To the nearest mile, what is the total distance that he ran?
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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:
Point-slope form of equation given as .
Slope-intercept form of equation is given as .
Step-by-step explanation:
In the question, it is given that the slope of a line is -2 and it passes from (-2,2).
It is asked to write the point-slope form of the equation and rewrite it as slope-intercept form.
To do so, first find the values which are given in the question and put it in the formula of point-slope form. Simplify the equation to rewrite as slope-intercept form.
Step 1 of 2
Passing point of the line is (-2,2).
Hence, and
Also, the slope of the line is -2.
Hence, m=-2
Substitute the above values in point-slope form of equation given by
Hence, point-slope form of equation given as y-2=-2(x+2).
Step 2 of 2
Solve y-2=-2(x+2) to write it as slope-intercept form given by y=mx+c.
Hence, slope-intercept form of equation is given as y=-2x-2.
Answer:
An algebraic expression is just an equation without an answer