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forsale [732]
3 years ago
9

Find the value of n so that the line perpendicular to the line with the equation -2y + 4 = 6x + 8 passes through the points at (

n, -4) and (2, -8).
Mathematics
1 answer:
kolezko [41]3 years ago
6 0
If the line must be perpendicular to the equation, that means the slope is the reciprocal of the one in the given equation. So first we find that, the slope of the given equation. 

- 2y + 4 = 6x + 8
- 2y = 6x + 4
 
y = - 3x - 2

So the slope of the given equation is - 3x. That means the slope of our perpendicular equation must be 1/3x 

Now to find the value of n, plug in our given information and perpendicular slope into the slope equation:

Slope = (Y₂ - Y₁ ) / (X₂ - X₁)

1/3 = (- 8 - (-4)) / (2 - n)
1/3 = (- 8 + 4) / (2 - n)
1/3 = ( - 4) / (2 - n)

Multiply both sides by (2 - n) to get the binomial out of the denominator

(1/3)(2 - n) = - 4

Multiply both sides by 3 to isolate the binomial

2 - n = - 4(3)
2 - n = - 12

Subtract 2 from both sides to isolate the variable

- n = - 14

Divide by - 1 to get rid of the negative.

n = 14. Your coordinate is ( 14, - 4)

Now to find the equation that is perpendicular. 

y = 1/3x + b

Plug in either of the coordinates. I'm going to use the ordered pair we just found. 

- 4 = 1/3(14) + b
- 4 = 14/3 + b
- 12/3 = 14/3 + b

Subtract 14/3 on both sides.

- 26/3 = b

Your equation is y = 1/3x - 26/3


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C

Step-by-step explanation:

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6 0
3 years ago
I need help with letters (D) and (E). My model equation from letter (C) is: P = -55/4 t+ 340.
IceJOKER [234]

Answer:

(a) The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope is m = -55/4

The slope means the rate of decreases of the owl population was 55/4

per year (P decreased by 55/4 each year)

(c) The model equation is P = -55/4 t + 340

(d) The owl population in 2022 will be 216

(e)  At year 2038 will be no more owl in the park

Step-by-step explanation:

* Lets explain how to solve the problem

- The owl population in 2013 was measured to be 340

- In 2017 the owl population was measured again to be 285

- The owl population is P and the time is t where t measure the numbers

 of years since 2013

(a) Let t represented by the x-coordinates of the order pairs and P

   represented by the y-coordinates of the order pairs

∵ t is measured since 2013

∴ At 2013 ⇒ t = 0

∵ The population P in 2013 was 340

∴ The first order pair is (0 , 340)

∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years

∴ At 2017 ⇒ t = 4

∵ The population at 2017 is 285

∴ The second order pair is (4 , 285)

* The two ordered pairs are (0 , 340) and (4 , 285)

(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)

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

∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)

∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285

∴ m = \frac{285-340}{4-0}=\frac{-55}{4}

* The slope is m = -55/4

∵ The slope is negative value

∴ The relation is decreasing

* The slope means the rate of decreases of the owl population was

  55/4 per year (<em>P decreased by 55/4 each year</em>)

(c) The linear equation form is y = mx + c, where m is the slope and c is

    the value of y when x = 0

∵ The population is P and represented by y

∵ The time is t and represented by t

∴ P = mt + c , c is the initial amount of population

∵ m = -55/4

∵ The initial amount of the population is 340

∴ P = -55/4 t + 340

* The model equation is P = -55/4 t + 340

(d) Lets calculate the time from 2013 to 2022

∵ t = 2022 - 2013 = 9 years

∵ P = -55/4 t + 340

∴ P = -55/4 (9) + 340 = 216.25 ≅ 216

* The owl population in 2022 will be 216

(e) If the model is accurate , then the owl population be be zero after

    t years

∵ P = -55/4 t + 340

∵ P = 0

∴ 0 = -55/4 t + 340

- Add 55/4 t to both sides

∴ 55/4 t = 340

- Multiply both sides by 4

∴ 55 t = 1360

- Divide both sides by 55

∴ t = 24.7 ≅ 25 years

- To find the year add 25 years to 2013

∵ 2013 + 25 = 2038

* At year 2038 will be no more owl in the park

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6 0
3 years ago
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