CPhill

#4       A) (7, 9)   B) (1, 5) 

Midpoint  ( [ 7 + 1] /2 , [ 5 + 9] /2)    =  ( 4, 7)

Slope  =  [9 - 5 ] / [ 7 - 1 ] =  4/6 = 2/3

Neg reciprocal slope = -3/2      (1)

Using  midpoint  and  (1)   we have

y = (-3/2) ( x - 4) + 7

y = (-3/2)x + 6 + 7

y = -(3/2)x + 13

#3     A) (8, 1)  B) (0, -1) 

1)  Find the midpoint  =  ( [ 8 + 0] / 2, [ -1 + 1] / 2)  =  (4, 0 )

2) Find the slope  =  [ -1 -1 ] / [ 0 - 8 ] =   -2/ -8 =  1/4

3) Take the negative reciprocal o the slope =  -4

Using the midpoint and  (3)   we have

y = -4(x - 4)

y = -4x + 16

54 - 10x <  20+7x      add 10x to both sides, subtract 20 from both sides

34 < 17x       divide both sides by 17

2 < x     ⇒    C

No phrases to choose from....!!!!

8y = (x + 1)^2 - 32

8y + 32 = (x + 1)^2

8(y + 4) = (x + 1)^2

The vertex is (-1, -4)

The parabola turns upward

8 = 4p

p = 2

The focus is  (-1, -4 + p)  =  (-1, -4 + 2)   = (-1, -2)

The directrix is  y = -4 - p = -4 - 2  =  -6  ⇒  y = -6

a)  

y = -(1/4)(x - 2)^2 + 5

y - 5 = (-1/4)(x - 2)^2       multiply through by 4

4(y - 5) = -(x - 2)^2

The vertex  is ( 2, 5)

4p = 4

p = 1

This parabola turns downward

The focus is  (2, 5 - p)  = (2, 5 - 1)   =  (2, 4)

The directrix is  y = 5 + p =  5 + 1  = 6   ⇒   y = 6

Variable  !!!!

CORRECT!!!

.20x + 1.80 < 7.80       subtract  1.80 from both sides

1.20x < 6.00      divide both sides by  1.20

x < 5   ⇒   D

[ The only thing strange here is that if she has   7.80.....she sould be able to buy EXACTLY 5 lbs. of tomatoes !!!]

Thanks, DBZ  !!!!