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natima [27]
3 years ago
12

Find the center and the radius of the circle with the equation x^2-4x+y^2-12y+31=0

Mathematics
1 answer:
ivanzaharov [21]3 years ago
5 0
<h2>C: Center: (2, 6)</h2><h2>Radius: 3</h2>

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Find the distance between the two points in simplest radical form.<br> (-1,2) and (-7, -6)
weeeeeb [17]

Answer:

10

Step-by-step explanation:

3 0
2 years ago
A bicyclist travels at a constant rate of 11miles in 1/4hour. Find the unit rate of the hikers in miles per hour
MissTica
11 miles in 1/4 hour
1/4 of an hour is 15 minutes
so 11 in 15 minutes
x /60 = 11/15
cross multiply
x*15 = 60 * 11
15x = 660
divide both sides by 15
x = 44

the unit rate of the hikers in miles per hour is 44 mph.

You can also solve like this
1/4 of hour is 15 minutes
to get to the whole hour you would multiply by four
so you'd (11miles in 1/4 hour) * 4
44 miles in 1 hour

Hope this helps :)
7 0
3 years ago
The slope of a line is 3 times the slope of another line
Nutka1998 [239]

Answer:

  • 4-√13 ≈ 0.394449
  • (4-√13)/3 ≈ 0.131483

Step-by-step explanation:

Let the lesser slope be represented by x. This is also the tangent of the angle it makes with the +x axis. Then the larger slope is 3x, and likewise, its angle has the tangent 3x.

So, we can use the tangent formula for the difference of angles to find the values of these slopes.

  tan(a -b) = (tan(a) -tan(b))/(1 +tan(a)tan(b))

We want this tangent to be 1/4, so ...

  1/4 = (3x -x)/(1 +(3x)(x))

  3x^2 +1 = 4(2x) . . . . . . . cross multiply

  3x^2 -8x +1 = 0 . . . . . . . write in standard form

Now, we can use the quadratic formula to find x.

  x = (-b ±√(b^2-4ac))/(2a) = (-(-8)±√((-8)^2 -4(3)(1)))/(2(3))

  = (8 ± √52)/6

  x = (4 ±√13)/3

We're only interested in the smaller of these two values.

The slope of one line is 4 -√13; the slope of the other is (4-√13)/3.

_____

<em>Check</em>

The line with the lesser slope makes an angle of arctan((4-√13)/3) ≈ 7.490° with the +x axis. The line with the greater slope makes an angle of arctan(4-√13) ≈ 21.527° with the +x axis.

The difference angle is about 14.036°, and the tangent of that is 0.25, as required.

6 0
3 years ago
21y(y+3) please i need the answer
LekaFEV [45]

Answer:

21y^2+63y

Step-by-step explanation:

21y(y+3)

21y^2+63y

7 0
3 years ago
Read 2 more answers
at an amusement park, children are charged an entrance fee of $20 plus $3 per ride and adults are charged an entrance fee of $28
const2013 [10]

Answer:

T=3r+20 for the children and T=4r+28 for the adults

Step-by-step explanation:

Let r equal the amount of rides the person took, let T equal the total cost of the trip

6 0
3 years ago
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