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2 years ago

Which equation best represents the line of best fit for the scatterplot? a) y = 2x b) y = 2x + 2 c) y = −2x + 2 d) y = −x + 2

1 answer:

6 0

The equation which best represents the line of best fit for the scatterplot in the image attached below is: B. y = 2x + 2.

<h3>What is a scatter plot?</h3>

A scatter plot refers to a type of graph which uses the cartesian coordinates (x-axis and y-axis) to illustrate the values of two variables, with the resulting points revealing any correlation between the set of data.

Based on the graph attached in the image below, y = 2x + 2 is an equation which best represents the line of best fit for the scatterplot because there is a corellation between the data at this point.

Read more on scatterplot here: brainly.com/question/6592115

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3 years ago

The point (−2,4) lies on the curve in the xy-plane given by the equation f(x)g(y)=17−x−y, where f is a differentiable function o

Nikitich [7]

The value of $\frac{dy}{dx}$ is -3. $\blacksquare$

<h2>Procedure - Differentiability</h2><h3 /><h3>Chain rule and derivatives</h3><h3 />

We derive an expression for $\frac{dy}{dx}$ by means of chain rule and differentiation rule for a product of functions:

$\frac{d}{dx}[f(x)\cdot g(y)] = [f'(x)\cdot \frac{dx}{dx}]\cdot g(y) + f(x) \cdot [g'(y)\cdot \frac{dy}{dx} ]$

$\frac{d}{dx}[f(x)\cdot g(y)] = f'(x)\cdot g(y) +f(x)\cdot g'(y)\cdot \frac{dy}{dx}$ (1)

If we know that $f(x) \cdot g(y) = 17-x-y$ , $f(-2) = 3$ ,<em> </em> $f'(-2) = 4$ ,<em> </em> $g(4) = 5$ and $g'(4) = 2$ , then we have the following expression:

$-1-\frac{dy}{dx} = (4)\cdot (5) + (3)\cdot (2) \cdot \frac{dy}{dx}$

$-1-\frac{dy}{dx} = 20 + 6\cdot \frac{dy}{dx}$

$7\cdot \frac{dy}{dx} = -21$

$\frac{dy}{dx} = -3$

The value of $\frac{dy}{dx}$ is -3. $\blacksquare$

To learn more on differentiability, we kindly invite to check this verified question: brainly.com/question/24062595

<h3>Remark</h3>

The statement is incomplete and full of mistakes. Complete and corrected form is presented below:

<em>The point (-2, 4) lies on the curve in the xy-plane given by the equation </em> $f(x)\cdot g(y) = 17 - x\cdot y$ <em>, where </em> $f$ <em> is a differentiable function of </em> $x$ <em> and </em> $g$ <em> is a differentiable function of </em> $y$ <em>. Selected values of </em> $f$ <em>, </em> $f'$ <em>, </em> $g$ <em> and </em> $g'$ <em> are given below: </em> $f(-2) = 3$ <em>, </em> $f'(-2) = 4$ <em>, </em> $g(4) = 5$ <em>, </em> $g'(4) = 2$ <em>. </em>

<em />

<em>What is the value of </em> $\frac{dy}{dx}$ <em> at the point </em> $(-2, 4)$ <em>?</em>

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2 years ago

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Answer:

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