CPhill

If   FG / GH   = 1......then G is the  midpoint of FH

So....to find the  x coordinate of  G we have  that  [ 6a + a ]  / 2 =   (7/2)a 

All the possible  numbers  are those from  - infinity  up to, bur not including 1

We obviously cannot list every value

(2) is  missing  something

" At the end of which week will my team have won at least ???? of its games total for the first time in the season? "

A couple

6)  hrs in a week  =  24 * 7  = 168......can you  take it from here??

5)    -4x > -24                   divide both sides by -4 and  reverse the inequality  sign

       x <  6   →   (-inf, 6)  

4)   2x ≥  -10      divide both sides by 2

       x ≥  -10/2

      x ≥  -5   →  [ -5, inf )

b^2 - a^2  =72

(b - a) ( b + a)  = 72

(19 -17) (19 + 17)  = 72

(2)  ( 36)  = 72

a = 17   b =19    c =21

c^2 - b^2  =  21^2  - 19^2  =  (21 - 19) (21 + 19)  = (2) (40)  =   80

-2 ( s - 7)  >  4s + 8

-2s + 14  > 4s + 8

6 > 6s

1 > s

Or we can read this as

s < 1

(-inf, 1 )

Let

D = (0, 0)

C = (1,0)

E = (0, 1/2)

F = (1/2, 1)

B = (1,1)

Slope of line connecting EB = [ 1 -1/2 / [ 1 - 0 ] =   1/2

Equation of lime  connecting EB    ....y = (1/2) x + 1/2      [ 1 ] 

Slope of line connecting CF   =  [ 1 - 0 ] / [1/2 -1 ] = 1 / -1/2   =  -2 

Equation of line  connecting CF  ......y = -2 ( x - 1) ..... y = -2x + 2    [2]

x intersection [1] and [2]  = x value of G

(1/2)x + 1/2  = -2x + 2

(5/2)x = 3/2

5x = 3

x = 3/5

And using either line to find the y value of G

y= -2(3/5) + 2 =  -6/5 + 10/5 =  4/5

G = ( 3/5 , 4/5)

DG =  sqrt  [ (3/5)^2  + (4/5)^2 ]  = sqrt  [9/25 + 16/25 '  =  sqrt  [25/25]  = sqrt [ 1 ]  =  1

LOL!!!

Total distance traveled =  80 (1)  + 60 (2)  = 80 + 120 =  200

Avg rate = Distance / Time   =  200 / [ 1 + 2 ] =   200 / 3 =   66 + 2/3 mph

If the lateral face is 75 m^2  and  the slant height is 25 m,  we  can find the  length of  one side of the base  as

75 = (1/2) base * 25    multiply by 2 on  both  sides

150 = base * 25     divide both sides by 25

6 (m)  = base length

y  >  -  (1/2)x  + 2

Easiest way is to list the coordinates of the points and test these in the inequality

        (x, y)

A = (3,3)    OK

B = (-5,- 4) No

C = (-4, 1)   No

D = (6, -1) No

E = (6,6)  OK

F = (-2, -2)  No

G = (-3, 5)  OK

H = (3, -6)  No

I  = ( 2, 4)  OK

J  = (2, -3) No