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lukranit [14]
2 years ago
12

Find the 14th term of the arithmetic sequence −5x+3, −3x+8, −x+13,

Mathematics
1 answer:
Lerok [7]2 years ago
8 0

Answer: 21x + 68

Step-by-step explanation: the left side is going up by 2 on each step and the right side is going up by 5. So add 2x + 5 , 14 times to get the answer

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We know that a triangle with side lengths , , and is a right triangle. Using those side lengths, find the missing triples and x-
Anit [1.1K]

The completed table for the Pythagorean triples are:

x \text{ value } \text{   Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (6,8,10)\\\text{ } \text{ } \text{ } 4 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)

  \text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ }  (10,24,26)\\\text{ } \text{ } \text{ } 6 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37).

A trio of positive numbers known as a Pythagorean triple fits into the Pythagoras theorem's formula, which is written as a² + b² = c², where a, b, and c are all positive integers. Here, "a" and "b" make up the other two legs of the right-angled triangle, and "c" serves as the triangle's "hypotenuse," or longest side. In terms of the Pythagorean triples (a, b, c).

In the question, we are given that a triangle with side lengths x² - 1, 2x, x² + 1 is a right triangle, and are asked to fill in the missing table:

x \text{ value } \text{   Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)\\

  \text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37).

Taking x as 3, and putting in the sides, we get:

x² + 1 = 3² + 1 = 10.

2x = 2*3 = 6.

x² - 1 = 3² - 1 = 8.

Thus, the triplet is 6,8,10.

For the triplet 8,15,17, we get the x value as:

2x = 8,

or, x = 8/2 = 4.

Thus, the x-value for the triplet (8,15,17) is 4.

Taking x as 5, and putting in the sides, we get:

x² + 1 = 5² + 1 = 26.

2x = 2*5 = 10.

x² - 1 = 5² - 1 = 24.

Thus, the triplet is 10,24,26.

For the triplet 12,35,37, we get the x value as:

2x = 12,

or, x = 12/2 = 6.

Thus, the x-value for the triplet (12,35,37) is 6.

Thus, the completed table for the Pythagorean triples are:

x \text{ value } \text{   Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (6,8,10)\\\text{ } \text{ } \text{ } 4 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)

  \text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ }  (10,24,26)\\\text{ } \text{ } \text{ } 6 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37).

Learn more about the Pythagorean triplets at

brainly.com/question/24211694

#SPJ4

The provided question is incomplete. The complete question is:

"We know that a triangle with side lengths x² - 1,2x and x² + 1 is a right triangle. Using those side lengths, find the missing triples and x-values.

Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.

Type the correct answer in each box.

x \text{ value } \text{   Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)\\

  \text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37).

6 0
1 year ago
PLS HELPPP
Olin [163]
I think 80 I’m not sure ........
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3 years ago
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Tara is making dinner for 9 people. She mixes 1 1/4 kilograms of rice with 500grams of vegetables and 410 grams of meat. If all
kotegsom [21]

Answer:

240 grams

Step-by-step explanation:

Tara uses:

  • 1 \dfrac{1}{4}\ kg=1 \ kg\ 250 \ g=1250\ g of rice
  • 500 g of vegatables
  • 410 g of meat

In total, Tara uses

1250+500+410=2160\ g of ingredients.

She is making dinner for 9 people, so the weight of each serving is

2160:9=240\ g

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Sally bought six pencils and three folders for 3.90. Henry bought two pencils and five folders for 3.30. Eric wants to buy the s
yulyashka [42]
He can buy 500 pencils
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The solution set, all real numbers greater than or equal to one, proves which of the following inequality statements to be true?
Juliette [100K]

Answer:

-5x ≤ 6x - 11

Step-by-step explanation:

Solving inequalities involves the same steps as equations with the exception that when multiplying or dividing by a negative coefficient of the variable, the inequality sign will flip.  The solution to one of the inequalities given must be x ≥ 1.  Given this answer, you can solve each to find the matching inequality:

-5x ≥ 6x - 11 or -11x ≥ -11 or x ≤ 1 (flip the sign due to negative coefficient)

-5x ≤ 6x - 11 or -11x ≤ -11 or x ≥ 1 (flip the sign)

5x ≤ 6x + 11 or -x ≤ 11 or x ≥ -1

-5x ≤ 6x + 11 or -11x ≤ 11 or x ≥ -1

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