Find the area of the figure, 5 in. 2 in. 4 in. 5 in.
2 answers:
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The standard equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is
The completed table for the Pythagorean triples are:
.
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:
.
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:
.
Learn more about the Pythagorean triplets at
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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.
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