First of all you know it wiill be a positive slope as both the rise and the run are negative. a negative divided by a negative equals a positive. so you can plot the points (2,3) and (-2,-3) as they will be points on this line. next you take a straight line and place it so that both points are intercepted. then extend the line outwards.
Answer:
see below
Step-by-step explanation:
Thankfully, these inequalities are already simplified, so all we have to do here is graph the inequalities as they are.
To graph y > 2x - 3, first draw the line y = 2x - 3. Make sure to make the line dashed because the sign is ">", which means that the points on the line do not belong to the solution set. Now, we need to figure out which side of the line to shade on. Since the sign is ">", that means that we will shade "above" the line, or on the left side of it. (This is the blue area in the image.)
Repeat a similar process to graph y < x + 1. As usual, first draw the line y = x + 1, and again, make it a dashed line since the sign is "<". And since the sign is "<", that means that we will shade "below" the line, or on the right side of it. (This is the red area in the image.)
The solution set to this system is the area where the two shaded areas overlap, which is the purple area in the image below. Hope this helps!
Octagon, stop sign.
Eight isoscles triangles. It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.
So each isosceles triangle has area (1/2)(9.9)(12) and we have eight of them,
area = 8(1/2)(9.9)(12) = 475.2
Answer: 475.2
Usually we wouldn't be told 9.9 -- this is the baby version. We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.
The area of the right triangle with long leg 12, short leg x,
tan 22.5 = x/12 or
x = 12 tan 22.5
Twice that is what we're told is 9.9; let's check:
2x = 24 tan 22.5 = 9.941125496954282
The area of the little right triangle is
(1/2) 12 × 12 tan 22.5
and there are 16 of these
16 (1/2) 12 × 12 tan 22.5 ≈ 477.174
<span>the smaller angle is 2x = 2 times 18 = 36 degrees.
the larger angle is 3x = 3x = 3 * 18 = 54 degrees.
</span>
Answer:18
Step-by-step explanation:
1/2x4+=2
4x4=16
16+2=18
