(w + 13)^2 = (3w + 7)(2w + 5) expand both sides
2^2 + 26w+169 = 6w^2 +29w + 35 now gather like terms all on one side of the eqaution
then use quadratic formula to calc w values
2.36*(1+y)^6 = 6 divide both sdes of the equation by 2.36
(1+y)^6 = 6/2.36 now take the sixth root of both sides ...with calculator (you could also use LOGs)
1+y = 1.16826 You can take it from here .....
2x(x + 10) = -50 expand to
2x^2 + 20x + 50 = 0 divide by 2 (for simplicity.....you could just use Quadratic Formula here)
x^2 + 10 x + 25 = 0
(x+5)(x+5) = 0 x = -5
1/2 r = y-2 y= 1/2r +2
1/2 r = 1/3 o 0= 3/2 r
1/2 r = 2 + w w = 1/2 r -2
r r
Add right column 3.5 r equals all of the marbles = 35
r = 10
multiply first equation by 7 to get 14x = 35y
multiply second equation by 5 to get 35y=75z use 1st equation in second equation
14x = 75z
z/x 14/75
t-27 = 4t subtractt from both sides
-27 = 3t divide both sides of the equation by 3
t = -9
24 -30 = 7 days in Nov + 19 days in Dec = 26 days
26 days * 6 show/day = ......... shows
side x side = area
side2 = 221 solve for 'side'
To have only one real root, the discriminant of the quadratic formula (b^2 - 4ac) for this equation must = 0
8^2 - 4 (a)(6) = 0
64 - 24 a = 0
24a = 64
a = 64/24 Simplify/reduce as needed.....
4= 12 (1 - .5)^n n = # half lives
1/3 = .5n
n= 1.585
1.585 * 1620 =2567.64 years
