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3 years ago

What is the slope of the line shown in the graph? A 3/2 B) 2/3 C) -3/4 D) -2/3

Mathematics

2 answers:

Alex777 [14]3 years ago

8 0

D. -2/3 because when you find when the line lies on 1 point twice. Count down it would be 2 and count over it would be 3. The direction of the line is going down so that would be negative.

garik1379 [7]3 years ago

6 0

Answer:

Step-by-step explanation:

y-intercept is (0, 3)

x-intercept is (4.5, 0)

formula to find the slope from two points is

$slope = m = \frac{y2 - y1}{x2 - x1} = \frac{y1 - y2}{x1 - x2} \\$

then the slope of the line that crosses (0, 3) & (4.5, 0) is

$m = \frac{3 - 0}{0 - 4.5} = \frac{3}{ - 4.5} = - \frac{3}{ \frac{9}{2} } = - \frac{2}{3}$

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Answer:

The function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

$\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

The function is continuous at point x=36 if:

The function $\\ f(x)$ exists at x=36.
The limit on both sides of 36 exists.
The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

$\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}$

$\\ f(36) = \frac{36*6}{900} = \frac{6}{25}$

The limit of the $\\ f(x)$ is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

$\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Since

$\\ f(36) = \frac{6}{25}$

And

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Then, the function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

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