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2 years ago

Y = 3(x-2)^2 + 5

Mathematics

1 answer:

Orlov [11]2 years ago

3 0

The y-intercept coordinate is at the point (0, 17)

<h3>Properties of functions</h3>

Given the following function expressed as:

$y = 3(x-2)^2 + 5$

The vertex of the function (h, k) is (2, 5) while the axis of symmetry is at x = 2
Domain are the input values for which the function exist. According to the function, the domain and range exists on all real values

The x-intercept is the point where y = 0

$3(x-2)^2 + 5=0\\3(x-2)^2 = -5\\(x-2)^2 = -5/3\\x - 2 = 25/9\\x = 25/9 + 2\\x = \frac{43}{9}$

Hence the x-intercept is (43/9, 0)

The y-intercept is the point where x = 0

$y=3(x-2)^2 + 5\\y=3(-2)^2 + 5\\y=12+5\\y=17$

The y-intercept coordinate is at the point (0, 17)

Learn more on vertex and axis of symmetry here: brainly.com/question/21191648

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The perimeter of a rectangular rug is 40 ft. It's length is 12 ft. What is it's width?

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Answer:

<h2>The answer is 8 ft</h2>

Step-by-step explanation:

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Miguel quiere entrenar para la carrera solidaria de verano en uno de los dos parques que tiene cerca de casa. Su plan es correr

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Answer:

<em>The square park is more convenient.</em>

Explanation:

The translation of the question is:

<em>Miguel wants to train for the summer solidarity race in one of the two parks that he has close to home. His plan is to run about 10 km each day and he wants to do an exact number of laps around the park to always start and end at the entrance. Since he has not quite decided between the square and the rectangular park, he decides to do some calculations to see which one suits him best.</em>

<em>Square park: 423 meters each side</em>

<em>Rectangular park: 673 meters measures the base and 218 meters the height</em>

<em />

<h2>Solution</h2>

<u />

<u>1. Calculate the perimeter of the square park</u>

The perimeter of a square is the sum of the four side lengths. Since they are equal it is:

Perimeter = 4 × side lenght

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<u />

<u>2. Calculate how many times 1,692m is in 10 km</u>

10 km is 10,000 m. Then, divide 10,000 by 1,692 m:

Number of laps = 10,000m / 1,692m ≈ 5.91 laps

<u>3. Calculate the perimeter of the rectangular park</u>

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Perimeter = 2×673m + 2×218m = 1,782m

<u>4. Calculate how many times 1,782 is in 10km</u>

Number of laps = 10,000m / 1,782m ≈ 5.61 laps

Then, since the number 5.91 is closer to an integer number than 5.61, you conclude that the square park is more conventient, because by running 6 laps around the square park the number of kilometers run will be closer to 10 km than with any number of complete laps in the rectangular park.

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