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tigry1 [53]
2 years ago
14

Last summer, Marrero was at Newgrange, a stone mound in Ireland that has a diameter of 250 feet. He found a walkway 62 feet long

that leads to the center of the mound. Help Marrero find perpendicular distance x from the end of the walkway to either side of the mound.

Mathematics
1 answer:
timofeeve [1]2 years ago
7 0

Answer:

  • 108 ft

Step-by-step explanation:

The line connecting the center with the end of the walkway is radius and is the hypotenuse of the right triangle.

Horizontal leg is the distance x.

<u>Vertical leg has the length:</u>

  • (250)/2 - 62 = 63 ft

<u>Using Pythagorean theorem to find the length of x:</u>

  • x² = (250/2)² - 63²
  • x² = 125² - 63²
  • x² = 11656
  • x = √11656
  • x = 107.96 ≈ 108

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x^2 - 10x = -8

x^2 - 10x + 25 = 17

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x^2 - 10x - 25 = -33

Begin with x^2 - 10x = -8.  Here's the process for completing the square:

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2.  Add this 25 to the first two terms of x^2 - 10x = -8 and also to the      constant -8:    x^2 - 10x + 25 = -8 + 25, or     x^2 - 10x + 25 = 17

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x^2 - 10x + 25 = 17

     

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dedylja [7]

The three consecutive odd integers whose sum is 495 are 163, 165, and 167.

What are consecutive numbers?

⇒ Integers that are listed in a consistent counting pattern are referred to as consecutive integers. There are no numbers missed while listing consecutive integers in a sequence, so the difference between them is always fixed. The difference between each subsequent integer is 1, for instance, can be written as -4, -3, -2, -1, 0, 1, 2, 3, and so on.

What are consecutive odd integers?

⇒ Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.

Calculation:

We are going to take an odd number, x, write its subsequent consecutive numbers, add all of them together, then equate them to  495 to find the number. The equation for x is then resolved.

We have been given that the sum of 3 consecutive odd numbers is equal to 495.

Let the first consecutive odd integer is x.

⇒ Then the next consecutive odd integers becomes x + 2 and the next term becomes x + 2 + 2 = x + 4.

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⇒ Hence, the three consecutive odd integers whose sum is 495 are 163, 165, and 167.

Learn more about consecutive numbers here: brainly.com/question/10853762

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