Area of hexagon = base * (apothem/2) * 6 = 3(base*apothem)
=3*15*20
=900 square units.
However, a hexagon consists of 6 equilateral triangles in which the apothem is 0.866 times the base, meaning that the apothem is shorter than the base.
Perhaps the base is 20 and apothem 15. The answer will come to be the same though.
6 feet * 7 feet = 42 feet²
18 feet * 21 feet = 378 feet²
42 feet² was painted for $52
1 feet² will be painted for $52/42
378 feet² will then be painted for: ($52/42) * 378
= $468
Hence 18 feet by 21 feet will be painted for $468
Hope this helps.
Answer:
(x,y) maps to (-y,x).
Step-by-step explanation:
Use vertex I as an example.
Pre-image I is graphed at point (-3,2), while image I' is graphed at point (-2,-3) .
In order to change between these points, the x and y coordinates must be swapped, as well as multiplying the y coordinate by -1.
An easy way to do this is by using the simplest equations you can:
x + y and x - y
(3, 5) is (x, y). all you have to do is plug those into your equations and get a result, so:
x + y = 8
(because 3 + 5 = 8)
x - y = -2
(because 3 - 5 = -2)
and those can serve as your system of equations.
you can check it by solving by substitution:
x - y = -2
x + y = 8
solve one of the equations for a single variable:
x = y - 2
plug it into the second equation:
(y - 2) + y = 8
y - 2 + y = 8
2y - 2 = 8
2y = 10
y = 5
then plug that result back into the equation:
x + y = 8
x + 5 = 8
x = 3
