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sattari [20]
3 years ago
5

Describe the circle given by the equation (x − 7)^2 + (y − 8)^2 = 9.

Mathematics
1 answer:
matrenka [14]3 years ago
8 0
<h2>The circle (x − 7)² + (y − 8)² = 9 is a circle with center (7,8) and radius is 3</h2>

Step-by-step explanation:

Equation of circle with (h,k) as center and radius r is given by,

          (x-h)²+(y-k)² = r²

Here we need to describe the circle given by the equation (x − 7)² + (y − 8)² = 9

Changing equation to  (x-h)²+(y-k)² = r² form

               (x − 7)² + (y − 8)² = 9

                (x − 7)² + (y − 8)² = 3²

So, h = 7 ,  k = 8 and r = 3

Center is (7,8) and radius is 3

The circle (x − 7)² + (y − 8)² = 9 is a circle with center (7,8) and radius is 3

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The Window has the shape of a kite. How many square meters of glass were used to make the Window
Elan Coil [88]

The window that has the shape of a kite has the area of the glass as 648 centimetre squared.

<h3>What is area of a figure?</h3>

Area can be defined as the space occupied by a flat shape or the surface of an object. Therefore,

The window is the shape of a kite. Therefore, the square meters of the glass used for the window is the area of the window(kite).

Therefore,

area of kite = ab / 2

where

  • a and b are the length of the diagonal

Therefore,

a = 18 + 18 = 36 cm

b = 15 + 21 = 36 cm

area of the window = 36 × 36 / 2 = 1296 / 2 = 648 cm²

learn more on area here:brainly.com/question/2494000

4 0
2 years ago
Tickets to a school play are $4.50 for an adult and $3.00 for a student. If 300 tickets are sold and $1087.50 collected, how man
Kryger [21]

Answer:

<h2>125 tickets for an adult</h2><h2>and 175 tickets for a student</h2>

Step-by-step explanation:

a-\text{number of the tickets for an adult}\\s-\text{number of the tickets for a student}\\\\(1)\qquad a+s=300\\(2)\qquad4.5a+3s=1087.5\\------------\\(1)\\a+s=300\qquad\text{subtstitute}\ s\ \text{from both sides}\\a=300-s\\\\\text{Put it to (2):}\\\\4.5(300-s)+3s=1087.5\qquad\text{use distributive property}\\\\(4.5)(300)+(4.5)(-s)+3s=1087.5\\\\1350-4.5s+3s=1087.5\qquad\text{subtract 1350 from both sides}\\\\-1.5s=-262.5\qquad\text{divide both sides by (-1.5)}\\\\\boxed{s=175}

\text{Put the value of}\ s\ \text{to (1):}\\\\a=300-175\\\\\boxed{a=125}

3 0
2 years ago
There are 60 new houses being built in a neighborhood. Last month 1/3 of them were sold. This month 1/5 of the remaining houses
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Answer:

4

Step-by-step explanation:

8 0
2 years ago
Two runners in a 400 meter race cross the finish line in a photo finish. From the photo, officials find that the second runner w
vodomira [7]
The second place runner had already completed 320 meters when the winner crossed the finish line

8 0
3 years ago
A sequence is defined by f(0) = -20, f(n) = f(n-1) - 5 forn &gt; 1.
bulgar [2K]

Answer:

1. Proved down

2. proved down

3. f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5

Step-by-step explanation:

Let us explain how to solve the question

∵ f(0) = -20, f(n) = f(n - 1) - 5 for n > 1

→ That means we have an arithmetic sequence with constant

   difference -5 and first term -20

1. → f(1) means we need to find the second term, which equal the

      term - 5

∵ f(1) means n = 1

∴ f(1) = f(1 - 1) - 5

∴ f(1) = f(0) - 5

∵ f(0) = -20

∴ f(1) = -20 - 5 → Proved

2. → f(3) means we need to find the third term, which equal the

   second term - 5

∵ f(3) means n = 3

∴ f(3) = f(3 - 1) - 5

∴ f(3) = f(2) - 5

→ f(2) = f(1) - 5

∵ f(1) = -20 - 5

∴ f(2) = [-20 - 5] - 5 = -20 - 5 - 5

∴ f(3) = [-20 - 5 - 5] - 5

∴ f(3) = -20 - 5 - 5 - 5 → Proved

3. → From 1 and 2 we notice that the number of -5 is equal to n,

      at n = 1 there is one (-5), when n= 3 there are three (-5)

∵ n = 10

∴ There are ten (-5)

∴ f(10) = -20 - 5(10)

∴ f(10) = -20 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 - 5 → Proved

6 0
3 years ago
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