2(-322 + x + 1) - 2(4x - 3x + 1)?
explain your reasoning or show the work that you decide on your answer.

-644

Step-by-step explanation:

2(-322 + x + 1) - 2(4x - 3x + 1)

First distribute the 2 and the -2 over the parentheses:

= - 644 + 2x + 2 - 8x + 6x - 2   Now add like terms.

= -8x + 2x + 6x - 644 + 2 - 2

= -8x + 8x - 644

= -644.

-644

Step-by-step explanation: by expanding, 2(-322+x+1) = -642+2x

And -2(4x-3x+1)= -2x-2.

Adding together, we have

-642 +2x -2x-2= -644

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

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!