hectictar

Here's another interpretation.

a + 1 + 4 + c  =  28       →       a + c  =  23

a + 3 + 5 + d  =  28       →       a + d  =  20

b + 4 + 2 + d  =  28       →       b + d  =  22

b + 1 + 3 + e  =  28       →       b + e  =  24

c + 2 + 5 + e  =  28       →       c + e  =  21      Add all five of these equations together to get...

2a + 2b + 2c + 2d + 2e  =  110      Divide through by  2 .

a + b + c + d + e  =  55

The formula at the top confused me too.

I don't know for sure what it is supposed to mean, but if it said

\(m_{sec}=\frac{f(x)-f(2)}{x-2}\)                  then I think it would make sense.

They'll sneak up right behind you...and suddenly....BOO!!

It  is close to Halloween, after all !!! Gotta watch out!!  

I went into hiding!!  

Well..... I logged out before I started answering because I didn't know for sure if I could get it   

There are  15  people in the science club.

80% of the people in the science club are in both the science and math clubs, so...

number of people in both clubs  =  0.8 * 15  =  12

Let the number of people in math club  =  m

30% of the people in the math club are in both the science and math clubs,

and remember there are  12  people that are in both clubs, so...

0.3m  =  12

m  =  12 / 0.3

m  =  40

(2k - 5) / (-6)    >    5

                                     Multiply both sides of the inequality by  -6  .

                                     Since we are multiplying by a negative, also flip the inequality sign .

2k - 5   <   5 * -6

2k - 5   <  -30

                            Add  5  to both sides.

2k   <  -30 + 5

2k   <  -25

                           Divide both sides by  2  . (2 is positive, so the sign stays the same.)

k   <   -25 / 2

In interval notation, the solution set should be:  (-∞, -25/2)

Ah! Now I see what is "wrong" with your answer....

"Use integers or decimals for any numbers in the  expression."

So just turn  -25/2  into  -12.5  and we have...    (-∞, -12.5)

And the number line looks roughly like this

Let's call the number of wins  " W ", and the number of losses  " L ".

There are  96  games altogether, so....       W + L  =  96

The number of wins is 15 more than twice the number of losses, so....     W  =  15 + 2L

W + L  =  96

                                      We can substitute  15 + 2L  in for  W  since  W  =  15 + 2L .

15 + 2L + L  =  96

                                      Subtract  15  from both sides.

2L + L  =  96 - 15

                                      Combine like terms.

3L  =  81

                                      Divide both sides by  3 .

L  =  27

They lost  27  of the games.

Remember, there are 96 games total...   W + L  =  96   →  W  =  96 - L  =  96 - 27  =  69

They won  69  of the games.

Let's pick two points off of the table:  (1, 0)  and  (0, -6)

slope of  f(x)  =  \(\frac{\text{change in f(x)}}{\text{change in x}}\,=\,\frac{-6 - 0}{0-1}\,=\,\frac{-6}{-1}\,=\,6\)

g(x)  =  2x + 6    Notice that this is in slope-intercept form, so we can already tell that its slope is  2 .

6 > 2 ,   so the slope of f(x) > the slope of g(x) . f(x) is "steeper" than g(x).

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The y-intercept is the value of the function when  x = 0 .

On the table, there is the point  (0, -6) .

So the y-intercept of f(x)  is  -6 .

To find the y-intercept of g(x), plug in  0  for  x  and solve for  g(x) .

g(0)  =  2(0) + 6

g(0)  =  6                So the y-intercept of g(x)  is  6 .

6 > -6 ,   so the y-intercept of g(x) > the y-intercept of f(x).  g(x) has a greater y-intercept.