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Wewaii [24]
2 years ago
6

Which of the following sets could be the sides of a right triangle?{2, 3, square root of 13} {5, 5, 2, square root of 10} { 5, 1

2, 15 }
Mathematics
1 answer:
MA_775_DIABLO [31]2 years ago
5 0

Answer:

{2, 3, √13}  

Step-by-step explanation:

In a right triangle, the sum of the squares of the two shorter sides equals the square of the third side (Pythagoras).

Let's check each set of sides in turn.

A. {2, 3, √13}

2² + 3² = 4 + 9 = 13

(√13)² = 13

This is a right triangle.

B. {5, 5, 2, √10}

This is a quadrilateral (four sides).

C. {5, 12, 15}

5² + 12² = 25 +144 = 169

15² = 225

This is not a right triangle.

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Mademuasel [1]
The answer is A. You can check by plugging in the numbers for x.
8 0
3 years ago
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Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. n distinct integers will be chosen from A. How big does n have to be
Hitman42 [59]
Partition the set A into 4 subsets: {1, 8}, {2, 7}, {3, 6}, and {4, 5}, each consisting of two integers whose sum is 9. If 5 integers are selected from A, then by the Pigeonhole Principle at least two must be from the same subset. But then the sum of these two integers is 9.
7 0
3 years ago
Find the equation of the sphere centered at (-9,9, -9) with radius 5. Normalize your equations so that the coefficient of x2 is
olganol [36]
<h2><u>Answer</u>:</h2>

(a) x² + y² + z² + 18(x - y + z) + 218 = 0

(b) (x + 9)² + (y - 9)² + 56 = 0

<h2><u>Step-by-step explanation:</u></h2>

<em>The general equation of a sphere of radius r and centered at C = (x₀, y₀, z₀) is given by;</em>

(x - x₀)² + (y - y₀)² + (z - z₀)² = r²               ------------------(i)

<em>From the question:</em>

The sphere is centered at C = (x₀, y₀, z₀) = (-9, 9, -9) and has a radius r = 5.

<em>Therefore, to get the equation of the sphere, substitute these values into equation (i) as follows;</em>

(x - (-9))² + (y - 9)² + (z - (-9))² = 5²

(x + 9)² + (y - 9)² + (z + 9)² = 25      ------------------(ii)

<em>Open the brackets and have the following:</em>

(x + 9)² + (y - 9)² + (z + 9)² = 25

(x² + 18x + 81) + (y² - 18y + 81) + (z² + 18z + 81) = 25

x² + 18x + 81 + y² - 18y + 81 + z² + 18z + 81 = 25

x² + y² + z² + 18(x - y + z) + 243 = 25

x² + y² + z² + 18(x - y + z) + 218 = 0    [<em>equation has already been normalized since the coefficient of x² is 1</em>]

<em>Therefore, the equation of the sphere centered at (-9,9, -9) with radius 5 is:</em>

x² + y² + z² + 18(x - y + z) + 218 = 0

(2)  To get the equation when the sphere intersects a plane z = 0, we substitute z = 0 in equation (ii) as follows;

(x + 9)² + (y - 9)² + (0 + 9)² = 25

(x + 9)² + (y - 9)² + (9)² = 25

(x + 9)² + (y - 9)² + 81 = 25        [<em>subtract 25 from both sides</em>]

(x + 9)² + (y - 9)² + 81 - 25 = 25 - 25

(x + 9)² + (y - 9)² + 56 = 0

The equation is therefore, (x + 9)² + (y - 9)² + 56 = 0

6 0
3 years ago
Can anybody find the answers to any of these please
Umnica [9.8K]

(A) SAS

<u>Explanation:</u>

According to the figure,

One angle of both the triangles are equal

Two sides of both the triangles are equal

If two sides and one angle are equal, then the given triangles are congruent to each other.

7 0
3 years ago
Help please!!!!!!!!!
ANEK [815]
The answer is (8,40.32)
4 0
3 years ago
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