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Mathematics : asked on teethebeast
 11.04.2023

You are setting up a zip line in your yard. you map out your yard in a coordinate plane. an equation of the line representing the zip line is y=2x+4y=2x+4. there is a tree in your yard at the point (−4, 11)(−4, 11). each unit in the coordinate plane represents 1 foot. approximately how far away is the tree from the zip line? round your answer to the nearest tenth.

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17.02.2022, solved by verified expert
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Nitin Arora
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Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee
5 288 answers
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The question is an illustration of distance between a point and a line.

The distance between the zip line and the tree is 6.70 feet

The zip line equation is given as:

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

The coordinates of the tree is given as:

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

The distance (d) between an equation and a point is:

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

Where:

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

Rewrite You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33 as You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

By comparison:

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33 and You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

So, we have:

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

Evaluate square root

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

Remove absolute bracket

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33  

You are setting up a zip line in your yard. you, №15217823, 11.04.2023 03:33

Hence, the distance between the zip line and the tree is approximately 6.70 feet

Read more about distance at:

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Faq

Mathematics
You are setting up a zip line in your yard. you map out your yard in a coordinate plane. an equation of the line representing the zip line is y=2x+4y=2x+4. there is a tree in your yard at the point (−4, 11)(−4, 11). each unit in the coordinate plane represents 1 foot. approximately how far away is the tree from the zip line? round your answer to the nearest tenth.
Step-by-step answer
P Answered by PhD
Solving this problem needs the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / √  (a^2 + b^2)

 
So we are given the equation: y = 2 x + 4

Rewriting this would be: y – 2 x – 4 = 0 ->  a = -2, b = 1, c = -4

 We are also given the points:

(-4, 11) = (x, y)

 Plugging it in the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / √ [(- 2)^2 + (1)^2]

= 15 / √ (5)

= 6.7

 So the tree is approximately 6.7 feet away from the zip line.
Mathematics
You are setting up a zip line in your yard. you map out your yard in a coordinate plane. an equation of the line representing the zip line is y=2x+4y=2x+4. there is a tree in your yard at the point (−4, 11)(−4, 11). each unit in the coordinate plane represents 1 foot. approximately how far away is the tree from the zip line? round your answer to the nearest tenth.
Step-by-step answer
P Answered by PhD
Solving this problem needs the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / √  (a^2 + b^2)

 
So we are given the equation: y = 2 x + 4

Rewriting this would be: y – 2 x – 4 = 0 ->  a = -2, b = 1, c = -4

 We are also given the points:

(-4, 11) = (x, y)

 Plugging it in the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / √ [(- 2)^2 + (1)^2]

= 15 / √ (5)

= 6.7

 So the tree is approximately 6.7 feet away from the zip line.
Mathematics
The value of a collectible coin can be represented by the equation y = 2 x + 15, where x represents its age in years and y represents its total value in dollars. What is the value of the coin after 19 years? $2 $23 $38 $53
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

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The answer is in the image 

The answer is in the image 

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A 4300-N force from a car s engines produces an acceleration of 3.3 m/s2. What is the mass of the car? A. 4300 kg B. 1300 kg C. 14,000 kg D. 390 kg
Step-by-step answer
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F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

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If a salesperson makes 6% commission, how much would they make from a $1,800 sale?
Step-by-step answer
P Answered by PhD

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

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Stefania pure 2 liters of orange juice and 1.5 liters of pineapple juice into a punch bowl how many kiloliters are in the punch bowl
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The answer is in the image 

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How much would the tip be if you left 18% on a 75.45 steak dinner?
Step-by-step answer
P Answered by PhD

tip=18% of 75.45

     =18/100 * 75.45 = $13.581

Tip = $13.581

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Determine the area of a rectangle with length of 12.4 cm and a width of 8.8 cm.
Step-by-step answer
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Area of rectangle= L*b

here,

L=12.4 cm

b= 8.8 cm

A= L*b

= 12.4 * 8.8 = 109.12 cm^2

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The gymnasium at Audubon middle school is 5/6 the height of a 30-foot-tall building that is next to the gymnasium what is the height (h) in feet of the gymnasium
Step-by-step answer
P Answered by PhD

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet

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