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3 years ago

What is the slope of a line parallel to the line 4x-7y=-14?

Mathematics

1 answer:

Sav [38]3 years ago

3 0

We have 7y = 4x + 14;

Then, y = (4/7)x + 2;

The slope of this line is 4/7;

Because another line is parallel with the first one, the chosen slope is 4/7.

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Determine the horizontal vertical and slant asymptote y=x^2+2x-3/x-7

lilavasa [31]

Answer:

<h2>A.Vertical:x=7</h2><h2>Slant:y=x+9</h2>

Step-by-step explanation:

$f(x)=\dfrac{x^2+2x-3}{x-7}\\\\vertical\ asymptote:\\\\x-7=0\qquad\text{add 7 to both sides}\\\\\boxed{x=7}\\\\horizontal\ asymptote:\\\\\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3}{x-7}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\frac{2}{x}-\frac{3}{x^2}\right)}{x\left(1-\frac{7}{x}\right)}=\lim\limits_{x\to\pm\infty}\dfrac{x\left(1+\frac{2}{x}-\frac{3}{x^2}\right)}{1-\frac{7}{x}}=\pm\infty\\\\\boxed{not\ exist}$

$slant\ asymptote:\\\\y=ax+b\\\\a=\lim\limits_{x\to\pm\infty}\dfrac{f(x)}{x}\\\\b=\lim\limits_{x\to\pm\infty}(f(x)-ax)\\\\a=\lim\limits_{x\to\pm\infty}\dfrac{\frac{x^2+2x-3}{x-7}}{x}=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3}{x(x-7)}=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3}{x^2-7x}\\\\=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\frac{2}{x}-\frac{3}{x^2}\right)}{x^2\left(1-\frac{7}{x}\right)}=\lim\limits_{x\to\pm\infty}\dfrac{1+\frac{2}{x}-\frac{3}{x^2}}{1-\frac{7}{x}}=\dfrac{1}{1}=1$

$b=\lim\limits_{x\to\pm\infty}\left(\dfrac{x^2+2x-3}{x-7}-1x\right)=\lim\limits_{x\to\pm\infty}\left(\dfrac{x^2+2x-3}{x-7}-\dfrac{x(x-7)}{x-7}\right)\\\\=\lim\limits_{x\to\pm\infty}\left(\dfrac{x^2+2x-3}{x-7}-\dfrac{x^2-7x}{x-7}\right)=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3-(x^2-7x)}{x-7}\\\\=\lim\limits_{x\to\pm\infty}\dfrac{x^2+2x-3-x^2+7x}{x-7}=\lim\limits_{x\to\pm\infty}\dfrac{9x-3}{x-7}=\lim\limits_{x\to\pm\infty}\dfrac{x\left(9-\frac{3}{x}\right)}{x\left(1-\frac{7}{x}\right)}$

$=\lim\limits_{x\to\pm\infty}\dfrac{9-\frac{3}{x}}{1-\frac{7}{x}}=\dfrac{9}{1}=9\\\\\boxed{y=1x+9}$

8 0

3 years ago

A painting crew reported that a job is 3/5 completed. What fraction of the job remains to be done?

Lunna [17]

Answer:

2/5

Step-by-step explanation:

5/5 = full job

3/5 = done

full job - done = remaining

5/5 job - 3/5 job

= 2/5 (remaining)

3 0

3 years ago

Read 2 more answers

If you needed to reflect (-4,-5) over the y-axis what would the<br> coordinates be?

Triss [41]

Answer: The coordinates would be (4,-5)

6 0

3 years ago

Read 2 more answers

HELPPP

Dmitriy789 [7]

Answer:D the last one

Step-by-step explanation:

7 0

3 years ago

Deborah has two paintings in her portfolio and paints three more each week.Kai has twelve paintings in her portfolio and paints

elena-14-01-66 [18.8K]

Well, we can set up these equations like this-
Deborah- 2+3w
Kai- 12+2w
w=number of weeks that pass
Now, we set them equal to each other:
2+3w=12+2w

Solve for w
2-12=2w-3w
-10 = -1w
w = 10
10 weeks. Hope this helped!

4 0

3 years ago