Please factor and find the zeros of each relation. (19 marks) E. y = 3x^2 + 12x
F. y = x^2 + 20x + 100

Step-by-step explanation:

y=3x^2+12x = 3x (x+4)

zeroes: x={0, -4}

y = x^2+20x+100 = (x+10)^2

zeroes: x = -10 (twice)  

or x={-10, -10}

step-by-step explanation:

mean or average is 40.6

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt