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natka813 [3]
3 years ago
6

Find the center and radius of a circle defined by the equation x^2+yy^2+4x-8y+13=0

Mathematics
1 answer:
gogolik [260]3 years ago
8 0
Hello : 
x²+y²+4x-8y +13 = 0
(x² +4x) +(y² -8y )+13 = 0
(x²+4x+4) -4 +(y-8y +16) -16 +13 = 0
(x+2)² +(y -4)² = 7
the center is : (-2 , 4) and radius <span>√7</span>
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Given: ∠AOC, ∠BOC - complementary angles
34kurt

Answer:

  • 30
  • COB . . . . or . . . . BOC

Step-by-step explanation:

The reason given on the line of interest is "substitution," so the problem boils down to determining what was substituted for what. The previous statement says ...

  AOC + COB = 90

and the first part of the statement we're to complete has BOC + ___.

We see from the given statements that m∠AOC = m∠BOC + 30°, so it appears that is the substitution that has been made: AOC has been replaced by BOC + 30.

This means the first blank is filled with 30.

__

The second part of the previous statement is ...

  AOC + COB = 90

so we believe this (COB) should go in the second blank.

__

Then the line of interest would read ...

  BOC + 30 + COB = 90

_____

<em>Comment on the problem</em>

There is a curious mix of notations here. Usually, (as in the beginning of this problem) we refer to the measure of an angle using "m∠" in front of the angle designator, and we use a degree symbol to indicate the units of that measure. Part-way through the problem statement written here, those notations were dropped, and we're to assume they are intended. IMO, this is a poor way to demonstrate careful problem solving.

The substitution given for AOC is BOC+30, but the line into which that is substituted has AOC +COB = 90. This means the equation after substitution is ...

  BOC +30 +COB = 90

Since BOC and COB are the same angle, we can sort of fudge the "algebra" to get to  BOC=30, but if the problem were more carefully written, the angle would be referred to by consistent nomenclature:

  m∠AOC + m∠BOC = 90° . . . . . . . . . preferred angle designations

  (m∠BOC + 30°) + m∠BOC = 90° . . . . substitution for m∠AOC

  2(m∠BOC) = 60° . . . . . . algebra (subtract 30°, collect terms)

  m∠BOC = 30° . . . . . . . . algebra (divide by 2)

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3 years ago
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d1i1m1o1n [39]
The answer you selected in that photo given, is correct. I can tell just by using common sense and by judging the other options second option (B) is looking the most clearest one to me.
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2 years ago
What is 11.375 in faction
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11 3/8 would be the simplified version and 91/8 would be the other way.
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3 years ago
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Look at the attachment.​
Sloan [31]

Answer:

12 cups

Step-by-step explanation:

21:7=3 i mean that's kinda it

3x4=12

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