For the data in the table, write an equation for the direct variation.

Mathematics

1 answer:

melisa1 [442]8 months ago

4 0

The equation of direct variation is,

$\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}$

Substitute the values of y and x.

$\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}$

So, the obtained equation will be y=1.35(x).

Let's check with the values of x.

1) If x=4

$\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}$

2) If x=2

$\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}$

3) If x=-2

You might be interested in

Alice gave Bob as many dollars as Bob had. Bob then gave Alice as many dollars Alice then had. At this point, each had 24 dollar

valentina_108 [34]

Answer:

x = y

Step-by-step explanation:

x = y

7 0

2 years ago

The change in water level of a lake is modeled by a polynomial function, W(x). Describe how to find the x-intercepts of W(x) and

Agata [3.3K]

First. Finding the x-intercepts of $W(x)$

Let $W(x)$ be the change in water level. So to find the x-intercepts of this function we can use The Rational Zero Test that states:

To find the zeros of the polynomial:

$f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{2}x^{2}+a_{1}x+a_{0}$

We use the Trial-and-Error Method which states that a factor of the constant term:

$a_{0}$

can be a zero of a polynomial (the x-intercepts).

So let's use an example: Suppose you have the following polynomial:

$W(x)=x^{4}-x^{3}-7x^{2}+x+6$

where the constant term is $a_{0}=6$ . The possible zeros are the factors of this term, that is:

$1, -1, 2, -2, 3, -3, 6 \ and \ -6$ .

Thus:

 $W(1)=0 \\ W(-1)=0 \\ W(2)=-12 \\ W(-2)=0 \\ W(3)=0 \\ W(-3)=48 \\ W(6)=840 \\ W(-6)=1260$ 

From the foregoing, we can affirm that $1, -1, -2 \ and \ 3$ are zeros of the polynomial.

Second. Construction a rough graph of $W(x)$

Given that this is a polynomial, then the function is continuous. To graph it we set the roots on the coordinate system. We take the interval:

$[-2,-1]$

and compute $W(c)$ where $c$ is a real number between -2 and -1. If $W(c)>0$ , the curve start rising, if not, the curve start falling. For instance:

$If \ c=-\frac{3}{2} \\ \\ then \ w(-\frac{3}{2})=-2.81$

Therefore the curve start falling and it goes up and down until $x=3$ and from this point it rises without a bound as shown in the figure below