Which of the following is the equation of a circle whose center is at the origin and whose radius is 4?

x²+y²=16

Step-by-step explanation:

the general equation for a circle is given as :

(x−h)²+(y−k)²=r²

where (h, k) is the coordinate of the center of the circle and r is the radius

in this case h=0, k=0 and r = 4

equation becomes

x²+y²=4²

or

x²+y²=16

Last option.

Step-by-step explanation:

The equation of a circle in Center-radius form is:

Where the center is at the point (h,k) and "r" is the radius.

If the center of this circle is at the origin, means that:

Since the radius is 4, then:

Now we need to substitute these values into the equation of the circle.

Simplifying the equation, we get:

This matches with the last option.

step-by-step explanation:

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.