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Maru [420]
2 years ago
8

c{x^{2}-x-2 }{x-5}" alt="f(x) = \frac{x^{2}-x-2 }{x-5}" align="absmiddle" class="latex-formula">
Domain:
V.A:
Roots:
Y-int:
H.A:
Holes:
O.A

Also draw on the graph.

Mathematics
1 answer:
Umnica [9.8K]2 years ago
6 0

The given function is

f(x)=\frac{x^2-x-2}{x-5}

i) We factor the numerator to obtain;

f(x)=\frac{(x-2)(x+1)}{x-5}

The vertical asymptote is where the denominator is zero.

V.A: x=5

ii) The roots are the zeros of the numerator;

Roots:

x^2-x-2=0

(x-2)(x+1)=0

x=2,x=-1

iii) At y-intercept x=0.

Put x=0 into the function and solve.

f(0)=\frac{0^2-0-2}{0-5}

f(0)=\frac{-2}{-5}

f(0)=\frac{2}{5}

Y-int: \frac{2}{5}

iv) Horizontal asymptote.

This is an improper rational function.

It has no horizontal asymptote.

v) Holes:

The given rational function has no common factors in both the numerator and the denominator.

Therefore the function has no holes.

6) For oblique Assymptote, we divide using lond division or synthetic division;

     1   -1    -2

5|  <u>      5   20</u>

     1    4    18

The quotient is x+4

The  oblique asymptote is

y=x+4

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2 years ago
Which is an equation in point slope form of the line that passes through the points (7 -8) and has a slope of -3
Nataly [62]
Y+8 = -3(x-7)
Distribute the -3
y +8 = -3x +21
Subtract 8 from both sides
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3 0
3 years ago
The Tucker Gym charges a one time fee of $50 plus a $25 monthly membership
FinnZ [79.3K]

Answer:

y = 50 + 25x.............(i)

y = 80 + 15x.............(ii)

x = 3

y = 125

Step-by-step explanation:

The tucker Gym charges a one time fee of $50 plus a $25 monthly membership charge.  

The NoFo health club charges a one time fee of $80 plus a $15 monthly membership fee.

Let

number of month = x

total cost = y

Tucker Gym

y = 50 + 25x.............(i)

NoFo Gym

y = 80 + 15x.............(ii)

combining the equation

y = 50 + 25x.............(i)

y = 80 + 15x.............(ii)

y - 50 = 25x

y/25 - 2 = x

insert x in equation (ii)

y = 80 + 15(y/25 - 2)

y = 80 + 3y/5 - 30

y = 50  + 3y/5

y - 3y/5 = 50

5y - 3y/5 = 50

2y/5 = 50

cross multiply

2y = 250

y = 250/2

y = 125

insert y in equation (i)

125 = 50 + 25x

125 - 50 = 25x

75 = 25x

x = 75/25

x = 3

6 0
3 years ago
There are 4000 books in the towns library. Of these 2600 are fiction percent equation
iVinArrow [24]
% = 2600/4000 = 0.65 = 65% fiction
7 0
3 years ago
How should I explain how I got my answer?
Ierofanga [76]

Answer:

What is meant by "Explain your answer?"

   On tests & problem sets students are often asked to explain the reasoning behind their answers. They are often frustrated and/or confused by “explain.” What & why are they supposed to explain? Here is one answer:

   It isn't enough to get the right answer -- you have to be able to explain how you got it. To be sure you get enough practice at explaining yourself, it pays to discuss the questions with your fellow students and/or to write out explanations of your reasoning. You need to both

           (1) Include the right facts, principles, etc., AND

           (2) Explain the logic that you used to solve the problem. How did you get from the facts to the answer?

   It is not sufficient to pile up unselected facts (even if they are correct), OR just to state the facts (even if they are the right ones), without explaining how they relate to the problem at hand, OR to just explain the logical train of thought (even if it is correct), without any specifics.

   That's what you shouldn't do. What should you aim for??

   Try to explain as if you were talking to a fellow student in the class who is generally intelligent, prepared, etc., but can't figure out this particular question.  In other words, explain your reasoning step by step.  Don't just repeat all the related facts in the book or notes--try to pick out the important, relevant points, put them in logical order, and explain (or diagram) how one leads to the next. (In other words, pretend you are writing a simple* answer key.)

*Note: The keys provided after each exam or problem set are usually quite complex and go beyond what we expect from an individual student. The posted keys tend to be so long and involved because they include not only correct answers (& explanations) but also explanations of common student misconceptions.

How to Get the Most out of Explaining

   When you explain things to yourself, or to others, try not to use pronouns. Use nouns instead. This may sound silly, but it really helps you to be sure that you understand what you are saying. If you use pronouns or vague terms you can fool yourself into thinking you understand when you really don't. An example: Suppose you say "The gene is transcribed and it goes to the cytoplasm and is translated, which uses tRNA and mRNA." What do you mean by it and/or which?  Is it the gene or the mRNA? Does which refer to translation or transcription? Sometimes you know, and you are just using shorthand. But sometimes you don't know, and you don't even realize it until you are forced to pick the right terms to replace "it" and "which."  So try to be as specific as possible instead of as vague and as general as possible. Being specific has multiple advantages. It helps you to learn, it helps listeners understand what you are saying, and it helps graders on exams know that you really understand what you are talking about.

7 0
3 years ago
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