For limit of startfraction x squared minus 4 x minus 12 over x minus 2 endfraction as x approaches 2 minus = and limit of startfraction x squared minus 4 x minus 12 over x minus 2 endfraction as x approaches 2 plus= . these limits indicate there is an asymptote of .

Answers

Answer 1

The given limit indicates that there is a vertical asymptote at x = 2.

What are the vertical asymptotes of a function f(x)?

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator. When x tends to these values laterally, the limit of f(x) goes to infinity.

In this problem, the function is:

[tex]f(x) = \frac{x^2 - 4x - 12}{x - 2}[/tex]

The vertical asymptote is:

x - 2 = 0 -> x = 2.

Hence:

[tex]\lim_{x \rightarrow 2^+} f(x)[/tex] and [tex]\lim_{x \rightarrow 2^-} f(x)[/tex] are either positive infinity or negative infinity.

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Related Questions

Factor f(x) = 4x2 + 11x? - 104x + 105 into linear factors given that – 7 is a zero of f(x).
f(x) = 4x + 11x2 - 104x + 105 = |
(Factor completely.)

Answers

Answer:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5)

Step-by-step explanation:

f(x) = 4x^3 + 11x2 - 104x + 105

has the coefficients {4, 11 -104, 105}.  We perform synthetic division using the given -7 as divisor:

-7   /   4      11     -104     105

                -28     119     -105

     -----------------------------------

          4      -17      15         0

Since the remainder is zero (0), we have shown that -7 is a zero of f(x).  The coefficients of the quotient (above) are {4, -17, 15}.  Let's try factoring the corresponding polynomial again using synthetic division.  Start out by using 5 as divisor and determining whether or not the remaindeer is zero:

5    /     4     -17      15

                    20     15

     -------------------------

             4        3     30           No, the remainder is 30 and so 5 is not a

                                               root of this quadratic.  Try the divisor 3 instead:

3     /     4      -17      15

                      12      -15

      ---------------------------

             4       -5        0        Yes, the remainder is 0 and so 3 is a root.

Thus, the given f(x) = 4x + 11x2 - 104x + 105 factors as follows:

f(x) = 4x + 11x2 - 104x + 105  =  (x - 3)(x + 7)(4x - 5).  Notice that the coefficients of the last factor come from those we found above when using 3 as a divisor in synthetic division.  

Matti rolled the six-sided number cube once, tossed the coin once, and flicked the spinner one time.
How many total possible outcomes are there if she does all three at the same time?

Answers

Answer:

60 outcomes

Step-by-step explanation:

6 x 2 x 5

60 possible outcomes are there if she does all three at the same time.

What is Combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Given:

Matti rolled the six-sided number cube once,

tossed the coin once,

and flicked the spinner one time.

So, the possibilities of doing three at the same time

= 6 x 2 x 5

= 60

Hence, there are 60 possible ways.

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2x + 6 y = 68
2x + 4y = 46

Answers

Answer:

1. x=34−3y

2. x=23−2y

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x+6y-(2x+4y)=68-46

2y=22

y=11

2x+4(11)=46

2x=2

x=1

!!!! Rectangle A’B’C’D is the image of rectangle ABCD after which of the following translations

Answers

Answer:

C

Step-by-step explanation:

help me plz if you can

Answers

Answer:

The first problem the answer is x= -25/4

Step-by-step explanation:

A heron is perched in a tree 50 feet above sea level. Directly below the heron, a pelican is flying 17 feet above sea level. Directly below the birds is a trout, swimming 23 feet below sea level.
A.What’s the difference in height between the pelican and the heron?
B.What’s the distance in height between the pelican.
C.what’s the difference in height between the pelican and the trout.
D.What’s the distance in height between the pelican and the trout.

Answers

Answer:

Step-by-step explanation:

Your answer

A = 73

B= 33

C = 40

D = 40

Mark it as Brainlist answer. Follow me.

Which value from the set
{1/2, 2/3, 4/3,5/2} is a value of x that will make the equation 3/4 + x = 9/8 true?
a.2/3
b.4/3
c.5/2
d.1/2

Answers

Answer:

2/3

Step-by-step explanation:

that does not say + it a division sign  how to got 2/3

(3/4) / x = (9/8)

To solve this equation, we want x alone so we start by multiplying x on both sides like this:

((3/4) / x)x = (9/8)x

Which equals:

(3/4) = (9/8)x

Then we divide each side by 9/8 to like this:

(3/4) / (9/8) = ((9/8)x) / (9/8)

(3/4) / (9/8) is 2/3 and ((9/8)x) / (9/8) leaves x which means we end up with x = 2/3. Therefore, the answer to "3/4 divided by what equals 9/8?" is as follows:

2/3

It is always good to double-check your math to make sure you did it right. When we entered 2/3 for x in this equation (3/4) / x = (9/8), we get the following true equation which means our math is correct.

(3/4) / (2/3) = (9/8)

The value of x will be 2/3

What is an equation?

Equation: An equation is basically a statement that equates two expressions.

An equation must contain an "equality" sign.

Given,

3/4 + x = 9/8

Let us make it correct . Replace + sign with / to get the required answer.

(3/4) / x = (9/8)

To solve this equation, we want x alone so we start by multiplying x on both sides like this:

((3/4) / x)x = (9/8)x

(3/4) = (9/8)x

Then we divide each side by 9/8 to like this:

(3/4) / (9/8) = ((9/8)x) / (9/8)

(3/4) / (9/8) is 2/3 and ((9/8)x) / (9/8) leaves x which means we end up with x = 2/3.

Therefore, the answer to "3/4 divided by what equals 9/8?" is as follows:2/3

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Mr. Patel bought lunch at a restaurant for $7.35. If he paid with a $10.00 bill, how much change did he get back?

A.
$2.55

B.
$2.65

C.
$3.35

D.
$3.65

Answers

Answer:

b. $2.65

Step-by-step explanation:

$10.00 - $7.35 = ?

$10.00 - $7.35 = $2.65

Answer:

your answer would be b. $2.65

OML PLEASE HELP! GIVING BRAINLIEST PLEASEE. Instruction are to answer all 3 questions naming their angle 4 ways. PLEASE

Answers

Answer: where is the image if there is ment to be one

Step-by-step explanation:

It is solving equations, Please tell me the answers and if you can show the work then that would be nice too.

Answers

Answer:

16. 53 = 14.50 + p  The answer is 38.50. 17a. Your final bowling score is 105-14, which is equal to 91.

Step-by-step explanation:

53 = 14.50 + p

53-14.50=p

38.50=p

For b... I don't know what a "10nth frame" is. Or a spare. Sorry...

which one of these would be correct for this?
AA
SSS
SAS

Answers

SAS - is the answer

How many 3/4 pound weights can be made from 6 pounds of steel?​

Answers

Answer:

8

Step-by-step explanation:

Solve this literal simultaneous equation for x and y.
[tex]ax+by=c[/tex]
[tex]bx+ay=c[/tex]

Answers

Answer:

The answer is below

Step-by-step explanation:

Firstly, let us find the value of x. Multiply the first equation by a and the second equation by b to get:

a²x + aby = ca             (3)

b²x + aby = cb             (4)

Subtract equation 4 from equation 3 to get:

x(a² - b²) = c(a - b)

but a² - b² = (a + b)(a - b)

x(a + b)(a - b) = c(a - b)

x(a + b) = c

[tex]x=\frac{c}{a+b}[/tex]

Secondly, let us find the value of y. Multiply the first equation by b and the second equation by a to get:

abx + b²y = cb             (5)

abx + a²y = ca              (6)

Subtract equation 5 from equation 6 to get:

y(a² - b²) = c(a - b)

but a² - b² = (a + b)(a - b)

y(a + b)(a - b) = c(a - b)

y(a + b) = c

[tex]y=\frac{c}{a+b}[/tex]

Is 14,48,50 a Pythagorean triplet
Step by step explanation please

Answers

Answer:

yes

Step-by-step explanation:

If the values are a Pythagorean triplet then the square of the largest value should equal the sum of the squares of the other 2

largest value = 50 ⇒ 50² = 2500

14² + 48² = 196 + 2304 = 2500

Since 50² = 14² + 48² then 14, 48, 50 are a Pythagorean triplet

Yes, it is a Pythagorean triplet. Refer to below for details as to how it is:

The boys' basketball team at Washington High School has been doing really well so far this year. In the past six games, they've scored the following points.

84, 67, 74, 87, 67, 73

What is the mean of their scores?

20
67
73.5
75.3

Answers

Answer:75.3

Step-by-step explanation:

Add all the numbers then divide by how many numbers their are

Answer:

75.3

Step-by-step explanation:

You add all the numbers together and you get 452. Then you you divide 452 by how many numbers are in the set which is 6 and you get 75.2 but since there is 75.3 but no 75.2, 75.3 is your anwser.

Hope this explains a lot!!!!!!!!!!!!!!

i need help urgently please :D

Answers

Answer:

y = 4

x = 5

y = 2

x = 1

x = 8

Step-by-step explanation:

to find y-intercepts, set x = 0

to find x-intercepts, set y = 0

1.)   4(0) + 5y = 20

     5y = 20

      y = 4 -------> y-intercept

2.)   4x + 5(0) = 20

      4x = 20

       x = 5 -------> x-intercept

3.)   2(0) + y = 2

      y = 2 -------> y-intercept

4.)    2x + 0 = 2

       x = 1 -------> x-intercept

5.)    x - 2(0) = 8

       x = 8 -------> x-intercept

Answer:

4x+5y=20 the answer is below

x= −5/4y+5

y= −4/5x+4

2x+y=2 the answer is below

x= −1/2y+1

y=−2x+2

x-2y=8 the answer is below

x=2y+8

y=1/2x−4

Step-by-step explanation:

Let's solve for x.

4x+5y=20

Step 1: Add -5y to both sides.

4x+5y+−5y=20+−5y

4x=−5y+20

Step 2: Divide both sides by 4.

4x/4 = −5y+20/4

x= −5/4y+5

Answer:

x= −5/4y+5

Let's solve for y.

4x+5y=20

Step 1: Add -4x to both sides.

4x+5y+−4x=20+−4x

5y=−4x+20

Step 2: Divide both sides by 5.

5y/5 = −4x+20/5

y= −4/5x+4

Answer:

y= −4/5x+4

Let's solve for x.

2x+y=2

Step 1: Add -y to both sides.

2x+y+−y=2+−y

2x=−y+2

Step 2: Divide both sides by 2.

2x/2= −y+2/2

x= −1/2y+1

Answer:

x= −1/2y+1

Let's solve for y.

2x+y=2

Step 1: Add -2x to both sides.

2x+y+ −2x=2+ −2x

y=−2x+2

Answer:

y=−2x+2

Let's solve for x.

x−2y=8

Step 1: Add 2y to both sides.

x−2y+2y=8+2y

x=2y+8

Answer:

x=2y+8

Let's solve for y.

x−2y=8

Step 1: Add -x to both sides.

x−2y+−x=8+−x

−2y=−x+8

Step 2: Divide both sides by -2.

−2y −2=−x+8−2

y=1/2x−4

Answer:

y=1/2x−4

What is 50% of 82 ? Please help !!

Answers

If you mean like half then 31?

Answer:

The answer is 41

Step-by-step explanation:

Find the equation in general form of the circle whose center is at (0,3) and

passing through the point (-2,1).​

Answers

Answer:

5.0

Step-by-step explanation:

evaluate the expression and enter your answer below

5x(4+5)-7^2

It's 5 times not X and 7 to the power ​

Answers

Answer:

hope it helps u

hope u find it helpful

A landscaping company estimates the price of a job,in dollars, using the expression 60 + 12nh, where n is the number of
landscapers who will be working and h is the total number of hours the job will take using n landscapers. Which of the
following is the best interpretation of the number 12 in the expression?
A The company charges $12 per hour for each landscaper.
B A minimum of 12 landscapers will work on each job.
The price of every job increases by $12 every hour.
D Each landscaper works 12 hours a day

Answers

A is your correct answer.

Which of the following is a factor of 7x2 + 42x - 49
x2 + 49
x+7
X-7
x+ 1

Answers

Answer:

[tex]x + 7[/tex]

is the answer because 7×2+42x-49

x + y = 400
10x + 5y = 2750

Answers

Answer:

fart

Step-by-step explanation:

X = 150
Y = 250
150 + 250 = 400
10(150) + 5(250) = 2750
1500 + 1250 = 2750

Solve the simultaneous equations
3
2x - y = 7
xy = 15

Answers

Answer:

(5, 3 ) and (- [tex]\frac{3}{2}[/tex], - 10 )

Step-by-step explanation:

Given the 2 equations

2x - y = 7 → (1)

xy = 15 → (2)

Rearrange (1) expressing y in terms of x , that is

y = 2x - 7 → (3)

Substitute y = 2x - 7 into (2)

x(2x - 7) = 15

2x² - 7x = 15 ( subtract 15 from both sides )

2x² - 7x - 15 = 0 ← in standard form

(x - 5)(2x + 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex]

Substitute these values into (3) for corresponding values of y

x = 5 : y = 2(5) - 7 = 10 - 7 = 3 ⇒ (5, 3 )

x = - [tex]\frac{3}{2}[/tex] : y = 2(- [tex]\frac{3}{2}[/tex] ) - 7 = - 3 - 7 = - 10 ⇒ (- [tex]\frac{3}{2}[/tex], - 10 )

PLease help asap!!! :)

Answers

7,3,10 are the answers

PLEASE HELP IF RIGHT WILL GIVE BRAINLIEST!!

Answers

Answer:

{-8, -4, 0, 4, 8}

Step-by-step explanation:

brainliest please

Answer:

D

Step-by-step explanation

The numbers in replace of x result in answers that equal or are greater than 0.

Which is bigger 8 kg or 850 grams



Which is bigger 1 kg or 1000 grams



Which is bigger 3 liters or 3500 milliliters




Which is bigger 5 liters or 520 milliliters





PLZ ANSWER ALL 3 WILL GIVE 15 PIONTS

Answers

A) 8 kilograms. 850 grams is only equal to .85 of a kilogram.

B) Neither. 1000 grams is the same as 1 kg. Kilo means 1000.

C) 3500 milliliters. Milli also means 1000, so it is equal to 3.5 L.



Which one is the answer for this question?

x =

5
6
10

Answers

Answer:

10

вот правильный ответ) я точно проверяла

Answer:

6

Step-by-step explanation:

Hope this helps.

Expression: 3x2t
If the value is 96 what is t?

Answers

Answer:

t = 16. This is the answer.!

the city of luckett is pilling rock salt for use during ice storms. if the pile from last year is 29 feet high and 14 feet are added this year, how high is the pile of rock salt?

Answers

29 + 14 = 43

The pile of rock salt is 43 feet high

What is is this graph representing??
A. Linear
B. Exponential
C. Neither

Answers

We know that a linear equation has a straight line graph. The graph represents an exponential equation or a quadratic equation. So the answer is B. Exponential
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