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In-s [12.5K]
3 years ago
7

Which set of numbers could represent the lengths of the sides of a right triangle?

Mathematics
2 answers:
jolli1 [7]3 years ago
8 0

Answer:

3, 4, 5

Step-by-step explanation:

We are given the sets of numbers and we are supposed to find Which set of numbers could represent the lengths of the sides of a right triangle

So, we need to use Pythagoras theorem

Hypotenuse^{2} =Perpendicular^{2} +Base^{2}

1) 9,10,11

Hypotenuse = 11

So, using Pythagoras theorem

11^{2} =10^{2} +9^{2}

121=100 +81

121\neq 181

Since the given set does not satisfy the Pythagoras theorem.So, the given set  of number could not represent the lengths of the sides of a right triangle.

2)16, 32, 36

Hypotenuse = 36

So, using Pythagoras theorem

36^{2} =32^{2} +16^{2}

1296=1024 +256

1296\neq 1280

Since the given set does not satisfy the Pythagoras theorem.So, the given set  of number could not represent the lengths of the sides of a right triangle.

3)8, 12, 16

Hypotenuse = 36

So, using Pythagoras theorem

16^{2} =12^{2} +8^{2}

256=144 +64

256\neq 208

Since the given set does not satisfy the Pythagoras theorem.So, the given set  of number could not represent the lengths of the sides of a right triangle.

4)3, 4, 5

Hypotenuse = 5

So, using Pythagoras theorem

5^{2} =4^{2} +3^{2}

25=16 +9

25\=25

Since the given set satisfy the Pythagoras theorem.So, the given set  of number could represent the lengths of the sides of a right triangle.

Hence 3, 4, 5 is the set of numbers could represent the lengths of the sides of a right triangle

Arisa [49]3 years ago
4 0
3,4,5 
using a^2 +b^2 = c^2 plug in any of the numbers i plugged in 
3^2 +4^2 which gave me 9+16 and that is 25 and 5^2 is 25

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A politician estimates that 61% of his constituents will vote for him in the coming election. How many constituents are required
Katyanochek1 [597]

Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which:

  • \pi is the sample proportion.
  • z is the critical value.
  • n is the sample size.

The margin of error is given by:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

In this problem, we have a 95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so the critical value is z = 1.96.

The estimate is of \pi = 0.61, while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}

0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}

\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}

(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2

n = 1015.5

Rounding up, 1016 constituents are required.

More can be learned about the z-distribution at brainly.com/question/25890103

8 0
1 year ago
What is the sum of the geometric sequence −4, 24, −144, ... if there are 8 terms?
Helga [31]

Answer:

The sum of 8 geometric sequence is 959780

Step-by-step explanation:

We are given

this sequence is geometric

-4 , 24 , -144

First term is -4

so, a_1=-4

now, we can find common ratio

r=\frac{24}{-4}=-6

we can use formula

S_n=a_1(\frac{1-r^n}{1-r} )

n=8

now, we can plug values

S_8=-4(\frac{1-(-6)^{8}}{1+6} )

now, we can simplify it

and we get

S_8=959780

4 0
3 years ago
Solve using long division
Mice21 [21]
19x-53 / x^2 + x + 2

You want to put a - ( 19 x / x^2 + x + 2 - 53/x^2 +x +2)
4 0
3 years ago
What is the modulus of |9+40i|?
Talja [164]

Answer:

41

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy = \sqrt{x^2+y^2}

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| =\sqrt{9^2+40^2} =\sqrt{1681}

By long division method we find that

|9+40i| =41


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