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Lady bird [3.3K]
3 years ago
9

What is the equation of the line that passes through (4,-1) and (-2,3)

Mathematics
1 answer:
vladimir1956 [14]3 years ago
8 0

Answer: y-6 = 0.5 (x-8)

Step-by-step explanation:

y − y1 = m(x − x1)

The equation is useful when we know:

one point on the line: (x1,y1)

and the slope of the line: m,

and want to find other points on the line.

Have a play with it first (move the point, try different slopes):

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square root of 166, 13, 14

Step-by-step explanation:

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Find the prime factorization of the number 12​
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First, you must use a factor tree to find the prime factors of the number.

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2 , 2 and 3 are the prime factors that make 12

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Round 4,088,432 to the nearest million
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<span>The basic idea is that you form a parallelogram with those two vectors as the two different side lengths another way to see it: start at the tip of one vector and move in the same direction as the other vector (and the same length as the other vector)

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3 years ago
Park rangers tagged fish in a state park to track their population. The function f(x)=200(1.05)x can be used to find the populat
Sedbober [7]

The given exponential function can be used to determine the

population of the fish at different times.

Response:

1. 200

2. 0.05

3. Please find attached the graph of the exponential function and the table

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. Range; [0, ∞)

Domain: [200, ∞)

5. 346 fishes (approximate value)

<h3>How is the population of the fish obtained from the exponential function?</h3>

The given function is f(x) = 200·(1.05)ˣ

1. The initial population is given by the value of the function when x = 0,

which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

  • The initial population of the fish is <u>200</u>

2. The rate of growth of the fish from the exponential function is given as follows;

The growth factor = 1.05

  • The growth rate =<u> 0.05</u>

3. Please find attached the graph of the exponential function created

with MS Excel.

The asymptote of the exponential function is the line, <u>y = 0</u>

The table of values is presented as follows;

\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}

4. The domain is the possible x-values which is; 0 ≤ x < ∞

The range is the possible y-values which is; 200 ≤ f(x) < ∞

Which gives;

  • Domain; [0, ∞)
  • Range: [200, ∞)

5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹

f(11) = 200 × (1.05)¹¹ ≈ 342

  • The population of the fish after 11 years is <u>346 (fishes)</u>

Learn more about exponential function here:

brainly.com/question/15662160

3 0
2 years ago
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