Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or 
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Remember that
The unit rate of change is the same as the slope
so
In this problem

The linear equation is equal to

To graph the line we need two points
we have (0,0) because the line passes through the origin
Determine other point
assume a value of x and calculate the value of y
For x=8

The other point is (8,3)
Plot the points and join them to draw the line
The graph in the attached figure
we have

we know that
<u>The Rational Root Theorem</u> states that when a root 'x' is written as a fraction in lowest terms

p is an integer factor of the constant term, and q is an integer factor of the coefficient of the first monomial.
So
in this problem
the constant term is equal to 
and the first monomial is equal to
-----> coefficient is 
So
possible values of p are 
possible values of q are 
therefore
<u>the answer is</u>
The all potential rational roots of f(x) are
(+/-)
,(+/-)
,(+/-)
,(+/-)
,(+/-)
,(+/-)
Answer:
The graph is shown below.
Step-by-step explanation:
Given:
The inequality of a line to graph is given as:

In order to graph it, we first make the 'inequality' sign to 'equal to' sign. This gives,

Now, we plot this line on a graph. The given line is of the form:
Where, 'm' is the slope and 'b' is the y-intercept.
So, for the line
, 
The y-intercept is at (0, -3).
In order to draw the line correctly we find another point. Let the 'y' value be 0.
Now, 
So, the point is (3, 0).
Now, we mark these points and draw a line passing through these two points.
Now, consider the line inequality
. The 'y' value is less than
. So, the solution region will be region below the line and excluding all the points on the line. So, we draw a broken line and shade the region below it.
The graph is shown below.
Answer:
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
is equal to
in this problem we have
so
substitute in the formula
therefore
x = StartFraction negative (negative 2) plus or minus StartRoot (negative 2) squared minus 4 (negative 3)(6) EndRoot Over 2(negative 3) EndFraction
G(x)=19x is the function that’ll grow at the fastest rate.