Question 3 (Fill-In-The-Blank Worth 5 points) (01.03 LC)

What number should be placed in the box to help complete the division calculation?

Long division setup showing an incomplete calculation. 16 is in the divisor, 3426 is in the dividend, and 2 hundreds and 1 tens is written in the quotient. 3200 is subtracted from 3426 to give 226. An unknown value represented by a box is being subtracted from 226.

Numerical Answers Expected!

Answer for Blank 1:

2229Step-by-step explanation:

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!

24 units

step-by-step explanation: