April has a small business during the winter months making hats and scarves. A hat requires 2 hours on machine A, 4 hours on machine B, and 2 hours on machine C. A scarf requires 3 hours on machine A, 3 hours on machine B, and 1 hour on machine C. Machine A is available 36 hours per week, machine B is available for 42 hours, and machine C is available 20 hours per week. The profit on a hat is $7.00 and the profit on a scarf is $4.00.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

246

step-by-step explanation: