CPhill

The equations for both plans are given by :

Horizon  = 45.99 +  .06x      where x is the number of minutes > 700

Singular = 29.99  + .35x

To find out where horzon's plan is the better deal, we need to solve this inequality

45.99  + .06x  <  29.99 + .35x        subtract  .06x, 29.99 from each side

16 < .29x   divide both sides by  .29

55.17 < x      [ Horizon's plan is better when the total minutes are  > 700 + 56 ≈   756 minutes ] 

Extra : 

Dash's plan can be modeled by   49 + .02x  where x is the number of minutes  > 500

However....this is for only 500 minutes...to equate the cost for 700 minutes, we need to add the cost for 200 additional minutes :

49  + .02 (200)  =  $53

So Dash's  plan for 700 minutes plus the additional charge of .02 / minute can be modeled by :

53 + .02x

So...to see where this is cheaper than Horizon's plan we have

53 + .02x  < 45.99 + .06x    subtract 45.99 , .02x  from  both sides

7.01  < .04x    divide both sides by .04

175.25 < x    [ Dash's plan is better than Horizon's when the total minutes  >  700 + 176 ≈  876 minutes ]

To find when Dash's plan is better than Singular's we have

53 + .02x  < 29.99 + 35x   subtract  .02x, 29.99  from  both sides

23.01 < .33x     divide both sides by .33

69.72 < x   [ Dash's plan is better than  Singular's when the total minutes >   700 + 70 ≈ 770 minutes  ]

So....Dash's  plan is the best when the number of minutes > 876

3.The graph of the equation y=ax^2+bx+c, where a,b, and c are constants, is a parabola with axis of symmetry x = -3.

Find b/a

This parabola  is  vertical....the axis of symmetry is x  = -3, which means that the  x coordinate of the vertex  is - 3

The x coordinate of the vertex  is given  by  - b /a  

So

-b/a  = -3     multiply both sides by  -1

b / a  = 3

1)   x-y^2+6y=8

Rearrange as

(x - 8)  = y^2 - 6y   complete the square on the right side

x - 8  + 9  =  y^2 - 6y + 9       factor the right side and simplify the left

(x + 1 )  = ( y - 3)^2

In the form  (x - h)  = (y - k)^2....the vertex  is   (h , k)  =   (-1,  3)

See the graph, here :  https://www.desmos.com/calculator/h9ee3oueph

Order the data  from  highest to lowest

25  35  45   50   60   80  90   95   100

The median  is   60

The first quartile is the median of the data points  to  the  left   the median

So...this median is    [35 + 45] / 2   = 80 / 2   = 40   [ just as tertre found  !!! ] 

Mary travels (at a minimum)    4 * 40  = 160 miles

And at a maximum of  4 * 60  = 240  miles

So....she travels between  160  and 240 miles

But...since she drives 50 miles less than Marty, Marty must travel  between 160 + 50  = 210 miles and 240 + 50  = 290 miles

So...the second choice is correct.....

Nice work, Melody!!!

b) 24 + 24x  > 150 + 10x      subtract 10x, 24 from  both sides

14x >  126     divide both sides by 22

x > 9     ...correct  !!!

a) 5x + 2(x - 2) ≤  -10

5x + 2x + 4 ≤ -10

7x + 4 ≤ -10    subtract 4 from both sides

7x ≤  -14     divide both sides by 7

x ≤ -2    correct!!!

arctan (3/1) ≈ 71.57°

Very nice, Gavin  !!!