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natulia [17]
3 years ago
14

(1.)Find the slope of the line that passes through the given pair of points. (If an answer is undefined, enter UNDEFINED.) (?a +

3, b ? 3) and (a + 3, ?b) *******(2.)If the line passing through the points (a, 1) and (6, 5) is parallel to the line passing through the points (2, 7) and (a + 2, 1), what is the value of a?
Mathematics
1 answer:
jekas [21]3 years ago
8 0

Answer:

1. The slope of the line is m=\frac{-2b+3}{2a}.

2. The value of a is 18.

Step-by-step explanation:

If a line passes through two points, then the slope of the line is

m=\frac{y_2-y_1}{x_2-x_1}

(1)

It is given that the line passes through the points (-a + 3, b - 3) and (a + 3, -b). So, the slope of the line is

m=\frac{-b-(b-3)}{a+3-(-a+3)}

m=\frac{-b-b+3}{a+3+a-3)}

m=\frac{-2b+3}{2a}

The slope of the line is m=\frac{-2b+3}{2a}.

(2)

If the line passing through the points (a, 1) and (6, 5), then the slope of the line is

m_1=\frac{5-1}{6-a}=\frac{4}{6-a}

If the line passing through the points (2, 7) and (a + 2, 1), then the slope of the line is

m_2=\frac{1-7}{a+2-2}=\frac{-6}{a}

The slopes of two parallel lines are same.

m_1=m_2

\frac{4}{6-a}=\frac{-6}{a}

On cross multiplication we get

4a=-6(6-a)

4a=-36+6a

4a-6a=-36

-2a=-36

Divide both sides by -2.

a=18

Therefore the value of a is 18.

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Answer: the rate of the jet in still air is 685 mph and the rate of the jetstream is 75 mph

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