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2 years ago

What is the circumference of the circle that circumscribes a triangle with side lengths 3, 4, and 5?

Mathematics

1 answer:

djyliett [7]2 years ago

6 0

Answer:

5π, about 15.708 units

Step-by-step explanation:

A 3-4-5 triangle is a right triangle. When a circle circumscribes a right triangle, the hypotenuse is the diameter of the circle. The circumference of a circle is given by ...

C = πd

For a diameter of 5 units, the circumference is ...

C = π(5) = 5π = 15.708 . . . units

_____

Additional comment

The (3, 4, 5) triple is one of the first Pythagorean triples you run across. It is the smallest integer triple, and the only primitive triple with values in an arithmetic sequence. You can show this is a Pythagorean triple by ...

3² + 4² = 9 +16 = 25 = 5²

That is, these numbers satisfy the Pythagorean theorem relation for sides of a right triangle.

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10. Create a scenario to explain why 3P3=3!.

Flauer [41]

Step-by-step explanation:

Permutation :The number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed.

$nPr = \frac{n!}{(n-r)!}$

Factorial : There are n! ways of arranging n distinct objects into an ordered sequence.

Considering a situation when n = r in a permutation, nPr reduces to n!, a simple factorial of n.

Proof: 3P3 = 3!

n = 3 and r = 3

$3P3 = \frac{3!}{(3-3)!}$

$3P3 = \frac{3!}{(0)!}$

But 0! = 1

3P3 = 3!

3 0

3 years ago

Read 2 more answers

Please answer asap please

Korvikt [17]

Answer:

14411

Step-by-step explanation:

7 0

2 years ago

So…I have been making 0’s on my math homework…cause I don’t understand it.

timurjin [86]

Well try working on the problem first

3 0

3 years ago

Solve the equation for x, where x is a real number (5 points): -2x^2 + 5x + 2 = -3

Juli2301 [7.4K]

Add 3 to both sides so that the equation becomes -2x^2 + 5x + 5 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
                              x = [ -b ± √(b^2 - 4ac) ] / (2a)
                              x = [ -5 ± √(5^2 - 4(-2)(5)) ] / ( 2(-2) )
                              x = [-5 ± √(25 - (-40) ) ] / ( -4 )
                              x = [-5 ± √(65) ] / ( -4)
                              x = [-5 ± sqrt(65) ] / ( -4 )
                              x = 5/4 ± -sqrt(65)/4
The answers are 5/4 + sqrt(65)/4 and 5/4 - sqrt(65)/4..

5 0

3 years ago

Find the equation of the graphed line.

belka [17]

<h3>Answer:</h3>

$\boxed{\boxed{\pink{\bf \leadsto Hence \ option\ [d]\ \bigg(y = \dfrac{5}{2}x + 5\bigg) \ is \ correct }}}$

<h3>Step-by-step explanation:</h3>

Here from the given graph we can see that the graph the graph intersects x axis at (2,0) and y axis at (5,0). On seeing options it's clear that we have to use Slope intercept form . Which is :-

$\large\boxed{\orange{\bf y = mx + c} }$

We know that slope is $\tan\theta$ . So here slope will be ,

$\red{\implies slope = \tan\theta} \\\\\implies slope =\dfrac{PERPENDICULAR}{BASE} \\\\\bf \implies slope =\dfrac{5}{2}$

Hence the slope is 5/2 . And here value of c will be 5 since it cuts y axis at (5,0).

$\purple{\implies y = mx + c }\\\\\implies y = \dfrac{5}{2}x + 5 \\\\\underline{\boxed{\red{\tt \implies y = \dfrac{5}{2}x + 5 }}}$

<h3>Hence option [ d ] is correct . </h3>

4 0

3 years ago