Does every rational function have a vertical asymptote?.

Answers

Answer 1

Yes, every rational function has a vertical asymptote.

A rational function is defined as a fraction of two polynomials such as P(x)/Q(x) where Q(x) ≠ 0.

A vertical asymptote is a vertical line that the graph of a function approaches but never touches.

It happens when the denominator of a rational function Q(x) = 0, so the fraction becomes undefined.

Therefore, the denominator of a rational function becomes zero at some point or several points in its domain, which results in a vertical asymptote.

For example, consider the following rational function f(x) = (3x² - 5x + 2)/(x - 1)(x + 2)

The denominator (x - 1)(x + 2) becomes zero when x = 1 or x = -2, so the rational function has two vertical asymptotes at x = 1 and x = -2.

Therefore, it can be concluded that every rational function has a vertical asymptote.

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Related Questions

SOMEONE PLSS HELP FOR QUESTION 1

SOMEONE PLSS HELP FOR QUESTION 1

Answers

Answer:

triangle abc is has same degres of angles with triangle def, but def is smaller in 3 times. it's only what i know, sorry if i not help

i think yea, they has a same angles, but def smaller in 3 times so i think yes

Through which angle measures can a regular hexagon be rotated so that it maps onto itself?

Choose ALL correct answers below:

Through which angle measures can a regular hexagon be rotated so that it maps onto itself?Choose ALL

Answers

Answer:

60,240,300

Step-by-step explanation:

Each subsequent rotation by 60° also maps a hexagon onto itself. There are 5 such rotations: by 60°, 120°, 180°, 240° and 300° (the next is 360° which isn't allowed by the conditions). So the answer is 5.

PLZ HELP WILL MARK BRAINLIEST TO THE QUICKEST CORRECT ANSWER!
Describe how to translate the graph of y=√x to obtain the graph of .y=√x+20

(the 20 is also under the sqrt symbol, so x+20 square rooted)


shift left 20 units

shift down 20 units

shift right 20 units

shift up 20 units

Answers

Answer:

Step-by-step explanation:

the answer is the first one -> shift left 20 units, see the graph in the image

PLZ HELP WILL MARK BRAINLIEST TO THE QUICKEST CORRECT ANSWER!Describe how to translate the graph of y=x

What equations go where? One solution, no solution, infinite solution. Picture attached of problem. Plsss
Help

What equations go where? One solution, no solution, infinite solution. Picture attached of problem. PlsssHelp

Answers

Answer:

see below

Step-by-step explanation:

1. x-9=-17-simplifies to a single solution-one solution

2.x+4=4+x-same thing on each side-infinite solutions

3. 0.4x=0.4x+2-same variable coefficient plus a number-no solutions

4. 5x=5x-3-same as above-no solutions

5. 5x=2-variable on one side, constant on another-one solution

6. x-5=x-5-same thing on each side-infinite solutions

7.3x=3x-same thing as above-infinite solutions

8.8x-10=8x-same coefficient for each variable plus a constant-no solutions

Answer:

One solution:

x + 9 = -17

5x = 10

No solution:

0.4x = 0.4x +2

5x = 5x - 3

8x - 10 = 8x

Infinite solutions:

x + 4 = 4 + x

x - 5 = x - 5

3x = 3x

Step-by-step explanation:

x + 9 = -17

  - 9     -9

x = -26 (one solution)

x + 4 = 4 + x

  - 4   - 4

x = x (infinite solutions)

0.4x = 0.4x +2

-0.4x  -0.4x

0 = 2 (no solution)

5x = 5x - 3

-5x  -5x

0 = -3 (no solution)

5x = 10

/5   /5

x = 5 (one solution)

x - 5 = x - 5

 + 5       + 5

x = x (infinite solutions)

3x = 3x (infinite solutions)

8x - 10 = 8x

    + 10  + 10

8x = 8x + 10

-8x   -8x

0 = 10 (no solution)

Hope this helps!

What equations go where? One solution, no solution, infinite solution. Picture attached of problem. PlsssHelp

two angles that add up to 90 degrees are called ________ angles.

Answers

Answer: Right/complementary angles

Step-by-step explanation:

Two angles that add up to 90 degrees are called complementary angles.

Complementary angles are a pair of angles that, when added together, equal a right angle, which measures 90 degrees.

In other words, the sum of the measures of complementary angles is always 90 degrees.

Complementary angles often arise in geometry and trigonometry, and understanding their properties is important when working with angles and solving problems involving right triangles.

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Write an inequality to express the relationship between -8 and -13

Answers

Answer:

The inequalities are used as:

a > b  (a is greater than b)

a < b (a is smaller than b)

a ≤ b (a is smaller than or equal to b)

a ≥ b (a is greater than or equal to b)

a ≠ b (a is different than b)

Now, let's apply these for our two numbers.

-8 and -13

We know that for negative numbers, the larger absolute value means that the number is smaller, then we relate these numbers in the next 3 ways.

-8 > -13  (-8 is greater than -13)

-13 < 8  (-13 is smaller than -8)

-13 ≠ -8 (-13 is different than -8)

the polynomial of degree 5, p ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 4 find a possible formula for p ( x ) .?

Answers

Polynomial of degree 5, p (x) has leading coefficient 1, has roots of multiplicity 2 at x = 3 and x = 0, and a root of multiplicity 1 at x = − 4.

The polynomial equation that satisfies the above information is:p(x) = (x - 3)²x²(x + 4)Here, (x - 3)² gives two roots at x = 3 and similarly x² gives two roots at x = 0, and (x + 4) gives one root at x = −4.The above equation is a possible formula for p(x). It can be expanded by multiplying the brackets together:p(x) = (x - 3)²x²(x + 4)= (x - 3)(x - 3)x²(x + 4)= (x³ - 6x² + 9x)(x + 4)= x⁴ + 4x³ - 6x² - 24x + 36x² - 54x= x⁵ + 4x⁴ - 6x³ + 12x² - 54xHence, p(x) = x⁵ + 4x⁴ - 6x³ + 12x² - 54x is a possible formula for the given information.

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In the souvenir shop, Gary finds a shirt and a key chain he would like to buy. The shirt costs $13.75 and the key chain costs $2.33. What will be the total of Gary's souvenirs?

Answers

Answer:

$16.08

Step-by-step explanation:

13.75+2.33=16.08

there are 7 red pens in jamals desk drawer. there are 3 more black pens than red pens. there are also 3 more blue pens than red pens. how many pens are there in all​

Answers

Answer:

27 pens

Step-by-step explanation:

red pen=7

3more black pen than red pen=3+7=10 black pen

3 more blue pen than red pen=3+7=10 blue pen

T=redpen + blackpen +blue pen

T=7+10+10

T=27 pen

Elena received a 25 dollar gift card to a fun center she drives a race car which costs 0.75 she also wants to use the grift card to play games each game costs 0.75 which of these inequalities describes this situation where n is is the number of games Elena wants to play ? A B C D WHICH ONE IS THE ANSWER I NEED HELP QUICK

Elena received a 25 dollar gift card to a fun center she drives a race car which costs 0.75 she also

Answers

B: 4.75+0.75n ≥25

Because she has already spent 4.75 and she only has $25 and she cannot spend more than$25

triganometryhelp help



jjhheke bwefbweu​

triganometryhelp helpjjhheke bwefbweu

Answers

Answer:

It looks really good! Lol, I wish I could art ✌

The graph of the equation y = - 3/4X - 3 has what slope?

Answers

Answer: 3/4x

Step-by-step explanation:

y = mx + b

m = slope b = y - intercept

y= 3/4x -3

The price of a pair of shoes increases from $20 to $32. What is the percent increase?

Answers

Answer:5%

Step-by-step explanation:

75% increase :)

hope that helped

The difference between the mean outcome of those who are treated and those who are untreated when the assignment of treatments is random is a good estimate of the A. Average treatment effect (ATE) but not the Treatment on the treated (TT) B. Selection bias C. Treatment on the treated but not the average treatment effect D. Average treatment effect which is equal to the treatment on the treated E. Sum of treatment on the treated and selection bias

Answers

The difference between the mean outcome of those who are treated and those who are untreated when the assignment of treatments is random is a good estimate of the Average Treatment Effect (ATE). (C)

The ATE is the average effect of treatment on the population, i.e., the difference in the mean outcomes of the treated group and the untreated group. If the assignment of treatments is random, the ATE is an unbiased estimate of the population average treatment effect.

On the other hand, the Treatment on the Treated (TT) is the average treatment effect on only those individuals who received the treatment. It represents the effect of the treatment on those who actually received it, and is not a good estimate of the population average treatment effect.

The TT can be biased if the treated and untreated groups differ in important ways that are not related to the treatment. The Selection bias refers to the systematic difference in the outcome between the treated and untreated groups due to factors other than the treatment.

It occurs when the assignment of treatment is not random, and can affect both the ATE and TT estimates.

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John has 3 ½ pounds of Skittles. He wants to share them with his friends. He decides to give ¾ pounds of Skittles to each friend. The leftover Skittles he keeps for himself.

Answers

Given :

John has 3 ½ = 7/2 pounds of Skittles.

He decides to give ¾ pounds of Skittles to each friend.

To Find :

How much the leftover Skittles are.

Solution :

Let, his number of bands are x.

So, amount of Skittles left is :

\(L= \dfrac{7}{2}-\dfrac{3x}{4}\\\\L = \dfrac{24-3x}{4}\)

Therefore, amount of leftover Skittles are \(\dfrac{24-3x}{4}\) pounds if number of friends are x.

Hence, this is the required solution.

What is the perimeter of figure I?

Answers

In geometry, the perimeter is the overall length of a shape's boundary. The perimeter of a shape is determined by adding the lengths of all of its edges and sides. 28 units make up Figure I's perimeter.

Its dimensions are expressed in linear units like centimetres, metres, inches, and feet. A rectangle in Figure I has four sides that are 8 units, 6 units, 6 units, and 8 units in length. You must total the lengths of all four sides in order to get a rectangle's perimeter. Figure I's perimeter is 8 + 6 + 6 + 8 units, or 28 units.

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14° plus what equals 90°

Answers

90° - 14° = 76°

hope this helps!

if 2y +8=18,what is y​

Answers

Answer:

y=5

Step-by-step explanation:

2y+8=18

2y=10

y=5

The value y is 5.

What is equation?

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

What are Arithmetic operations?

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculations

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given equation as:

⇒ 2y + 8 = 18

Substract from 8 both the sides of equation,

⇒ 2y + 8 - 8 = 18 - 8

⇒ 2y = 10

Divided by 2 both the sides of equation,

⇒ y = 5

Hence, the value y is 5.

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Please helppp


The function ƒ(x) = 2x − 1 indicates:
a downward shift of 1 unit.
a shift of 1 unit to the left.
an upward shift of 1 unit.
None of these choices are correct.

Answers

Answer:

It is a downward shift of one unit

Maddie has $100. She worked for 5 days and she now has $200. What
integer represents the average increase in value PER DAY?

Answers

She gets 20 dollars every day.

area of a pentagon 16 18 20 15

Answers

The area of the pentagon (assuming it is valid and regular) is approximately 1693.08 square units.

The given sides do not form a valid pentagon as the sum of any three sides of a pentagon must be greater than the fourth side. However, assuming that the sides are valid and the pentagon is regular,

we can use the formula A = (1/4) * n * s^2 * cot(pi/n), where n is the number of sides and s is the length of each side. Since we are given the length of each side (16, 18, 20, 15), we can substitute these values into the formula to find the area of the pentagon.

A = (1/4) * 5 * (16^2) * cot(pi/5) + (1/4) * 5 * (18^2) * cot(pi/5) + (1/4) * 5 * (20^2) * cot(pi/5) + (1/4) * 5 * (15^2) * cot(pi/5) A = 1693.08

Therefore, the area of the pentagon (assuming it is valid and regular) is approximately 1693.08 square units.

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Three friends were playing a game of marbles.
At the end of the game, Marcy had 25% of the
marbles, Roger had
2
1
of the marbles, and Ann
had the rest of the marbles. If there were 100
marbles altogether, how many marbles did Ann
have at the end of the game?

Answers

The number of marbles Ann had at the end is 54.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total marbles = 100

The number of marbles:

Marcy:

= 25% of 100

= 1/4 x 100

= 25

Roger:

= 21

Now,

The number of marbles:

Ann = 100 - (25 + 21) = 100 - 46 = 54

Thus,

Ann has 54 marbles at the end.

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A. f(x)=17.78(4.86)x

i.The value of the function when x=0 is?

ii. Find the ratio of output values that correspond to increases of 1 in the input value in order to determine the 1-unit growth factor.?

iii. Determine the 1-unit percent change.? %

B. h(x)=94.71(0.57)x

i. The value of the function when x=0 is?

ii. Find the ratio of output values that correspond to increases of 1 in the input value in order to determine the 1-unit growth factor.?

iii. Determine the 1-unit percent change.? %

Answers

-57 decrease

In this equation.

The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.

ii. The ratio of output values ​​corresponding to an increment of 1 in input values ​​is (4.86)^1 = 4.86.

iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.

For the function h(x) = 94.71(0.57)^x:

Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.

ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.

iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction

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derive the decision boundaries in the above case. • derive the conditional mle estimator of θ.

Answers

The form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.

what is decision boundaries.?

Decision boundaries refer to the dividing lines or regions that separate different classes or categories in a classification problem. They are determined based on the features or attributes of the data and the classification algorithm being used. The decision boundary serves as a threshold or criterion for assigning new or unseen data points to specific classes based on their feature values.

To derive the decision boundaries in the given case, more specific information or context is needed. Decision boundaries are determined based on the specific classification or grouping criteria and the underlying data distribution. Please provide additional details or specifications regarding the problem or classification task.

Regarding the conditional maximum likelihood estimator (MLE) of θ, more information is required to proceed with the derivation. The MLE involves finding the parameter value that maximizes the likelihood function based on the observed data and any relevant assumptions or models. Please provide the specific context, assumptions, and the form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.

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19 The length of a rectangle is represented by (x + 4) and the
width is represented by (x – 2). Which expression represents
the area of the rectangle?
A 7-8
B 2x + 2
C 4x + 4
D 2 + 2x – 8

Answers

Answer:

ans D

Step-by-step explanation:

area of rectangle is

l*b

(x+4)(x-2)

x^2-2x+4x-8

x^2+2x-8

What is the difference in the y values? 62 70 72

Answers

When we look for the constant rate of change, we subtract the first two y-values in the first place:

\(216-144=72\)Hence, the difference is 72.

Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are
4
44 apples and
5
55 bananas in his pantry.
What is
P(select an apple
)
P(select an apple)start text, P, left parenthesis, s, e, l, e, c, t, space, a, n, space, a, p, p, l, e, end text, right parenthesis?
If necessary, round your answer to
2
22 decimal places.

Answers

If Cam randomly selects a piece of fruit from his pantry, the probability of selecting an apple is 4/9 or 0.44.

To find the probability of selecting an apple, we need to divide the number of apples by the total number of fruits in Cam's pantry.

Total number of fruits = number of apples + number of bananas = 4 + 5 = 9

P(select an apple) = number of apples / total number of fruits = 4/9

So, the probability of selecting an apple is 4/9 or approximately 0.44 when rounded to two decimal places.

Therefore, the probability is 4/9 or 0.44.

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Complete question is:

Cam can't figure out what to eat. He is going to randomly select a piece of fruit from his pantry. There are 4 apples and 5 bananas in his pantry.

What is P(select an apple)?

If necessary, round your answer to 2 decimal places.

What is the solution to this equation?
x- 13 = -4
O A. x= 9
O B. x = 17
O c. x= -17
O D. x= -9

Answers

A. X=9

Solution:

x-13=-4
+13 +13
_________
X= 9
X = 9. Since 9-13=-4

Can u guys solve this fast?

Can u guys solve this fast?

Answers

Answer:

$336

Step-by-step explanation:

The slope is (277-100)/(3-0) = 59.

So, since the cost is $100 when t=0, C=59t+100.

After 4 months, the cost is 59(4)+100 = $336.

Find the equation of the line that contains the given point and is parallel to the given line. Write the equation in slope-intercept form, if possible.
(-1.-4); y = 0
Select the correct choice below and fill in the answer box to complete your choice.
A. The equation of the parallel line cannot be written in slope-intercept form. The equation of the parallel line is
B. The equation of the parallel line in slope-intercept form is

Answers

The equation of the line in slope intercept form and parallel to y = 0 is y = -4

How to find the equation of a line?

The equation of a line can be express in different form such as slope intercept form, point slope form, standard form and general form.

We are to write the equation of the line in slope intercept form.

The equation in slope intercept form is as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, the equation of the line passes through (-1, -4) and it is parallel to the line y = 0. This means the lines have the same slope.

Hence,

m = 0

y = mx + b

Using (-1, -4)

- 4 = 0(-1) + b

b = - 4

Therefore, the equation is y = -4

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