Write the equation of a circle with a center at (1, 4) where a point on the circle is (4, 8).
a. (x - 4)2 + (y - 1)2 = 25
b.(x - 1)2 + (y - 4)2 = 25
c. (x - 1)2 + (y - 4)2 = 5
d.(x + 1)2 + (y + 4)2 = 25

B) (x - 1)² + (y - 4)² = 25.

Step-by-step explanation:

Given : A circle with a center at (1, 4) where a point on the circle is (4, 8).

To find : Write the equation of a circle.

Solution : We have given that center (1 ,4)

A point on a circle (4 ,8).

Distance between center and point on circle is called diameter .

Distance formula : .

Diameter =  .

Diameter =  .

Diameter =  .

Diameter =  .

Diameter = 5.

Radius = 2.5

Equation of center = (x - h)² + (y - k)² = r².

Where , (h , k) in coordinates of center and r is radius.

Equation of circle :  (x - 1)² + (y - 4)² = 5².

(x - 1)² + (y - 4)² = 25.

Therefore, B) (x - 1)² + (y - 4)² = 25.

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.