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11111nata11111 [884]
3 years ago
5

The center of a circle is located at (3, 8), and the circle has a radius that is 5 units long. What is the general form of the e

quation for the circle?
A- x2 + y2 − 6x − 16y + 48 = 0
B- x2 + y2 − 6x − 16y − 25 = 0
C- x2 + y2 + 6x + 16y + 48 = 0
D- x2 + y2 + 6x + 16y − 25 = 0
Mathematics
2 answers:
babymother [125]3 years ago
8 0
The answer is A. To understand that, you need to put it in order by the x's and the y's to get x^2-6x + y^2-16y = -48. Now complete the square on both the x and the y terms to get (x^2-6x+9) +(y^2-16y+64) = -48+9+64. Rewriting that in vertex form on the left and doing the math on the right gives you
(x-3)^2 + (y-8)^2 = 25, which shows you a center of (3,8) and a radius of 5.
TiliK225 [7]3 years ago
8 0

Answer:

The correct option is A.

Step-by-step explanation:

The standard from of a circle is

(x-h)^2+(y-k)^2=r^2

Where, (h,k) is center of the circle and r is the radius.

It is given that the center of the circle is (3,8) and the radius of the circle is 5 units.

Substitute h=3, k=8 and r=5 in the above equation .

(x-3)^2+(y-8)^2=5^2

x^2-6x+9+y^2-16y+64=25          [\because (x-y)^2=x^2-2xy+y^2]

x^2+y^2-6x-16y+9+64=25

x^2+y^2-6x-16y+73=25

Subtract 25 from both the sides.

x^2+y^2-6x-16y+73-25=0

x^2+y^2-6x-16y+48=0

Therefore the correct option is A.

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nasty-shy [4]
Isolate k by dividing both sides by 8

8k=4/9
k=4/72

Reduce if possible

4/72 -> 1/18
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3 years ago
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3 years ago
Please help!!!!!!!!!!!!!!!
babunello [35]

Answer:

Answer A

Step-by-step explanation:

Answer A indicates some minimal value for the set of points to the left (negative side of the distribution) which are associated with negative skewness since the mean is at 22 also with larger deviation to the left shown in the median of the points to the left further to the negative side of the plot.

Answers B and C show symmetric distributions (no skewness at all).

Answer D would represent skewness to the right (positively skewed)

So the correct answer is answer A.

8 0
3 years ago
The angles in a triangle are represented by 5x, 8x, and 2x+9. What is the value of x?
Ahat [919]

Answer:

x = 11.4

Step-by-step explanation:

The sum of the angles of any triangle must add up to 180°.  Since we have the expressions for each angle:  5x, 8x, and (2x +9), we can solve for the variable of 'x' by adding the expressions together and setting them equal to 180:

5x + 8x + (2x +9) = 180

Combine like terms:  15x + 9 = 180

Use inverse operations: 15x + 9 - 9 = 180 - 9

                                                     15x = 171  or x = 11.4

Check:  5(11.4) + 8(11.4) + 2(11.4) + 9 = 57 + 91.2 + 22.8 + 9 = 180

8 0
3 years ago
Write the slope-intercept form of the equation of the line; (-5,-4) and prep. To y equals 5x plus 1
ohaa [14]

Answer:

y=-\frac{1}{5} x-5

Step-by-step explanation:

The given line is defined by:  y=5x+1, where we see that the slope is 5 and the y-intercept 1.

In order to find a line perpendicular to the given one, we need it to have a slope that is the "opposite of the reciprocal" of the given slope.

"Opposite" means it would have its sign inverted (in our case from positive to negative); and "reciprocal means that instead of 5, it would be its reciprocal: \frac{1}{5}.

We can write this new line with such slope, and try to find its y-intercept (b) by using the given condition that requires it to go through the point (-5,-4) on he plane:

y=-\frac{1}{5} x+b

we require then that when x=-5, the value of y=-4.

Therefore: -4=-\frac{1}{5} (-5)+b\\-4=\frac{5}{5} +b\\-4=1+b\\b=-4-1=-5

Then our final answer is that the new line should have the form: y=-\frac{1}{5} x-5

4 0
3 years ago
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