Our current equation is: 2(4z - 9 - 11) = 166 - 46 First, let's simplify the right side of the equation. 166 - 146 = 120 Now, we have: 2(4z - 9 - 11) = 120
Since we have 2(4z - 9 -11), this side of the equation is looking for the "Distributive Property." The Distributive Property allows any variable/number outside of a parenthesis to multiply by all inside numbers/variables.
For example: 3(1 + 2) 3(1) + 3(2) 3 + 6 9.
Now that we've explained what we're dealing with, let's distribute!
2(4z - 9 - 11) 2(4z) + 2(-9) + 2(-11) Remember when you multiply a positive number by a negative, it becomes a negative product. 8z -18 -22 = 120 Combine like-terms. -18 -22 = -40 (When subtracting a positive from a negative, you're essentially just adding two positive numbers with negative signs as the sum.) We now have: 8z -40 = 20 Add 40 to both sides. 8z = 60 Divide both sides by 8 to solve for z. 8z / 8 = z 160 / 8 = 20
Area of the square: A s = s². Area of the circle: A c = ( 1/2 s )² π = 1/4 s² · 3.14 = 0.785 s² Area inside the square but outside the circle: s² - 0.785 s² = 0.215 s² The ratio: 0.215 s² : s² = 0.215 : 1 = 215 : 1000 = 43 : 200 .
