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2 years ago

Consider the rational expression x2+6x−2/6x−5 .

Mathematics

2 answers:

pychu [463]2 years ago

8 0

Answer:

Correct choices are C, D and E

Step-by-step explanation:

Consider expression $\dfrac{x^2+6x-2}{6x-5}.$

Note that numerator $x^2+6x-2$ consists of three terms: $x^2,\ 6x,\ -2$ and the denominator $6x-5$ consists of two terms: $6x,\ -5.$

A. False option.

The term in the numerator and in the denominator can be divided out, if both numerator and denominator are factored. Since $6x$ is a term in numerator and denominator and is not a factor, then it cannot be divided out.

B. False option.

The numerator is quadratic trinomial. Each quadratic trinomial has at most 2 factors. Since 3>2, then the numerator cannot have three factors.

C. True option, because three terms of the numerator are $x^2,\ 6x,\ -2.$

D. True option, because two terms of the denominator are $6x,\ -5.$

E. True option. The linear polynomial is always single factor.

DaniilM [7]2 years ago

3 0

Answer:

The last three terms are true.

Step-by-step explanation:

The last three statements are true. Yes, the numerator has 3 terms: x^2 + 6x - 2. Yes, the denominator has 2 terms: 6x - 5. Yes, that denominator is a single factor.

No, the numerator does not have three factors. It does, however, have three terms. No, 6x in the numerator does not cancel out the 6x in the denominator.

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Consider the equation

muminat

Answer:

A. $a=10\\ \\b\neq -8$

B. $a=10\\ \\b= -8$

Step-by-step explanation:

Consider the equation

$2(5x-4) = ax + b$

A. This equation has no solutions when the coefficients at x are the same and the free coefficients are not the same.

First, use distributive property:

$2(5x-4)=2\cdot 5x-2\cdot 4=10x-8$

So, the equation is

$10x-8=ax+b$

This equation has no solutions when

$a=10\\ \\b\neq -8$

B. The equation has infinitely many solutions when the coefficients at x are the same and the free coefficients are the same too.

So, the equation

$10x-8=ax+b$

has infinitely many solutions when

$a=10\\ \\b= -8$

In other cases, the equation has a unique solution

5 0

2 years ago

A complete graph of the polynomial function f is provided. Use your knowledge of the domain, range, behavior at each x intercept

Papessa [141]

The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

<h3>How to determine the equation?</h3>

From the graph, we have the following observations:

The graph has a turning point at x = 2
The graph changes the factor of its direction at x = -5

This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5

So, we have:

f(x) = a(x + 5)³(x - 2)²

The curve is inverted,

This means that a < 0

Assume a = -1.

Then, we have:

f(x) = -(x + 5)³(x - 2)²

Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

Read more about polynomials at:

brainly.com/question/4142886

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1 year ago

Suppose a set of data about the spread (in hundreds of acres) of a food-borne bacteria (after t weeks) in lettuce has the follow

Alexxandr [17]

Answer:

A sinusoidal model would be used

The kind of function that have consistency in the periodic rate of change is the Average rate of changes

Step-by-step explanation:

The type of model that would be used is sinusoidal model and this is because there is periodic change in the values given ( i.e the rate of changes given )

For percentage rate of changes :

starting from 0.9% there is an increase to 1.3% then a decrease to 1.1% and a further decrease to 1% before an increase to 1.3% and another decrease to 1%

For Average rate of changes:

starting from 2.9 there is a decrease to 2.4, then an increase to 3.7 and another decrease to 3.1 followed by an increase to 3.6 and a decrease back to 3.2

This relation ( sinusoidal model ) is best suited for a linear model because there is a periodic rate of change in the functions

The kind of function that have consistency in the period rate of change is the Average rate of changes

6 0

3 years ago

A chord divides a circle into

Pani-rosa [81]

<span>A chord divides a circle into 2 segments.

A major segment and a minor segment.

If the chord passes through the center of the circle, then it divides the circle into equal segments.</span>

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2 years ago

What of the following exponential functions is represented by the data in the table?

patriot [66]

Answer:

f(x) = ( 1/3) ^ (x)

Step-by-step explanation:

The function is

f(x) = (1/3) ^ (x)

When x = 1 f(x) = 1/3

when x=2 f(x) = 1/9

When x = -1 f(x) = ( 1/3) ^ -1 = 3/1 =3

7 0

2 years ago