Answer:-2/39
Step-by-step explanation:
Answer:
Yes, all three of them are proportional
Step-by-step explanation:
First, let's simplify them all the way:
10/45 = 2/9
20/90 = 2/9
6/27 = 2/9
All three of these ratios simplified down to their simplest form are 2/9, meaning that they are all proportional.
Answer:
k = 4
Step-by-step explanation:
In order for the claim to be true, (x-3) must be a factor of each of the terms in the first expression. That is, you must have that expression factor as ...
(x -3)(2x +5) +(x -3)(x +7)
Factoring out (x -3), we get ...
= (x -3)(2x +5 +x +7) = (x -3)(3x +12)
= 3(x -3)(x +4)
The value of k must be 4.
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.