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3 years ago

I don’t get how to solve this

Mathematics

1 answer:

Annette [7]3 years ago

3 0

<EFD is also shown as e on the diagram. It is 90 degrees. <EFG is made up of the same two lines and is equal to 90 degrees (shown by the little box) so <EFD must be equivalent.

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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

The simple interest earned on a deposit of $4,000 at 5% for 120 days.

fgiga [73]

B. I=PRT is the simple interest formula. 120 days is 4 months, or 1/3 of a year.
I=(4,000)(0.05)(0.33333)
I=$66.67

5 0

3 years ago

Read 2 more answers

Help me please: answer as an improper fraction

rewona [7]

1) $\frac{7}{24}$
2) $\frac{2}{7}$
3) $\frac{1}{5}$
4) $\frac{3}{14}$
5) $\frac{1}{3}$
6) $\frac{7}{20}$
7) $\frac{6}{10}$
8) $\frac{1}{12}$
9) $\frac{1}{3}$
10) $\frac{1}{90}$
11) $\frac{1}{40}$
12) $\frac{1}{50}$
13) $\frac{20}{21}$
14) $\frac{1}{4}$
15) $\frac{5}{6}$
16) $\frac{9}{35}$
17) $\frac{35}{12}$ ( $2 \frac{11}{12}$ )
18) $\frac{9}{1}$ (9)

7 0

3 years ago

Solve for 2.<br> -9x +5 < 17 AND<br> 13x + 25 < -1

Elena L [17]

Answer:

no solution

Step-by-step explanation:

-9x +5 < 17 AND 13x + 25 < -1

Solve each part separately and then put back together

-9x +5 < 17

Subtract 5 from each side

-9x+5-5< 17-5

-9x < 12

Divide each side by -9 remembering to flip the inequality

-9x/-9>12/-9

x > -4/3

and

13x + 25 < -1

subtract 25 from each side

13x +25-25 < -1-25

13x <-26

Divide by 13

13x/13 < -26/13

x <-2

There is no overlap so there is no solution

5 0

3 years ago

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HELP ASAP Write an equation for a line that satisfies the given conditions which are through (9,5); slope 0

Darina [25.2K]

Answer:5=0+9

Step-by-step explanation:

8 0

3 years ago