Question

Lines passing through the same point are concurrent. Into how many regions do 35 concurrent lines divide the plane?

Answer 1

The relationship between the lines and the number of region is an illustration of a linear equation.

35 concurrent lines divide the plane into 70 regions

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From the complete question (see attachment), we have the following observations

• $\mathbf{1\ line = 2\ regions}$
• $\mathbf{2\ lines = 4\ regions}$
• $\mathbf{3\ lines = 6\ regions}$

Using the above sequence as a guide, the number of regions for n lines is:

$\mathbf{f(n) = 2n}$

So, when $\mathbf{n = 35}$; i.e. 35 lines

The number of region is:

$\mathbf{f(35) = 2 \times 35}$

$\mathbf{f(35) = 70}$

This means that:

35 concurrent lines divide the plane into 70 regions

Read more about linear equations at:

brainly.com/question/11897796