CPhill

First one 

2x + y   ≥ -4  ⇒  y ≥ -2x - 4

This line will have a negative slope  and a y intercept of -4   .it will be   solid line because of the  " ≥"

y ≥ 2x

This line will also be solid...it will have a positive slope and a y intercept of 0

y - 3  > (1/3) x  ⇒  y  > (1/3)x  + 3

This will be a dashed  line  with a positive slope and  a  y intercept  of 3

We can eliminate the top left graph and the bottom right graph as these have lines with all positive sopes

Let's pick a point  ...say (-1, -1)  and see which equations this sattisfies.....notice that this point makes all three equations false...

So...the correct graph must be the one at the top right since the shaded area of this graph graph does not  include the point (-1, -1)

Less than or equal to 5....there are 5 cards  ...1,2,3,4,5

Multiple of 7....there are 4 cards   ....  7, 14, 21 , 28

So....  [5  + 4 ] / 30   = 9 / 30  =   3 /10

This is an irreducible quadratic  [ cannot be factored  ]

You are correct, RP....63  mph  is the answer  !!!

Here's another way to figure it

Assuming that  the data  points are linear...let  ( x , y)  = ( 4 , 252)  and  (6 , 378)

The slope between these will be the rate of change

[ 378  -252  ] / [ 6  - 4  ]   =  126  / 2   = 63 miles  /  1  hr   

Just as RP  found....!!!!

Using dimensional analysis

1.  2500 m   x   1 km  / 1000m     [cancel  m ] =  [2500 * 1  /1000]km   =  2.5 km

2. 7.1 hr  x  60min / 1 hr   [cancel hr ] =  [7.1 * 60 / 1 ] min  = 426 min

3 . 460 microliters x  1 L  / 1000000 microliters   [ cancel microliters ] =

[ 460 * 1 / 1000000]  mkicroliters  = .00046  L

4.  4.83 kg  x   1000g / 1 kg   [ cancel kg] =  4.83 x 1000/1 =  4830  g

Thanks for that excellent answer, Daisy...!!!

We can also find the slope using the two points Daisy chose in another manner [we actually could use any two points on the line  ....they will give the same result  ]

slope  = [ subtract the y coordinates in some order ] / [ subtract the x coordinates in the same order ]

[ 5 - 3 ] / [ 1 - 0 ]  =   2  / 1    =  2

OK....look at the slope

[ Subtract the y coordinates in some order ] / [ Subtract the x coordinates in the same order ] =

[2 - 2 ] / [ 5 - 1 ] =    0  / 4     =   0

See???

Mathtoo...The common ratio  can be found by dividing a successive term by the preceding one

So   [-5/3 ]  / [ -3/5 ] =  -5/3 * -5/3   =  25  / 9

Check for yourself that  [-125 / 27]  / [ -5/3 ]  gives the same result...!!!

Note....NSS....when  the y coordinates are the same....the slope has to  be 0.....because both points lie  - in this case  - on the line   y  = 2...this is a horizontal line....and a horizontal line always has a slope  = 0

Does that make sense???....if not....we  can prove it mathematically, if you want

Let  the  x coordinates  of the vertices be   x1, x2 and x3

And we know that  x1  + x2  + x3  = 10

And the   x coordinates of the midpoints of the sides  are

( x1 + x2 ) / 2     =  x1 /2 +  x /2    

(x2 + x3)/2  =     x2 / 2  +  x3 /2

(x1 + x3) / 2  =    x1 /2  + x3/2

Summing these, we get

(x 1/ 2) *2   +  ( x2 / 2) * 2   +  (x3 /2) *2  =

x1   +  x2  +  x3     =      10