Write the equation of the graph shown below in factored form.

Mathematics

2 answers:

IgorC [24]3 years ago

4 0

F(x) = (x+1)(x+2)(x+3)

zloy xaker [14]3 years ago

3 0

Answer:

f(x) = (x - 1)(x - 2)(x - 3)

Step-by-step explanation:

Each intercept in the graph is a factor of the equation. When the intercept has a multiplicity of 1 (to the 1st power, or normal), it simply goes through the point, and when it has a multiplicity of 2 (to the 2nd power), it curves back.

Because the graph simply passes through all 3 intercepts, and the graph shown is a cube ( $x^{3}$ graph, we know that there has to be 3 factors, all with a multiplicity of 1. Multiplicity in the equation is simply the power that the factor is raised by.

If you multiply all the intercepts together [or (x - 1)(x - 2)(x - 3)], you will have the equation already in factored form, meaning you have your answer.

<em>Hope this helped! :)</em>

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Three rational numbers between 5/31 and 6/31

Ludmilka [50]

Answer:

$\dfrac{26}{155}$ , $\dfrac{27}{155}$ , and $\dfrac{28}{155}$ .

Step-by-step explanation:

What is a rational number? By definition, a rational number can be represented as the fraction of two integers.

The goal is to find three fractions in the form $\dfrac{p}{q}$ between $\dfrac{5}{31}$ and $\dfrac{6}{31}$ .

$\dfrac{5}{31} < \dfrac{p}{q} < \dfrac{6}{31}$ .

At this moment, there doesn't seems to be a number that could fit. The question is asking for three of these numbers. Multiple the numerator and the denominator by a number greater than three (e.g., five) to obtain

$\dfrac{25}{155} < \dfrac{p}{q} < \dfrac{30}{155}$ .