Is Amit's work correct? No, he should have used the origin as the center of the circle. No, the radius is 10 units, not 5 units. No, he did not calculate the distance correctly. Yes, the distance from the center to (2, –2) is not the same as the radius.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A circle centered at (–1, 2) has a diameter of 10 units. Amit wants to determine whether (2, –2) is also on the circle. His work is shown below. The radius is 5 units. Find the distance from the center to (2, –2). The point (2, –2) doesn’t lie on the circle because the calculated distance should be the same as the radius. Is Amit’s work correct? No, he should have used the origin as the center of the circle. No, the radius is 10 units, not 5 units. No, he did not calculate the distance correctly. Yes, the distance from the center to (2, –2) is not the same as the radius.

For Amit to determine whether the point (2, -2) is on the circle, we will need to find the distance between the coordinates  (–1, 2) and (2, -2) using the formula:

D = √(y₂-y₁)² + (x₂-x₁)²

D = √(-2-2)² + (2-(-1))²

D = √(-4)² + (2+1)²

D = √16 + 9

D =   √25

D = 5 units

Since the distance between the coordinate is equal to the radius of the circle, hence the coordinate (2, -2) lies on the circle.

Hence Amit is wrong because he did not calculate the distance correctly

14

step-by-step explanation:

14 x 3 = 42

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x