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Rufina [12.5K]
3 years ago
6

write the equations of the line passing through the point (2,4) and parallel to the line whose equation is y=x

Mathematics
1 answer:
anastassius [24]3 years ago
3 0

Answer:

y = x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x is in this form

with slope m = 1 and c = 0

• Parallel lines have equal slopes, thus

y = x + c ← is the partial equation of the parallel line

To find c substitute (2, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = x + 2 ← equation of parallel line

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A population of deer inside a park has a carrying capacity of 200 and a growth rate of 3%. If the initial population is 80 deer,
otez555 [7]

Answer:

The population of deer at any given time = 200(e^0.03t)  ÷ (1.5 + (e^0.03t))

Step-by-step explanation:

This is an example of logistic equation on population growth

carrying capacity, k = 200

Rate, r = 3% = 0.03

Initial Population, P1 =  80

P(t) =?

P(t) = (P1 (k)(e^rt)) ÷ (k- P1 + P1(e^rt))

P(t) = (80 (200)(e^0.03t)) ÷ (200 - 80 + 80(e^0.03t))

     = (16000(e^0.03t))  ÷ (120 + 80(e^0.03t))

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8 0
3 years ago
Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following we
AlekseyPX

Due to length restrictions, we kindly invite to see the explanation below to know the answer with respect to each component of the question concerning linear equations.

<h3>How to determine a linear equation describing the daily distance of a runner</h3>

In this question we need to derive an expression of the <em>daily</em> distance as a function of time. Now we proceed to complete the components:

  1. <em>Linear</em> equations have an <em>independent</em> variable (t - time) and a dependent variable (x - daily distance).
  2. We notice that the daily distance increases linearly in time, then then we have the following pattern:

    t          1            2            3             4            5              6
    x          2          2.5          3           3.5           4             4.5
  3. The equation that represents the n-th term of the sequence is x(n) = 2 + 0.5 · (n - 1).
  4. The week when Susie will run 10 miles per day is:

    10 = 2 + 0.5 · (n - 1)
    8 = 0.5 · (n - 1)
    n - 1 = 16
    n = 17

    Susie will run 10 miles per day in the 17th week.
  5. It is not reasonable to think that pattern will continue indefinitely as it is witnessed in the difficulties experimented by <em>fastest</em> runners in the world to increase their <em>peak</em> speeds.
  6. A marathon has a distance of 26 miles, then we must solve the following equation:

    26 = 2 + 0.5 · (n - 1)
    24 = 0.5 · (n - 1)
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    Susie should start her training 49 weeks before the marathon.

To learn more on linear equation: brainly.com/question/11897796

#SPJ1

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