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wlad13 [49]
2 years ago
6

Write an equation of the line that passes through the given points. (-1,5) and (2, - 7)

Mathematics
1 answer:
Vanyuwa [196]2 years ago
6 0

Answer:

The equation of the straight line is 4x +y = 1

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given points are (-1,5) and ( 2,-7)

Slope of the line

m =\frac{y_{2}-y_{1}  }{x_{2} -x_{1} }  =\frac{-7-5}{2-(-1)}  = \frac{-12}{3} = -4

slope of the line m = -4

<u><em>Step(ii):-</em></u>

The equation of the straight line passing through the point (-1,5) and having slope 'm' = -4

y - y_{1} = m( x-x_{1} )

y - 5 = -4 ( x-(-1))

y -5 = -4 x -4

4 x + y -5 +4=0

4x +y -1 =0

<u><em>Final answer:-</em></u>

The equation of the straight line is 4x +y = 1

<u><em>  </em></u>

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Answer:

The actual area of the town is 14 miles.

Step-by-step explanation:

Since you know that the scale is 1 inch:4 miles and that the map shows a town with an area of 3.5 inches, you can expressed this as follows:

Scale: 1 inch:4 miles

map area: 3.5 inches

If the actual area is x, you can say that:

3.5:x=1:4

This would be:

\frac{3.5}{x}=\frac{1}{4}

Now, you can solve for x:

x=(3.5*4)/1

x=14

According to this, the answer is that the actual area of the town is 14 miles.

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Please add the diagram

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It is given in the question that

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Therefore in triangles BAD and BCD,

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The calculated areas of both are the same instead of using the different formulas that are 43. 5 squared unit.

<h3>What is the area of a regular polygon?</h3>

The area of the polygon is the product of half of the apothem of the triangle and perimeter.

The area of the polygon = \frac{1}{2} \times h \times p

The side of the triangle is 10 units.

Apothem of an equilateral triangle

s = \frac{\sqrt{3} a}{6}

s= \sqrt{3} \times 10/6

s = 2.88

Here, a is the side of the triangle.

Thus the apothem of the triangle is 2.9 units.

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Perimeter of the equilateral triangle ,

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P = 30

Therefore, the perimeter of the equilateral triangle is 30 units.

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A = 1/2 \times 2.9 \times 30

A = 43.5

Thus the area of the equilateral triangle is 43.5 squared units.

Therefore, The calculated areas of both are the same instead of using the different formulas.

Learn more about the apothem;

brainly.com/question/10580427

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