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amid [387]
2 years ago
6

Write the equation in standard form. Identity the center and radius. x² + y2 + 8x-4y-7=0

Mathematics
1 answer:
Masteriza [31]2 years ago
3 0

Answer:

  • See below

Step-by-step explanation:

<u>Given equation:</u>

  • x² + y² + 8x - 4y - 7 = 0

<u>Convert this to standard form by completing the square:</u>

  • (x - h)² + (y - k)² = r², where (h, k) - center, r - radius
  • x² + 2*4x + 4² + y² - 2*2y + 2² - 16 - 4 - 7 = 0
  • (x + 4)² + (y - 2)² - 27 = 0
  • (x + 4)² + (y - 2)² = 27
  • (x + 4)² + (y - 2)² = (√27)²

The center is (- 4, 2) and the radius is √27

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The ceiling of Katie’s living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe
egoroff_w [7]

Answer:

<u><em>6</em></u> rolls because the total perimeter is 102 ft and five rolls is only 100 feet. So she needs <em><u>6</u></em> rolls.

Step-by-step explanation:

to find perimeter, add up all the side lengths.

so 15*4 (it's easier than 15+15+15...)

60 ft.

now we have to use Pythagorean's Theorum to find corner to corner.

so a^2+b^2=c^2

we have a and b

15^2+15^2=c^2

do the math...

225+225= 450

square root of 450=

21.213

double that because it's used twice (corner to corner and corner to corner)

42.426

now add it all up

42.426 + 60 = 102.426

we can round

102

20*5 = 100

so she needs 6

MY ORIGINAL ERROR WAS 5, BUT 5 TIMES 20 IS ONLY 80, SO THEREFORE 6 IS REQUIRED SO THERE IS ENOUGH TO COVER 102.

6 0
3 years ago
Find the 10th term of an arithmetic sequence if the common difference is 32 and the first term is 2
zaharov [31]

Answer:

290

Step-by-step explanation:

If the first term is 2 and the common difference is 32, then the formula for a(n) is:

a(n) = 2 + 32(n-1).

Thus, the 10th term is a(10) = 2 + 32(10-1)  =  2 + 32(9) = 290

6 0
3 years ago
Identify the scale factor
nydimaria [60]

Answer:

Step-by-step explanation:

k = 4/24 = 1/6

3 0
3 years ago
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Answer:

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3 years ago
A clothing pattern calls for 4.81 yd2 of fabric. How many square inches of fabric does the pattern use?
Vera_Pavlovna [14]
Total square inches of fabric. 
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1296 square inches makes one square yard. 

Therefore total square inches =
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4 0
3 years ago
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