a rectangle has a diagonal 20 inches long that forms angles of 60 and 30 with the sides. find the perimeter of the rectangle.
1 answer:
Answer:
P = 47.32
Step-by-step explanation:
This triangle is a special triangle. Because it is 30-60-90 it will have measurements similar to . If the longest side is 20 then it corresponds to 2. This means the shortest side of 1 corresponds to half this or 10.
So the triangle will have sides .
To find the perimeter add all these lengths.
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Answer:
Solutions: b, c, d, e
Not Solutions: a
Step-by-step explanation:
There are two ways to solve this problem: you could graph the system and check which points fall in the solution set or you could substitute the and
values of each point into the inequalities that make up the system. I'm going to use the former because it's quicker, in my opinion.
Step 1: Graph
Rewriting the first inequality gives us:
To graph this, draw the line and then, because the sign is "
", shade below the line and make it a dashed line. This is the red inequality on the graph.
Rewriting the second inequality gives us:
To graph this, draw the line and then, because the sign is "
", shade below the line and keep it a solid line. This is the blue inequality on the graph.
The solution set of the system will be the region where the two shaded areas overlap, which is the purple area.
Step 2: Check Points
Now, all we need to do is check whether each point lies in the purple region on the graph.
lies above the purple region, but it isn't in the region, so it is not a solution to the system.
does lie in the purple region, so it is a solution to the system.
does lie in the purple region, so it is a solution to the system.
does lie in the purple region, so it is a solution to the system.
Finally, lies in the purple region, so it is a solution to the system.
Hope this helps!
