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3 years ago

. What is the y intercept of the line represented by the equation 3x+2y = 6?

Mathematics

1 answer:

Alla [95]3 years ago

5 0

Answer:

Step-by-step explanation:

To identify the y-intercept represented by the given equation, we need to get the equation into slope-intercept from:

$y=mx+b$

$m=slope$

$b=y-intercept$

Start with:

$3x+2y=6$

Subtract $3x$ from both sides of the equation:

$2y=-3x+6$

Divide both sides of the equation by the coefficient of $y$ , which is $2$ :

$y=-1.5x+3$

Identify the y-intercept:

$b=3$

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Find the domain of the rational expression: x-3/2x-8

miss Akunina [59]

Answer:

$\huge\boxed{x\neq4\to x\in\mathbb{R}\backslash\{4\}}$

Step-by-step explanation:

$\dfrac{x-3}{2x-8}$

We know: the denominator must be different than 0.

Therefore

$2x-8\neq0$ <em>add 8 to both sides</em>

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$\dfrac{2x}{2}=\dfrac{8}{2}\\\\x\neq4$

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3 years ago

Analyzing a Graph In Exercise, analyze and sketch the graph of the function. Lable any relative extrema, points of inflection, a

Anit [1.1K]

Answer:

Analyzed and Sketched.

Step-by-step explanation:

We are given $y=\frac{\ln\left(5x)}{x^2}$

To sketch the graph we need to find 2 components.

1) First derivative of y with respect to x to determine the interval where function increases and decreases.

2) Second derivative of y with respect to x to determine the interval where function is concave up and concave down.

$y'=\frac{1-2\ln\left(5x)}{x^3}=0$

$x = \sqrt e/5$ is absolute maximum

$y''=\frac{6\ln\left(5x)-5}{x^4}=0$

$x=e^{5/6}/5$ is the point concavity changes from down to up.

Here, x = 0 is vertical asymptote and y = 0 is horizontal asymptote.

The graph is given in the attachment.

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3 years ago

I don’t understand this question. Can anyone help? I need answers ASAP. Thanks for all the help

zavuch27 [327]

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

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The expression would be (5*6)+(5*6)=x
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