The three figures below are composite figures:
two-dimensional diagrams built from layered lines, circles, polygons,
and other basic shapes. The mathematical challenge here is to find the
total amount of colored area in the figure, given some baseline
measurement. For example, assume that the large circumscribing circle
in each of the examples below has area 1.
I'm not actually sure what your question really is, but I'll take a guess.
Before I go to work on that problem, let me ask you a few other questions:
-- If you have 2 cows and you subtract 4 cows, what do you end up with ?
-- If you have 2 rocks and you subtract 4 rocks, what do you end up with ?
-- If you have $2 in the bank and you subtract $4, what do you end up with ?
-- If you have 2 puppies and you subtract 4 puppies, what do you end up with ?
-- If you have 2x and you subtract 4x, what do you end up with ?
Did you say "negative 2 of them" for each question ? Good, good.
So now, if you have 2 ' y⁵ 's and you subtract 4 ' y⁵ 's, what do you suppose
you would end up with ?
I'm going to take your points and just let you think about that, because I think
I've given you all the help you need to answer the question on your own.
(That's if I actually understand <u>what</u> your question is.)
3x -y ⩾ 6
3x - 6 ⩾ y
now, with inequalities, what we do is, we graph the line of 3x - 6 = y, and then we shade the "true region".
if we pick a point on say hmmm (4, 0), namely x = 4 and y = 0, we can plug that in the inequality and see what we get,
3(4) - 0 ⩾ 6
12 - 0 ⩾ 6
12 ⩾ 6
is 12 really greater or equals to 6? well yes, therefore, the point (4, 0) lies on the "true region", since it's true, 12 is indeed ⩾ 6, so, where that point is, we shade.
now, the ⩾ means equals to or greater, and therefore, since the values could also equal the boundary points, the line is a solid line, because it includes the line itself, as well as the shading.
check the picture below.
[ Answer ]
[ Explanation ]
- Calculate Slope Given (-2, 6) & (0, 4)
--------------------------------
Slope (m) = -1
Ф = 315°
Distance (d) = 2.8284271247462
ΔX = 2
ΔY = -2
m - Slope
Ф - Angle of incline