CPhill

Since this is a straight line....The slope will give us the rate of change

We have the points   (0, 400)  and  (12 ,0)

slope  =   [ 400 - 0 ] / [ 0 - 12 ] =  -400 /12    =  -100/3....just as Mathtoo found !!!

Correct  !!!

Look at the graph carefully, NSS

The broken line  is for Store B

The solid line is  for Store A

In which month is the broken line above the solid line  ??

I agree with your choice, NSS ⇒  "C"

A little hard to tell but 1998 was right on the average, with 2000 and 2002 just a little below the average...so    1998, 2000, 2002 ⇒  "C"

I think your question left something out at the end, Ten Tacion....

1/6....What is   7/6  - 1 ???

11/14 ....What is  1 - 3/14  ???

We can use dimensional analysis to solve this....

1 ml   / 125 mg  x  15 mg / 1 kg  x  1 kg / 2.2 lbs  x 66 lbs

Cancel the units  and we have  (15 / 125) * (66/2.2) ml  =  3.6 ml  

OK...similar to the last one

This parabola also turns upward....

The x coordinate of the vertex is    -3/2

So...put this into the function  and set up an inequality where the function is  greater than  -2

Thus...when we find solutions....we wil exclude those from the possible answers...so we have

(-3/2)^2 + 3(-3/2)  + c  > -2    simplify

9/4 - 9/2 + c > -2

-9/4 + 2 > - c

-9/4 + 8/4 > - c

-1/4 > - c    divide both sides by -1 and reverse the inequality sign

1/4 <  c

So...-2  will be in range whenever c  ≤ 1/4

See the graph, here : https://www.desmos.com/calculator/8uqpiabiz6

Note that when c = 1/4....-2 is still in the range

But..for instance..when c  = 1/2, -2 is out of range

x^2 + bx + 2

This parabola turns upward....so...the x coordinate of the vertex is given by

-b/ 2  = x

So....we'd ike to solve this

(-b/2)^2 + b(-b/2)  + 2  >  - 2    simplify

b^2/4 - b^2/2 + 4  >  0     

-b^2/4 + 4 > 0

-b^2 + 16 > 0  multiply through by  -1  and change the inequality sign

b^2 - 16 < 0

(b - 4) ( b + 4) < 0

The values  that make this true  are  ( -4, 4)

So...the values that put  -2 out of range  are  (-4, 4)