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:
75 - 52.5 = x
Step-by-step explanation:
is the correct answer.
Answer:
Step-by-step explanation:
A parallel line will have the same slope as the reference line. In this case, I don't see the "given line" as promised in the question. If it does appear, and it looks like y = 5x + 3, for example, the slope is 5 and the new line will have the same slope.
<h3>
<u>If this slope is correct</u>, we can start the equation for the parallel line that goes through point (-3,2) by starting with:</h3><h3 /><h3>y = 5x + b</h3><h3 /><h3>We need a value of b that forces the line to go through point (-3,2). We can do that by using the given point in the equation and solving for b:</h3><h3>y = 5x + b</h3><h3>2 = 5(-3) + b</h3><h3>b = 17</h3><h3 /><h3>The parallel line to y=5x+3 is</h3><h3>y = 5x + 17</h3><h3 /><h3>See attachment.</h3><h3 /><h3 /><h3 />
Answer: Approximately 4.7 hours.
Step-by-step explanation:
He rode the bicycle for some time before it broke down and he walked the remaining distance. This means that Jim covered a total of 165 miles by riding at a speed of 35 miles per hour and walking at a speed of 3 miles per hour.
Let x = the distance covered by riding the bicycle.
Let y = the distance covered by walking.
Time = distance /speed
Time he used in riding would be x/35
Time he used in walking would be y/3
Since the entire trip took 7 hours,
x/35 + y/3 = 7
3x + 35y = 735 - - - - - - - - 1
Total miles covered is 165. Therefore,
x + y = 165 - - - - - - - - -- - -2
Substituting x = 165-y into equation 1, it becomes
3(165-y) + 35y = 735
495-3y + 35y = 735
-3y + 135y = 735-495
132y = 240
y = 240/132
y = 1.81m
x = 165 - 1.81 = 163.19
Amount of time that he spent on the bicycle will be
x/35 = 163.19/35
= 4.66
Approximately 4.7 hours.
