Consider the rational expression 4x+5/3x^2+x+5 which statements are true about the rational expression? select each correct answer. a.) the numerator has two terms b.) the denominator has three terms c.) 5 in the numerator divides out with 5 in the denominator d.) the denominator has three factors e.) 3x^2 + x + 5 is a single factor in the denominator

Statement a, b are true.

Step-by-step explanation:

First we have to define term,

A term is any constant, variable, or product of constants and variables in an expression, typically separated by a + or - sign.

For statement a,

The numerator has two terms. One is 3x and the other is 5.

For Statement b,

The denominator has three terms. One is 3x^2, second is x and the third term is 5.

For Statement c,

The number 5 in both numerator and denominator is added to the other terms, it had to be a multiplicative factor in both to cancel out. So it cannot be cancelled out.

For Statement d,

The number of factors of a polynomial are equal to its degree. The denominator is a polynomial of degree two/Quadratic, so it will not have more than 2 factors. So statement d is false.

For Statement e

The denominator is not a single factor as it is a degree 2 polynomial which can be further broken down to 2 factors.

it is x=-4

step-by-step explanation:

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.