Which point lies on the circumference of a circle with center (6,5) that passes through the point (9,8)? A. (3,2) B. (4,7) C. (6,2) or D. (12,11)

A. (3,2)

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center of the circle and any point on the circumference is equal to the radius of the circle

we have the ordered pairs

(6,5) and (9,8)

the formula to calculate the distance between two points is equal to

substitute

step 2

Find the equation of the circle

substitute the given values

step 3

Verify each ordered pair

Remember that

If a ordered pair lie on the circumference of the circle, then the ordered pair must satisfy the equation of the circle

A) we have

(3,2)

substitute the value of x and the value of y in the equation of the circle

----> is true

so

The ordered pair lie on the circumference of the circle

B) we have

(4,7)

substitute the value of x and the value of y in the equation of the circle

----> is not true

so

The ordered pair not lie on the circumference of the circle

C) we have

(6,2)

substitute the value of x and the value of y in the equation of the circle

----> is not true

so

The ordered pair not lie on the circumference of the circle

D) we have

(12,11)

substitute the value of x and the value of y in the equation of the circle

----> is not true

so

The ordered pair not lie on the circumference of the circle

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%