1/ x

Let the portion of the job that Bob can complete in one hr  =1/ y

Let the portion of the job that Charlie can complete in one hr  = 1/ z

So  we have this system

2 [ 1/x + 1/y]  =  1    ⇒   1/x + 1/y  = 1/2    (1)

3 [ 1/x + 1/z ]  = 1    ⇒  1/x + 1/z  =  1/3  (2)

4[ 1/y + 1/z]  = 1    ⇒   1/z  + 1/y =  1/4    (3)

Subtract  (3)  from (1)     ⇒   1/x - 1/z  =  1/4   ( 4)

Add  (2)  + (4) =    2/x  =  7/12   ⇒   1/x =  7/24

Using (1)  to find y, we have that

 1/y  =  `1/2  - 7/24  =  5/24

And  using  (3)  to find 1/z  we have

1/z  =  1/4  - 5/24  =      6/24  - 5/24   =  1/24

So.....Alice completes 7/24 of the job in an hour......Bob completes 5/24  of the job in an hour  and Charlie completes 1/24  of the job in an hour

Add these  and take the reciprocal  =    [7 + 5  + 1 ] / 24  =   13/24

So.......they take  24/13 hrs  ≈ 1.846  hrs to complete the job working together

It is possible  to find a solution

For instance

17¹  + 2⁶ =  3⁴ 

17 + 64  =  81

Thanks 

Random fact: Whenever I hear the word "stab", my mind replaces it with the word "shank". Is something wrong with me?

She is a bad teacher, kids should be able to be good at math..  

Profit  =  Revenue - Expenses

So

P(n)  =  R(n) - E(n) =   [ 20n ]   -  [ 10 √n ]

P(n)  is in terms of n...so....the second answer is the same as the first 

Why did you want to know?

Not My Best Work of Art Though

Yes! I'm glad you noticed!

Just curious.

Is that image photoshopped by you?

Ohhh yes yes it makes sense!! Thanks!!

We probably need a graph for this one

https://www.desmos.com/calculator/mkrzieddkk

The "overlap" of the graphs is the solution area....

Note, NSS....only the first two choices appear to be plausible...however....we need to consider the boundaries

Note that the "bottom" graphed function,    y < -x^2 - 8x -14,    will have a "dashed" boundary  [ due to the "<"  ]

And  the other graphed  function [ the "top" one ] will have a solid boundary due to the  "≥" 

So......the first answer is correct

Does that make sense ???

Anyone can..

I'll give this one a shot.....whether it's correct....Mmmmmm...!!!!!

ab+bc+cd+da  =

ab + ad  + bc + dc  =

a(b + d) + c (b + d) =

(a + c) (b + d)

Note  that  the only possible values, no matter the arrangements,  are  

(9 + 11) (13 + 15)  = 360

(9 + 13) (11 + 15) = 572

(9+ 15) (13 + 11) = 576

To see this more clearly.....we are choosing any 2 of the 4 numbers to occupy the first set of parentheses without regard to order ....and this means that the second sum is "fixed"

So.....C(4,2)  = 6

But  we  can permute the order of the parentheses' sums in 2 ways.....so   6 / 2   =   3 different values

Post something And I will like your post.

LOL that's funny

Your profile picture looks like a neurographic drawing of what happens when an evil force overcomes a small, yellow chubby being.