Physics
25 * 30 = 750 cm = 7.5 meters 2/30 = .067 tons or 133 pounds
geometry
9 is side sqrt (9^2 + 9^2) = 9 sqrt 2
geometry
11
math:vertex,axis of symmetry,min/max,
complete the square I will do the last one y = 5 x^2 + x + 4 need 1 as coef of x^2 so divide by 5 y/5 = x^2 + (1/5) x + 4/5 subtract 4/5 from both sides y/5 - 4/5 = x^2 + (1/5)x half of 1/5 is 1/10, square it and add to both sides Y/5 -80/100 + 1/100 = x^2 + (1/5) x + 1/100 y/...
physics
g, 9.81 m/s^2 downward
Algebra
(x+1)(x+2) = A x^2 + 3 x + 2 = A x^2 + 3 x + 2 = 56 x^2 + 3 x - 54 = 0 (x+9)(x-6) = 0 x = 6
Algebra
P = 42 x - 850 x intercept is when P = 0, break even
Algebra
2(2w+1) + 2 W = 35 4 w + 2 + 2 w = 35 6 w = 33 w = 5.5 then L = 2 w + 1 = 12
math
combinations of 20 taken 12 at a time = 20! / [ 12! (8!) ] = 125,970 ( I looked it up in a table of binomial coefficients )
Quadratic to vertex form
y = x^2 + 1 x + 1 y-1 = x^2 + 1 x y-1 + 1/4 = x^2 + x + 1/4 y - 3/4 = (x+1/2)^2 vertex at (-1/2 , 3/4)
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