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77julia77 [94]
3 years ago
5

Write the standard equation for the circle 30. Center (2,7), r=4. 31. Center (-6,-8), that passes treough (0,0)

Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
3 0
The standard equation of the circle is:

(x-h)^2+(y-k)^2=r^2 where (h,k) it the center of the circle and r is the radius...

so

30.

(x-2)^2+(y-7)^2=16

31.

We need to find the radius...(I'll just use the Pythagorean Theorem)

r^2=6^2+8^2

r^2=36+64

r^2=100  (so the radius is 10) and its center is (-6,-8) so

(x+6)^2+(y+8)^2=100
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WILL GIVE 100 POINTS
padilas [110]

(a) The explicit rule to model the sequence formed by the number of seats in each row is a_{n}=15+3n

(b) The 35th row has 120 seats

Step-by-step explanation:

The rule of the nth term of an arithmetic sequence is

a_{n}=a+(n-1)d , where

  • a is the the first term
  • d is the common difference between each two consecutive terms

∵ There are 18 seats in the 1st row

∵ There are 21 seats in the 2nd row

∵ 21 - 18 = 3

∵ The number of seats is increased by 3 with each additional row

- The number of seats in each row represents an arithmetic

   sequence because there is a common difference between

   each two consecutive rows

∴ The number of seats in each row formed an arithmetic sequence

∵ The number of seats in the first row = 18 seats

∴ a = 18

∵ The number of seats in a row continues to increase by 3 with each

   additional row

∴ d = 3

- Substitute the values of a and d in the rule of nth term

∴ a_{n}=18+(n-1)3

- Simplify the right hand side

∴ a_{n}=18+3n-3

- Add like terms

∴ a_{n}=15+3n

(a) The explicit rule to model the sequence formed by the number of seats in each row is a_{n}=15+3n

∵ There are 120 seat in a row

- Substitute a_{n} by 120 in the rule above

∴ 120 = 15 + 3n

- Subtract 15 from both sides

∴ 105 = 3n

- Divide both sides by 3

∴ n = 35

∴ The number of the row is 35

(b) The 35th row has 120 seats

Learn more:

You can learn more about the sequences in brainly.com/question/7221312

#LearnwithBrainly

6 0
3 years ago
(–8) + (–5) =<br> (–8) + 2 =
andreyandreev [35.5K]
First one is -13
second one is 16
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3 years ago
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Which of following is the graph of y = -(x + 1)2 -3?
Degger [83]

Answer:

c

Step-by-step explanation:

5 0
3 years ago
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Un avión puede volar con la velocidad de 400 km por hora en atmósfera tranquila si cuando se dirige hacia el este el viento vien
Bumek [7]

Answer:

84,3 ° Sureste

Step-by-step explanation:

El diagrama vectorial que tipifica la pregunta se muestra en la imagen adjunta.

La dirección del avión es la dirección de la velocidad resultante.

Si esta dirección es θ

θ = tan ^ -1 (400/40)

θ = 84,3 ° Sureste

3 0
2 years ago
4. Find the value of x.
oksano4ka [1.4K]

Answer:

x = 50°

Step-by-step explanation:

The sum of the measures of the angles of a quadrilateral is 360°

360 - 40 - 80 - 110 = 130

130 is the measure of the quad that is adjacent to the angle of x° and is supplementary to that angle also.

Therefore, x = 180 - 130 = 50

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3 years ago
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