Simplify the expression by combining like terms . 2(3t + 4) + 6(t + 2)

2(3t + 4) + 6(t + 2)

First, distribute. The Distributive Property: a(b + c) = ab + ac. Distribute 2 and 6 to get rid of the parentheses.

2(3t + 4) + 6(t + 2)

6t + 8 + 6(t + 2)

6t + 8 + 6t + 12

Collect like terms (constants and variable terms).

6t + 8 + 6t + 12

12t + 20

The expression now has one variable term and one constant; it cannot be simplified further.

12t + 20

Distribute 2 to 3t and 4, and 6 to t and 2

2(3t + 4) = 6t + 8

6(t + 2) = 6t + 12

Combine like terms:

6t + 8 + 6t + 12 = 12t + 20

12t + 20 is your answer

hope this helps

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!

answer: 1, 3 and 5 are correct

step-by-step explanation: