Question 3 (essay worth 10 points) (06.01, 06.04 mc) a rectangle has sides measuring (6x + 4) units and (2x + 11) units. part a: what is the expression that represents the area of the rectangle? show your work. (4 points) part b: what are the degree and classification of the expression obtained in part a? (3 points) part c: how does part a demonstrate the closure property for polynomials? (3 points)

  A: 12x² +74x +44

  B: degree 2 trinomial

  C: the product of two polynomials is a polynomial

Step-by-step explanation:

A: The area is the product of length and width, so will be the product ...

  (6x +4)(2x +11) = 6x(2x +11) +4(2x +11) = 12x² +66x +8x +44

  = 12x² +74x +44

__

B: The highest power of x is 2, so this is a 2nd-degree polynomial. It has 3 terms, so is classified as a trinomial.

__

C: In part A we multiplied two polynomials and obtained a result that is a polynomial. The closure property of multiplication on a set requires that any product of members of the set also is a member of the set. Thus the closure property of multiplication on the set of polynomials is not violated by the answer to part A.

__

Closure for one product does not demonstrate closure. It provides an example for which closure is not violated.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.