Radius of 1 button = r = 3x
Fabric required to cover 1 button = Area of the circle
= 
= 
= 
Total number of buttons = x
Fabric required to cover 1 button =
Fabric required to cover x buttons = 
Hence, fabric required to cover x buttons sq. units
You flip the inequality.
Example: if x > -y and you divide both sides by (-1) then you flip the inequality so: -x < y
Answer:
Option A - Neither. Lines intersect but are not perpendicular. One Solution.
Option B - Lines are equivalent. Infinitely many solutions
Option C - Lines are perpendicular. Only one solution
Option D - Lines are parallel. No solution
Step-by-step explanation:
The slope equation is known as;
y = mx + c
Where m is slope and c is intercept.
Now, two lines are parallel if their slopes are equal.
Looking at the options;
Option D with y = 12x + 6 and y = 12x - 7 have the same slope of 12.
Thus,the lines are parrallel, no solution.
Two lines are perpendicular if the product of their slopes is -1. Option C is the one that falls into this category because -2/5 × 5/2 = - 1. Thus, lines here are perpendicular and have one solution.
Two lines are said to intersect but not perpendicular if they have different slopes but their products are not -1.
Option A falls into this category because - 9 ≠ 3/2 and their product is not -1.
Two lines are said to be equivalent with infinitely many solutions when their slopes and y-intercept are equal.
Option B falls into this category.
Answer:
Step-by-step explanation:
We want to simplify:
We rewrite as:
We split the radical sign to obtain:
Simplify the square root for the perfect squares to get:
Therefore the simplified form is:
