Question

find the number of bounded and unbounded regions that 4 lines in general position divide a plane into. then find the number of regions for 5 through 10 lines. organize the information in a chart. (ALL THE BLANK SPOTS IN THE ATTACHMENT ARE WHAT I AM CONFUSED ON) please help I have till friday to finish!

Answer 1

To find the number of bounded and unbounded regions that 4 lines in general position divide a plane into, we can use the formula: Regions = n*(n+1)/2 + 1, where n is the number of lines. For 4 lines, this gives us 11 regions. We can continue this pattern to find the number of regions for 5 through 10 lines and organize the information in a chart.

Step-by-step explanation:

To find the number of bounded and unbounded regions that 4 lines in general position divide a plane into, we can use the formula: Regions = n*(n+1)/2 + 1, where n is the number of lines. For 4 lines, this gives us: Regions = 4*(4+1)/2 + 1 = 11.

For 5 lines, the formula gives us: Regions = 5*(5+1)/2 + 1 = 16.

We can continue this pattern to find the number of regions for 6 through 10 lines and organize the information in a chart:

Number of Lines Number of Regions
4 11
5 16
6 22
7 29
8 37
9 46
10 56

Answer 2

10, 15, 21, 28, and 36

Step-by-step explanation:

The rule is the number of line which is n. (n-2)*(n-1) divided by 2