Expert: Richard J. Raridon - 5/11/2007

Question
here are a few questions I need help with? Thanks so much!!!

1.) solve -9(x-3)^2=-7

2.) Solve 9x^2=14

3.) The demand and supply equations for a certain item are given by
d= -5p +40
s= -p^2+30p-8
find equilibrium price?

4.) Solve by using quadratic formula
3x^2=11x+4

5.) Solve x^2=5x + 2

6.) A rectangler garden is to be  surrounded by a walkway of constant width.  The garden's dimensions are 30ft by 40 ft.  The total area garden plus walkway is to be 1800ft^2.  What must be the width of the walkway to the nearest thousandth?

Answer
1) (x-3)^2 = 7/9
x-3 = +/- (7/9)^1/2 so x = 3 +/- (7^1/2)/3
2) x^2 = 14/9, x = +/- (14^1/2)/3
3) -5p+40 = -p^2 +30p -8
P^2 -35p +32 = 0 so p = 0.94, 34.06
4) you can factor 3x^2 -11x -4 = (3x+1)(x-4)
5) x = [5 +/-(33)^1/2]/2
6) if w = width, then (30+2w)(40+2w) = 1800
so w = 3.860