Find the center of a circle with the equation:
x² + y² + 2x -20y – 20 = 0

Explanation:

If we had x^2+2x + ___, then 1 must go in the blank so that we have x^2+2x+1 = (x+1)^2

So we must add 1 to both sides to complete the square for the x terms. To find this value '1' we take half of the x coefficient 2 to get 1, then square it to get 1^2 = 1.

We have

x^2+y^2 + 2x - 20y - 20 = 0

x^2+y^2 + 2x - 20y - 20 + 1 = 0 + 1

(x^2+2x+1) + y^2 - 20y - 20 = 1

(x^2+2x+1) + y^2 - 20y = 1 + 20

(x+1)^2 + y^2 - 20y = 21

After completing the square for the x terms. Repeat for the y terms. Take half of -20 to get -10, which squares to 100. Add this to both sides

(x+1)^2 + y^2 - 20y = 21

(x+1)^2 + y^2 - 20y + 100 = 21+100

(x+1)^2 + (y - 10)^2 = 121

The equation is in the form (x-h)^2 + (y-k)^2 = r^2 where

The center is (h, k) = (-1, 10). The radius is r = 11.

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation:

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

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m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0