53:15 Which polynomial function f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3? f(x) = 3(x + 5)(x + 4)(x – 2)(x – 9) f(x) = 3(x – 5)(x – 4)(x + 2)(x + 9) f(x) = (x + 5)(x + 5)(x + 5)(x + 4)(x – 2)(x – 9) f(x) = (x – 5)(x – 5)(x – 5)(x – 4)(x + 2)(x + 9)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

2x + 8

step-by-step explanation:

the area of the rectangle is 35units^2.

step-by-step explanation:

graph it and find the distance.

it is a 5*7 rectangle.

therefore the area is 35units^2.

ιт ιѕ вє¢αυѕє:

6: 4= 3/2

18: 8= 9/4

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