Rob works part time at the fallbrook riding stable. he makes $5 an hour exercising horses and $10 hour cleaning stalls. because rob is a full time student he can work no more than 12 hours per week. however he must make $60 per week.

 5x + 10y ≥ 60 ⇒ x+2y ≥ 12           (i)  

                x + y ≤ 12                                     (ii)  

Step-by-step explanation:

    Let the hours spent on exercising horse be x

    Let the hours spent on cleaning stalls be y

According to question:

Rob can't work more than 12 hours. So eq. (i) will be x + y ≤ 12

Rob earns $5 an hour by exercising horses and $10 an hour cleaning stalls and he must make $60 . So eq. (ii) will be 5x + 10y ≥ 60.

Dividing eq. (ii) by 5, it will become x + 2y ≥ 12.

∴ system of inequalities are x + y ≤ 12 and x + 2y ≥ 12.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.