Michael is paid $9 per hour to work at the movie theater and $7 per hour when he his aunt at her bakery. michael cannot work more than 32 hours in a week, but he wishes to earn at least $251 each week. which work schedule is within michael’s constraints?
a) 8 hours at the movie theater and 25 hours at the bakery
b) 15 hours at the movie theater and 20 hours at the bakery
c) 19 hours at the movie theater and 12 hours at the bakery
d) 21 hours at the movie theater and 8 hours at the bakery

Let

x-------> the number of hours working to the movie theater

y------->  the number of hours working at the bakery

we know that

------> inequality A

-----> inequality B

we will proceed to verify each case to determine the solution of the problem

 If the work schedule is within Michael's limitations, then he must meet both of these inequalities.

case A)   hours at the movie theater and hours at the bakery

Verify inequality A

------> is not true

therefore

The work schedule of case A) is not within Michael's limitations

case B)   hours at the movie theater and hours at the bakery

Verify inequality A

------> is not true

therefore

The work schedule of case B) is not within Michael's limitations

case C)   hours at the movie theater and hours at the bakery

Verify inequality A

------> is  true

Verify inequality B

------> is true

therefore

The work schedule of case C) is within Michael's limitations

case D)   hours at the movie theater and hours at the bakery

Verify inequality A

------> is  true

Verify inequality B

------> is not true

therefore

The work schedule of case D) is not within Michael's limitations

the answer is the option C

hours at the movie theater and hours at the bakery

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

hope this !