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3 years ago

Write the standard equation of a circle that passes through (-5 5) with center (-10 -5) brainly

Mathematics

1 answer:

timama [110]3 years ago

8 0

Answer:

The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form

Step-by-step explanation:

* lets study the standard form of the equation of a circle

- If the coordinates of the center of the circle are(h , k) and its radius

is r, then the standard equation of the circle is:

(x - h)² + (y - k)² = r²

* Now lets solve the problem

∵ The coordinates of the center of the circle are (-10 , -5)

∵ The standard form of the equation is (x - h)² + (y - k)² = r²

∵ h , k are the coordinates of the center

∴ h = -10 , k = -5

∴ The equation of the circle = (x - -10)² + (y - -5)² = r²

∴ The equation of the circle = (x + 10)² + (y + 5)² = r²

- To find the value of the radius lets use the point (-5 , 5) to

substitute their coordinate instead of x and y in the equation

∵ The circle passes through point (-5 , 5)

∵ (x + 10)² + (y + 5)² = r²

- Use x = -5 and y = 5

∴ (-5 + 10)² + (5 + 5)² = r² ⇒ simplify

∴ (5)² + (10)² = r²

∴ 25 + 100 = r²

∴ r² = 125

* Now lets write the equation in standard form

∴ (x + 10)² + (y + 5)² = 125

* The equation of the circle is (x + 10)² + (y + 5)² = 125 in standard form

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3 years ago

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Answer:

a) 0.913

b) 0.397

c) 0.087

Step-by-step explanation:

We are given the following information:

We treat wearing tie too tight as a success.

P(Tight tie) = 15% = 0.15

Then the number of businessmen follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 15

We have to evaluate:

a) at least one tie is too tight

$P(x \geq 1) = P(x = 1) +....+ P(x = 15)\\=1 - P(x = 0)\\= 1 - \binom{15}{0}(0.15)^0(1-0.15)^{15}\\=1 - 0.087\\= 0.913$

b) more than two ties are too tight

$P(x > 2) = P(x = 3) +....+ P(x = 15)\\=1 - P(x = 0) - P(x=1) - P(x=2)\\= 1 - \binom{15}{0}(0.15)^0(1-0.15)^{15}-\binom{15}{1}(0.15)^1(1-0.15)^{14}-\binom{15}{0}(0.15)^2(1-0.15)^{13}\\=1 - 0.087 - 0.231 - 0.285\\= 0.397$

c) no tie is too tight

$P(x = 0)\\=\binom{15}{0}(0.15)^0(1-0.15)^{15}\\=0.087$

d) at least 18 ties are not too tight

This probability cannot be evaluated as the number of success or the failures exceeds the number of trials given which is 15.

The probability is asked for 18 failures which cannot be evaluated.

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3 years ago

a jar contains 16 marbles of which 1 is blue 5 are red and the rest are green what is the ratio of green marbles to all marbles

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16-(5+1)=10

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3 years ago

Jack has written the name of each planet of the solar system on a separate piece of paper and has placed all these pieces of pap

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Answer:

The probability that it would contain at least 6 letters is: 5/8

Step-by-step explanation:

From the question given above,

We know that there are 8 planet that was given.

Mercury 7 letters

Venus 5 letters

Earth 5 letters

Mars 4 letters

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Therefore,

P(at least 6 letters) + P( Less than 6 letters) = 1

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3 years ago

Can someone help me with this :/

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Answer:

2x² + x - 1 = 0

a= 2 b= 1 c= -1

x = [ -b +- sqr rt( b^2 -4ac) ] / 2*a

x = -1 +- sqr rt (1 - 4 *2*-1) / 4

x1 = [ -1 + (sqr rt (1 +8)) / 4

x1 = ( -1 + sqr rt (9)) / 4

x1 = (-1 + 3) / 4

x1 = .5

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x2 = -4 / 4

x2 = -1

And to check that answer: http://www.1728.org/quadratc.htm

Step-by-step explanation:

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