3 points) For speeds between 40 mph and 65 mph, a diesel truck gets 490x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 4.7 dollars per gallon. The driver is paid 25 dollars per hour. A) What is the total cost to have the truck driven 50 miles at a constant speed of 45 miles per hour

Part A: (12x² +74x + 44) Square units.

Part B: A Second ( 2nd ) Degree Trinomial

Part C: Part A which is the multiplication of 6x + 4) units and (2x + 11) units to find the Area of a rectangle demonstrate closure property because it is the multiplication of two Binomials to give us a second degree Trinomial which is

(12x² +74x+ 44) Square units.

Step-by-step explanation:

Part A: What is the expression that represents the area of the rectangle?

The formula for the Area of a rectangle is given as Length × Breadth

We are told in the question that rectangle has sides of (6x + 4) units and (2x + 11) units

Therefore, Area of the rectangle is calculated as:

(6x + 4) units × (2x + 11) units

6x(2x +11) + 4(2x + 11)

12x² + 66x + 8x + 44

(12x² +74x+ 44) Square units.

Part B: What are the degree and classification of the expression obtained in Part A?

A polynomial can be defined as a mathematically expression that consists of one or more than one algebraic terms in it. One of the characteristics of a polynomial is the degree is carries. The degree of a polynomial can be defined as one of algebraic terms that carries the highest exponential values.

For example

4x⁴ + 2x³ + 5x² + 1 : The degree of this polynomial is 4 because the algebraic term with the highest exponential values is "4x⁴".

A polynomial can be classified into 3 types based on the number of terms that it contains.

a) A monomial : = 7x

b) A Binomial = 6x² + 4

c) A Trinomial = 3x³ + 2x + 1

Hence, for the above question, the degree and classification of the expression obtained in Part A which is

(12x² +74x + 44) Square units is that it is a second (2nd ) degree Trinomial. This is because it consists of 3 terms and the algebraic terms with the highest exponential values is 12x².

Part C: How does Part A demonstrate the closure property for polynomials?

Closure property for polynomials is one of the characteristics that a polynomial shows when it undergoes either Addition, Subtraction or Multiplication in other to give us another polynomial.

Therefore, in the question above,

Part A which is the multiplication of 6x + 4) units and (2x + 11) units to find the Area of a rectangle demonstrate closure property because it is the multiplication of two Binomials to give us a second degree Trinomial which is

(12x² +74x+ 44) Square units.