Answer:
34
Step-by-step explanation:
The mean is calculated as
mean = ![\frac{frequency(midpoint)}{frequency}](https://tex.z-dn.net/?f=%5Cfrac%7Bfrequency%28midpoint%29%7D%7Bfrequency%7D)
let x be the missing frequency, then
Total frequency × midpoint
= (16 × 2) + 7x + (20 × 12) + (10 × 17) = 32 + 7x + 240 + 170 = 442 + 7x
Total frequency = 16 + x + 20 + 10 = 46 + x, thus
= 8.5 ( cross- multiply )
442 + 7x = 8.5(46 + x)
442 + 7x = 391 + 8.5x ( subtract 8.5x from both sides )
442 - 1.5x = 391 ( subtract 442 from both sides )
- 1.5x = - 51 ( divide both sides by - 1.5 )
x = 34
The missing frequency is 34
The equations that express the relationship between the side lengths of the triangles are
<h3>Pythagorean triple</h3>
From the question, we are to write an equation that expresses the relationship between the side lengths of each triangle
From the Pythagorean theorem,
In a right triangle, the square of the longest side (hypotenuse) equals sum of squares of the other two sides
That is,
c² = a² + b²
Where c is the longest side (hypotenuse)
a and b are the other two sides
The equation is
10² = 6² + 8²
- For
![\sqrt{5}, \sqrt{3}, \sqrt{8}](https://tex.z-dn.net/?f=%5Csqrt%7B5%7D%2C%20%5Csqrt%7B3%7D%2C%20%5Csqrt%7B8%7D)
The equation is
![(\sqrt{8} )^{2} = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7B8%7D%20%29%5E%7B2%7D%20%20%3D%20%28%5Csqrt%7B5%7D%20%29%5E%7B2%7D%20%2B%20%28%5Csqrt%7B3%7D%20%29%5E%7B2%7D)
- For
![5, \sqrt{5}, \sqrt{30}](https://tex.z-dn.net/?f=5%2C%20%5Csqrt%7B5%7D%2C%20%5Csqrt%7B30%7D)
The equation is
![(\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7B30%7D%20%29%5E%7B2%7D%20%3D%205%5E%7B2%7D%20%2B%20%28%5Csqrt%7B5%7D%20%29%5E%7B2%7D)
- For
![1, \sqrt{37}, 6](https://tex.z-dn.net/?f=1%2C%20%5Csqrt%7B37%7D%2C%206)
The equation is
![(\sqrt{37} )^{2} = 1^{2} + 6^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7B37%7D%20%29%5E%7B2%7D%20%20%3D%201%5E%7B2%7D%20%2B%206%5E%7B2%7D)
- For
![3, \sqrt{2}, \sqrt{7}](https://tex.z-dn.net/?f=3%2C%20%5Csqrt%7B2%7D%2C%20%5Csqrt%7B7%7D)
The equation is
![3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}](https://tex.z-dn.net/?f=3%5E%7B2%7D%20%3D%20%28%5Csqrt%7B2%7D%20%29%5E%7B2%7D%20%2B%20%28%5Csqrt%7B7%7D%20%29%5E%7B2%7D)
Hence, the equations that express the relationship between the side lengths of the triangles are
Learn more on Pythagorean triple here: brainly.com/question/3223211
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Answer:
Going from left to right:
1.) Yes
2.) No
3.) Yes
4.) No
5.) No
6.) Yes
7.) No
8.) No
9.) Yes
10.) No
11.) Yes
12.) Yes
13.) No
14.) Yes
15.) Yes
16.) No
Step-by-step explanation:
Functions cannot have any repeating x-coordinates.
6 - 6, 12, 18, 24, 30, 36, 42, 48 54, 60, 66, 72, 78, 84, 90, 96