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2 years ago

Which expression is equivalent to 1/3b+2/3b−5/6(b+1)?

1 answer:

3 0

First convert -5/6(b+1) to -5/6b-5/6 which looks like:
1/3b+2/3b-5/6b-5/6
second add 1/3b+2/3b=3/3b, convert to 6/6b so:
6/6b-5/6b-5/6
subtract 6/6b-5/6b = 1/6b so:
1/6b-5/6 is the answer

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Line g passes through points (5, 9) and (3, 2). Line h passes through points (9, 10) and (2, 12). Are line g and line h parallel

icang [17]

For this case we find the slopes of each of the lines:

The g line passes through the following points:

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So, the slope is:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {9-2} {5-3} = \frac {7} {2}$

Line h passes through the following points:

$(x_ {1}, y_ {1}) :( 9,10)\\(x_ {2}, y_ {2}) :( 2,12)$

So, the slope is:

$m = \frac {y_ {2} -y_ {1}}{x_ {2} -x_ {1}} = \frac {12-10} {2-9} = \frac {2} {- 7} = - \frac {2} {7}$

By definition, if two lines are parallel then their slopes are equal. If the lines are perpendicular then the product of their slopes is -1.

It is observed that lines g and h are not parallel. We verify if they are perpendicular:

$\frac {7} {2} * - \frac {2} {7} = \frac {-14} {14} = - 1$

Thus, the lines are perpendicular.

Answer:

The lines are perpendicular.

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