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notka56 [123]
3 years ago
5

What is the length of the diameter of a circle inscribed in a right triangle with the length of hypotenuse c and the sum of the

legs' lengths equal to m?
Mathematics
1 answer:
jeyben [28]3 years ago
5 0

Answer:

  diameter = m - c

Step-by-step explanation:

In ΔABC, let ∠C be the right angle. The length of the tangents from point C to the inscribed circle are "r", the radius. Then the lengths of tangents from point A are (b-r), and those from point B have length (a-r).

The sum of the lengths of the tangents from points A and B on side "c" is ...

  (b-r) +(a-r) = c

  (a+b) -2r = c

Now, the problem statement defines the sum of side lengths as ...

  a+b = m

and, of course, the diameter (d) is 2r, so we can rewrite the above equation as ...

  m -d = c

  m - c = d . . . . add d-c

The diameter of the inscribed circle is the difference between the sum of leg lengths and the hypotenuse.

You might be interested in
A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessi
Elza [17]

Question:

A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessionary ticket holders.

What is the number of seats occupied by concessionary ticket holders?.

Answer:

60 seats

Step-by-step explanation:

Given

Number of seats = 270

Occupied Seats = 5/9

Concessionary ticket holders = 40% of occupied Seats

Required

The number of seats occupied by concessionary ticket holders

First the number of occupied seat has to be calculated.

Occupied\ Seats = \frac{5}{9} * 270

Occupied\ Seats = \frac{1350}{9}

Occupied\ Seats = 150

Next is to determine the number of seats occupied by concessionary ticket holders.

Number = 40\%\ of\ occupied\ seats

Number = 40\%\ of\ 150

Convert percentage to decimal

Number = 0.4 * 150

Number = 60

<em>Hence, 60 seats were occupied by concessionary ticket holders.</em>

5 0
3 years ago
Calculate the standard score of the given X value, X=28.3, where μ=26.3 and σ=28.1 and indicate on the curve where z will be loc
zmey [24]

Answer:

Standard score z=0.07

Step-by-step explanation:

The z-score, or standard score, represents an equivalent value for X but in the standard normal distribution, where μ=0 and σ=1.

For X=28.3 in a normal distribution with μ=26.3 and σ=28.1, the standard score can be calculated as:

z=\dfrac{X-\mu}{\sigma}=\dfrac{28.3-26.3}{28.1}=\dfrac{2}{28.1}=0.07

This value is 0.07 standard deviations right to the mean.

In the picture attached, we have located the z-score.        

5 0
3 years ago
Please help will mark brainliest
TEA [102]

we know that

total of sum of arc is 360

so, sum of both arc must be 360

so, we get

90+x=360

now, we can solve for x

90+x-90=360-90

x=270............Answer


6 0
3 years ago
5x3 + 14x2 + 9x <br> help
Cerrena [4.2K]
<h3>Answer:    x(x+1)(5x+9) </h3>

===================================================

Work Shown:

5x^3 + 14x^2 + 9x

x( 5x^2 + 14x + 9 )

To factor 5x^2 + 14x + 9, we could use the AC method and guess and check our way to getting the correct result.

A better way in my opinion is to solve 5x^2 + 14x + 9 = 0 through the quadratic formula

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(14)\pm\sqrt{(14)^2-4(5)(9)}}{2(5)}\\\\x = \frac{-14\pm\sqrt{16}}{10}\\\\x = \frac{-14\pm4}{10}\\\\x = \frac{-14+4}{10} \ \text{ or } \ x = \frac{-14-4}{10}\\\\x = \frac{-10}{10} \ \text{ or } \ x = \frac{-18}{10}\\\\x = -1 \ \text{ or } \ x = \frac{-9}{5}\\\\

Then use those two solutions to find the factorization

x = -1  or  x = -9/5

x+1 = 0  or  5x = -9

x+1 = 0  or  5x+9 = 0

(x+1)(5x+9) = 0

So we have shown that 5x^2 + 14x + 9 factors to (x+1)(5x+9)

-----------

Overall,

5x^3 + 14x^2 + 9x

factors to

x(x+1)(5x+9)

6 0
3 years ago
I need help fast!!!!!!!!!!!!!!!¡!!!!!¡!!!!!!!!!m!!!!!!​
raketka [301]
I think the answer is shelter B
4 0
3 years ago
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