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Kryger [21]
3 years ago
9

The endpoints of a diameter of a circle are located at (5,9) and (11,17) which is an equation of the circle?

Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

(x - 8)² + (y - 13)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The centre is located at the midpoint of the endpoints of the diameter.

Use the midpoint formula to find the centre

[\frac{x_{1}+x_{2}  }{2}, \frac{y_{1}+y_{2}  }{2} ]

with (x₁, y₁ ) = (5, 9) and (x₂, y₂ ) = (11,17)

centre = ( \frac{5+11}{2}, \frac{9+17}{2} ) = (8, 13)

The radius is the distance from the centre to either end of the diameter

Calculate r using the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 13) and (x₂, y₂ ) = (5, 9)

r = \sqrt{(5-8)^2+(9-13)^2}

  = \sqrt{(-3)^2+(-4)^2}

  = \sqrt{9+16} = \sqrt{25} = 5 ⇒ r² = 25

Hence

(x - 8)² + (y - 13)² = 25

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Y = 2x + 3<br> y = 3x - 1
lilavasa [31]

Answer:

 x= 4 and y= 11

Step-by-step explanation:

The problem to solve is:

y = 2x + 3 (equation 1)

y = 3x - 1 (equation 2)

Since y = 3x - 1 Solve x from equalution 1

3x - 1 = 2x + 3

3x - 2x = 3 + 1

x = 4

Since x is 4, solve for y

y  = 3x - 1

y = 3(4) - 1

y = 12 -1

y = 11

x =4 and y =7

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3 years ago
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BabaBlast [244]

Answer:

Step-by-step explanation:

3/4

7 0
3 years ago
Write the rational number 0.3 in the form ab , where a and b are integers.
grandymaker [24]

Answer: 3/10

Step-by-step explanation:

Given a decimal number 0.3

To Write the rational number 0.3 in the form ab , where a and b are integers, take it to be :

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0.3/1 × 10/10 = 3/10

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the rational number 0.3 in the form ab , where a and b are integers is

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5 0
3 years ago
Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as signi
JulijaS [17]

Answer:

1/18

Step-by-step explanation:

We are considering that we have 2 dices with 6 faces each (so, the probability to gettig any face in any dish is 1/6). To get an 11, we only have two ways to obtain it:

Dice 1= 6 and Dice 2 =5

or

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So, the probability of the event is given as:

P(Dice1=5 ∧ Dice2=6) ∪ P(Dice1=6 ∧ Dice2=5) = P(Dice1=5) x P(Dice2=6) + P(Dice1=6) x P(Dice2=5) = 1/6 x 1/6 + 1/6 x 1/6 = 1/36 + 1/36 = 2/36 = 1/18.

As 1/18 = 0,055, and 0,055 > 0,05, we consider the event as not significative (according to the definition of significance in the sentence).

7 0
3 years ago
Read 2 more answers
A question on notation: Does sine inverse have an exponent? If not, why is there a negative one there? If so, why can't you just
NNADVOKAT [17]

Answer:

Step-by-step explanation:

When you write

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y = sin    x      can also be written as     y = arcsin x.

No exponentiation here, and no division here.

7 0
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