How many solutions over the complex number system does this polynomial have?
7x^3 – 33x^4 – 4x² + 3x + 52 = 0
2

4 solutions counting any possible multiplicity

Step-by-step explanation:

Recall that if one considers the Complex Number System, a polynomial has as many solutions (including multiplicity) as its degree.

So in this case, where we are considering a polynomial of order 4 Notice that the term , is in reality the leading term (term with the highest power of the variable) of this polynomial.

Therefore, in the Complex Number System, this polynomial would have 4 solutions.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: