I need help asap can someone explain the answer to me plz, question is how many total inches of string is aloe using
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The change in the water vapors is modeled by the polynomial function c(x). In order to find the x-intercepts of a polynomial we set it equal to zero and solve for the values of x. The resulting values of x are the x-intercepts of the polynomial.
Once we have the x-intercepts we know the points where the graph crosses the x-axes. From the degree of the polynomial we can visualize the end behavior of the graph and using the values of maxima and minima a rough sketch can be plotted.
Let the polynomial function be c(x) = x ² -7x + 10
To find the x-intercepts we set the polynomial equal to zero and solve for x as shown below:
x ² -7x + 10 = 0
Factorizing the middle term, we get:
x ² - 2x - 5x + 10 = 0
x(x - 2) - 5(x - 2) =0
(x - 2)(x - 5)=0
x - 2 = 0 ⇒ x=2
x - 5 = 0 ⇒ x=5
Thus the x-intercept of our polynomial are 2 and 5. Since the polynomial is of degree 2 and has positive leading coefficient, its shape will be a parabola opening in upward direction. The graph will have a minimum point but no maximum if the domain is not specified. The minimum points occurs at the midpoint of the two x-intercepts. So the minimum point will occur at x=3.5. Using x=3.5 the value of the minimum point can be found. Using all this data a rough sketch of the polynomial can be constructed. The figure attached below shows the graph of our polynomial.
Answer:
Question 4:
Question 5:
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: where <em>m</em> is the slope of the line and <em>b</em> is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).
<u>Question 4</u>
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
where two points that pass through the line are
and
In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:
Therefore, the slope of the line is . Plug this into
as the slope (<em>m</em>):
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (<em>b</em>) is 0. Plug this into :
<u>Question 5</u>
<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>
Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:
Therefore, the slope is -5. Plug this into :
<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>
On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (<em>b</em>) is -3. Plug this into :
I hope this helps!