Me, 1. jack ran 4 miles more than ryan ran. the sum of their distances is 26 miles. how far did ryan run? the domain of the solution is {0,4,11,22} 2. explain how the order of operations determines how you simplify a numeric expression. provide examples to illustrate your points.

Ryan ran "r" miles.

Jack ran 4 miles more than Ryan so he ran r+4 miles

sum equals 26 miles

r + r + 4 = 26

2r + 4 = 26

2r = 26 - 4

2r = 22

r = 22/2

r = 11 miles

The order of operations is a set of rules that define which operations you perform first to evaluate a mathematical expression..  

remember the acronym PEMDAS

Parenthesis - You start by doing math in parenthesis

Exponents - Next do any exponents or radicals

Multiplication & Division - Then do multiplication or division

Addition & Subtraction - last do any left over addition or subtraction

example:

(2+3)² + 3 × 4 ÷ 6 - 1 = ??

parenthesis

(5)² + 3 × 4 ÷ 6 - 1 = ??

exponents or radicals

25 +  3 × 4 ÷ 6 - 1 = ??

multiplication/division (3 × 4 ÷ 6 = 2)

25 + 2 - 1 = ??

addition/subtraction

26

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1