Mathematics, 20.09.2019 00:00 nauticajanke03

Asegment has endpoints a(3, 4) and b(5, 8). what is the slope of the line parallel to the segment ab, and what is the slope of the line perpendicular to the segment ab?

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Answer from: starlabayliss

For this case we have that by definition, the slope of a line is given by:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

We have the following points: $(x_ {1}, y_ {1}) :( 3,4)\\(x_ {2}, y_ {2}) :( 5,8)$

Substituting:

$m = \frac {8-4} {5-3} = \frac {4} {2} = 2$

By definition, if two lines are parallel then their slopes are equal. Thus, a line parallel to segment AB has slope m = 2 .

On the other hand, if two lines are perpendicular, then the product of their slopes is -1. So:

$m * 2 = -1\\m = - \frac {1} {2}$

Thus, a line perpendicular to segment AB has slope $m = - \frac {1} {2}$

a line parallel to segment AB has slope m = 2 .

a line perpendicular to segment AB has slope $m = - \frac {1} {2}$

Answer from: connorvoss7345

Slope of a line perpendicular to the line AB = $-\frac{1}{2}$

Slope of a line parallel to AB = 2

Step-by-step explanation:

Let slope of a line = $m_{1}$

And slope of the other line is = $m_{2}$

If these lines are parallel then $m_{1}=m_{2}$

If these lines are perpendicular then $m_{1}\times m_{2}=-1$

Slope of the line passing through two points (x, y) and (x', y') = $\frac{y-y'}{x-x'}$

Therefore, slope of the line passing through A(3, 4) and B(5, 8) = $\frac{y-y'}{x-x'}$

$m_{1}=\frac{8-4}{5-3}$

$m_{1}=2$

a). If a line having slope $m_{2}$ is parallel then $m_{1}=m_{2}$

$m_{2}=2$

b). If a line having slope $m_{2}$ is perpendicular then $2\times m_{2}=-1$

$m_{2}=-\frac{1}{2}$

Answer from: Quest

b. the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

Answer from: Quest

m∠5 + m∠3 = m∠1 is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6 is true

m∠2 +m∠3 +m∠5 = 180 is true

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Asegment has endpoints a(3, 4) and b(5, 8). what is the slope of the line parallel to the segment ab...