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2 years ago

1.) Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?

Mathematics

1 answer:

erastova [34]2 years ago

3 0

The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

<h3>How to find the length of Line Segment?</h3>

1) The coordinates of the point located 5/6 of the way from A to B is;

x = ⁵/₆(7 - 1) + 1

x = 6

y = ⁵/₆(-4 - 8) + 8

y = -2

x, y = (6, -2)

2) The coordinates of the point located ¹/₄ of the way from A to B is;

x = -3 + ¹/₄(5 - (-3))

x = -1

y = 0 + ¹/₄(4 - 0)

y = 1

x, y = (-1, 1)

3) The coordinates of the point located ¹/₆ of the way from A to B is;

x = ¹/₆(7 - 1) + 1

x = 2

y = ¹/₆(-4 - 8) + 8

y = 6

x, y = (2, 6)

Read more about Length of Line Segment at; brainly.com/question/27064838

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Answer:

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2 years ago

A lake was stocked with 360 trout. Each year, the population decreases by 10. The population of trout in

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Answer:

Part A) The y-intercept is the point (0,360) and the x-intercept is the point (36,0)

Part B) The graph in the attached figure

Part C) see the explanation

Step-by-step explanation:

Part A) Find the intercepts

Let

x ----> the number of years

f(x) ----> the population of trout in the lake

we have

$f(x)=360-10x$

This is a linear function in slope intercept form

$f(x)=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

$m=-10\ \frac{trout}{year}$ ---> is negative because is a decreasing function

$b=360\ trouts$ ---> initial value

The y-intercept is the point (0,360)

<em>Find the x-intercept</em>

The x-intercept is the value of x when the value of f(x) is equal to zero

For f(x)=0

$0=360-10x$

Solve for x

$10x=360\\x=36$

The x-intercept is the point (36,0)

Part B) Graph the function

Plot the intercepts and join the points to graph the line

see the attached figure

Part C) Complete the interpretation of the intercepts

The x-intercept is the value of x when the value of f(x) is equal to zero

In this context, the x-intercept is the number of years, when the population of trouts is equal to zero

In 36 years, the population of trouts will be equal to zero

The y-intercept is the value of f(x) when the value of x is equal to zero

In this context, the y-intercept is the population of trouts when the number of years is equal to zero

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4 years ago

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Ainat [17]

Answer:

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Step-by-step explanation:

Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.

To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,

b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.

So, making, Ф subject of the formula, we have

b² - (a² + c²) = 2accosФ

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Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

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Ф = cos⁻¹{-51/96}

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h = asinФ

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PLEASE HELPPPPPPP!!!!!

Tanya [424]

Approx 7. Brainliest?