1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tju [1.3M]
3 years ago
12

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

Mathematics
1 answer:
lilavasa [31]3 years ago
8 0

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}

You might be interested in
The repeating decimal,0.27 repeting, is converted to the fraction 3/x. What is the value of x in the fraction?
Nuetrik [128]

Answer:5/18=.2777777777777

Step-by-step explanation:

.27777 (7 repeating)

100x=27.7777

10x=   2.7777

Subtract

90x=25

x=25/90=5/18

Check

5/18=.2777777777777

Hope that helps.

7 0
3 years ago
Solve each equation. Check your solution.<br><br> –3b + 7 = –15 + 2b
Gnoma [55]
Exact form: b= 22/5

Decimal form: b= 4.4

Mixed number form: b= 4 2/5
6 0
3 years ago
Read 2 more answers
(4x-8)-(-3x + 10)<br> HELP
ArbitrLikvidat [17]

Answer:

7x-18

Step-by-step explanation:

brainlliest plz

7 0
3 years ago
Read 2 more answers
Please someone what is the total surface area of this pryamid ​
Dimas [21]

Answer:

\large\boxed{C.\ (25+25\sqrt3)\ in^2}

Step-by-step explanation:

We have the square and four equilateral triangles.

The formula of an area of a squre:

A_S=a^2

a - length of side

The formula of an area of an equilateral triangle:

A_T=\dfrac{a^2\sqrt3}{4}

a - length of side

Clculate the areas:

SQURE:

A_S=x^2\ in^2

TRIANGLE:

A_T=\dfrac{x^2\sqrt3}{4}\ in^2

The SURFACE AREA of a square pyramid:

S.A.=A_S+4A_T\\\\S.A.=x^2+4\cdot\dfrac{x^2\sqrt3}{4}=x^2+x^2\sqrt3

Put x = 5:

S.A.=5^2+5^2\sqrt3=(25+25\sqrt3)\ in^2

7 0
3 years ago
Lin's job pays $8.25 an hour plus $10 of transportation allowance each week. She has to work at least 5 hours a week to keep the
Usimov [2.4K]
Y=8.25x+10

10 is the allowance plus the 8.25 times x which is the hours
5 0
3 years ago
Other questions:
  • What is the measure of the missing angle?
    11·1 answer
  • What did Pinocchio say to his barber
    5·2 answers
  • 700/200 in a terminating decimal
    8·1 answer
  • (-5)+(-2)+3 do the arrows correctly represent the numbers that Jessica is using in her expression
    9·2 answers
  • Graph.<br> y+1= 1/3(x-3)
    6·1 answer
  • Slope Of (5,-5) and (-1,-5)
    7·1 answer
  • Helppp i need help on this question on my hw
    9·2 answers
  • mrs. Kenny teaches a ceramics class. She finds that she has 7/8 of a pound clay project. The project requires 1/6 of a pound. ho
    8·1 answer
  • A ribbon is cut into n parts. The length of each part increases such that they form a geometric progression. SPM Given the lengt
    11·1 answer
  • Yolanda was pouring glasses of juice for brunch. She used a 48-ounce bottle of apple juice to fill 8 glasses equally, and she us
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!