"All rational functions have asymptotes and points of discontinuity." Katlyn wants to put this statement in her math book. Is this statement true? Explain, for her benefit, using 2 examples

Answers

Answer 1

Answer:

Not true.

Step-by-step explanation:

A  rational function is like P(x) / Q(x) where P and Q are polynomials.

Examples would be x^2 / (x^2 - 2)  and  x^2 / (x^2 + 2).

Now the first one will have a vertical asymptote at x = √2 because this value would make the denominator zero.

The second one will have no asymptotes because the only value that would make x^2 + 2 = zero is not real (it would be √2i). So the domain of this  is all real numbers ,  and  no asymptotes.


Related Questions

+
Sasha earns $10,50 per hour at
her job. She deposits everything she earns into
her savings account. She currently has $150 in
his savings account. Jack earns $9.00 per hour
at his job. He deposits everything he earns into
his savings account. He currently has
$300 in his savings account.
What month will both Sasha and Jack have the
same amount of money in their account?

Plssssss helpp me

Answers

To start off you will need to set an equation that Will representate a change of both Sasha and Jack. Since we have the constants for both Sasha and Jack you will set up an equation that adds onto their balance. let X represent the rate of change which is hours.

Sasha = $10.50x + 150
Jack = $9.00x + 300

Now that you know these equations you must have them equal to each other to find what value of X how many hours they will be equal. We cannot find out the months that Sasha and Jack will have the same amount of money on the account because there is no information regarding the hours they work per month. However by setting both of the equations equal to each other you can find the number of hours it will take for them to have the same amount of money in their accounts.

I need to find the answer to...
20% of $80 = ???

Answers

All u need to do is change the % into a decimal and multiply so .2 x $80=$16

Answer:

16

Step-by-step explanation:

0.20 x 80 = 16

We can double check this by dividing :)

16/80 = 0.20 = 20%

Have an amazing day!!

Please rate and mark brainliest!!

The radius of a circle is 14 meters. What is the circle's area?
r=14 m
Use 3.14 for .

Answers

Answer:

The formula for the area of a circle:

[tex]A = \pi r^{2}[/tex]

You have said:

[tex]r = 14m[/tex]

So substitute the values of pi and r into the formula:

[tex]A = \pi r^{2} \\A = (3.14)(14m)^{2} \\A = (3.14)(196m^{2} )\\A = 615.44m^{2}[/tex]

Area of a circle = pi * r^2

So in this case: (3.14) * (14)^2 = 615.44

Find the value of x. 5x° 65°​

Answers

Answer:

B. 23

Step-by-step explanation:

Total = 180° for a supplementary angle.

5x + 65 = 180

5x = 180 - 65

5x = 115

x = 115/5

x = 23

Answer:

B. 23

Step-by-step explanation:

The sum of the angles that creates a straight line is 180 degrees. So we can write the equation

5x + 65 = 180

Solve for x by first subtracting 65 on both sides

5x = 115

Then divide both sides by 5

x=23

The first six steps of the derivation of the Quadratic Formula are listed below.
b
x
lo
=
a
a
+
1. ax2 + bx +c=0
2. Cx2 + x + =
3. x2 + x+8 = 0
b
4. x2 +
X=
a
b2
5. x2 + x +
4a2
6. (x + )2
4a2
a
+
a
b2
4a2
b2-4ac
2a

Answers

The ninth step in the derivation is to find the lowest common multiple (LCM) to give [tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

The derivation of quadratic formula.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is given by this equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

The sixth step in the derivation is:

[tex](x + \frac{b}{2a} )^2 = \frac{b^2 - 4ac}{2a}[/tex]

The seventh step in the derivation is:

We would take the square of both sides to have;

[tex]x + \frac{b}{2a} = \frac{\sqrt{b^2 - 4ac}}{2a}[/tex]

The eigth step in the derivation is:

We would substract b/2a from both sides to have;

[tex]x = -\frac{b}{2a} \pm \frac{\sqrt{b^2 - 4ac}}{2a}[/tex]

The ninth step in the derivation is:

We would find the lowest common multiple (LCM) to have;

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

Read more on quadratic equation here: brainly.com/question/1214333

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you are traveling for work. You fly out of las vegas at 4:45 Am. you arrive in miami 6 hours later. what time is it when you arrive ? explain how you got your answer.

Answers

Answer:

The time wil be 1:45

Step-by-step explanation:

4:45 + 6 hours is 10:45

But since Miami is 3 hours ahead (different time zone), you
will add 3 hours. So that makes it 1:45 when you land!

Hope this helps!!

Please help me with question 2 with explanation u will get 50 points thanks !!

Answers

2. volume of the box would be height x length x width so 2 x 8 x 8 = 128


A French professor gives Sections 1 and 2 of a French course the same passage to translate. Section 1 has 28 students, and 5
translate the passage correctly. Section 2 has 22 students, and 8 translate the passage correctly. (See Example 3.)
(a) If one of the papers is selected at random, what is the probability that it is a correct translation? (Round your answers
to three decimal places.)
(b) One of the papers is selected and is known to be from Section 1. What is the probability that it is a correct translation?
(Round your answers to three decimal places.)
(c) A paper is selected and is known to be a correct translation. What is the probability that it is from Section 2? (Round
your answers to three decimal places.)

Answers

Using it's concept, it is found that the probabilities are given by:

a) 0.26 = 26%.

b) 0.179 = 17.9%.

c) 0.615 = 61.5%.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Item a:

8 + 5 = 13 correct translations out of 28 + 22 = 50 students, hence:

p = 13/50 = 0.26 = 26%.

Item b:

5 correct translations out of 28, hence:

p = 5/28 = 0.179 = 17.9%.

Item c:

There are 13 correct translations, and of those, 8 are from section 2, hence:

p = 8/13 = 0.615 = 61.5%.

More can be learned about probabilities at https://brainly.com/question/14398287

HOW DO U DO THIS I LITERALLY TRIED EVERYTHING pls explain

Answers

Answer:

you just convert them into simple fractions the first one become -1159/9 and second one -790/3.

the difference in thier height is 1211/9.

what is 66.6% as a fraction

Answers

Answer:

[tex]\frac{333}{500}[/tex]

66% = [tex]\frac{33}{50}[/tex]

In that case, for the tenths place existing as your ones place, you only need to add on one more digit to make the fraction.

Answer:

66.6% as a fraction is 33/50

Step-by-step explanation:

Which object would weigh closest to 1 ton? ​

Answers

Answer:

The answer is 73 billion bars of gold

I believe it would be a car

What is the x -value of the ordered pair (0, 4)?

Answers

the x value of the ordered pair is 0

34. Find the surface area for the following rectangular prism ​

Answers

[tex] \huge\fbox\green{ANSWER} [/tex]

Surface Area = 2×(8.25×1.5 + 8.25×3 + 1.5×3) = 83.25 centimeters^2

[tex] \mathsf \blue{83.25 {cm}^{2} }[/tex]

Select three ratios that are equivalent to 7:6,

Answers

Answer: 12:14 21:18 42:36

Sasha is mailing a photo box that has the dimensions shown in a rectangular box that is 12.5 inches long, 4.2 inches wide, and 12.5 inches tall. If one bag of packing material holds 75 cubic inches of material, how many bags does Sasha need to buy to fill the space around the photo box?

Answers

The number of bags that Sasha would need to fill the space around the photo box is 9 bags.

How many bags would be needed?

The first step is to determine the volume of the photo box. The photo box has the shape of a cuboid. A cuboid is a three-dimensional object. It has six sides and six vertices.

Volume = length x width x height

12.5 x 4.2 x 12.5 = 656.25

Bags needed - 656.25 / 75 = 9

To learn more about how to determine the volume of a cuboid, please check: https://brainly.com/question/8890358

yah..... help please bro

Answers

Answer:

I think D but I'm not too sure.

Change them all into decimals:

The square root of 2 = 1.41421356

3/2 = 1.5

15% = 0.15

Arrange them:

3/2, square root of 2, 1.3333..., 1.3, 15%

So, B is the correct answer.

A baseball traveled 330 feet in 5 seconds. Which rate is equivalent to the rate at which the baseball traveled?

A.
55 feet per second


B.
66 feet per second


C.
55 seconds per foot


D.
66 seconds per foot

(just the answer pls)

Answers

Answer:

I think it's B.

Step-by-step explanation:

Rachel is going for a walk. She walks 6.4 miles in 4 hours. What is her speed

Answers

Answer:

[tex]speed= \frac{6.4}{4} = 1.6[/tex]

.....

if the diameter of the clock face is 10.5 inches, what is the radius?​

Answers

Answer:

The radius is 5.25

Step-by-step explanation:

The radius is always exactly 1/2 of the diameter!

Hope this helps! <3

Which statements are true about fractions and ratios? Select all that apply. All ratios are fractions. Some ratios are not fractions. All fractions are ratios. All ratios compare wholes and parts.

Answers

The only correct statement is that ratios are not fractions.

Answer: the person above is wrong

Step-by-step explanation: Some ratios are not fractions.

and All fractions are ratios

Help please I’m not sure what I’m supposed to do

Answers

Answer:

6r & 30

Step-by-step explanation:

5(6r+6)

=5*6r+5*6

=30r+30

What is the area of the shape?

Answers

Answer:12 units^2

Step-by-step explanation:

2*2=4

2*2*1/2=2

2*6*1/2=6

4+2+6=12

12 units^2

I need help, please and thank you

Answers

Answer:

See below ↓

Step-by-step explanation:

Problem

[tex]\frac{5x}{x+7} + \frac{7}{x}[/tex]

Work

[tex]\frac{5x(x)+7(x+7)}{x(x+7)}[/tex][tex]\frac{5x^{2} +7x+49}{x(x+7)}[/tex]The student's mistake was that instead of taking x(x + 7) as the LCM (Least Common Multiple), he took x + 7, which is not possible in this case

Solution

[tex]\frac{5x^{2} +7x+49}{x(x+7)}[/tex]

Using the equation below, what is the
value of p when v = 7?
p = 6v + 21

Answers

Answer:

p = 63

Step-by-step explanation:

It is given that the variable v is equal to 7:

v = 7

Plug in 7 for v, and then solve the given equation:

p = 6v + 21

p = 6(7) + 21

Simplify. Remember to follow PEMDAS.
PEMDAS is the order of operation, and stands for:

Parenthesis, Exponents (& Roots), Multiplications, Divisions, Additions, Subtraction.

First, multiply 6 with 7:

p = (6 * 7) + 21

p = 42 + 21

Next, add:

p = 42 + 21

p = 63

63 is your answer for p.

~

Answer:

p = 63

Step-by-step explanation:

p = 6(v) = 21

add in 7 in place of v

p = 6(7) + 21

do 6(7)

p = 42 + 21

add those together

p = 63

Here you go! :)

In a pizza restaurant, you can get a basic pizza with two toppings: cheese and tomato.
You can also make up your own pizza with extra toppings. You can choose from four
different extra toppings: olives, ham, mushrooms and salami.
Ross wants to order a pizza with two different extra toppings.
How many different combinations can Ross choose from?

Answers

The number of different topping combination illustrates combination

Ross have 6 different topping combination to select from

The number of different combination

The given parameters are:

Extra toppings, n = 4

Toppings to select, r = 2

The number of extra topping that Ross can select is then calculated  using the following combination formula

Toppings = nCr

This gives

Toppings = 4C2

Evaluate the combination expression

Toppings = 6

Hence, Ross have 6 different topping combination to select from

Read more about combination at:

https://brainly.com/question/11732255

how do you graph y=2x-3

Answers

Answer:

so on the graph you can

Step-by-step explanation:

first the y axis number comes first so you look at that the you do the x axis it should look like 2,3 or 2,-3 hope this works

Answer: 2x3=y. 2x3=6

Step-by-step explanation:

one: figure out what the question is asking you. Two: do 2x3 and then get the answer. Last: switch it around to find your answer.

Imagine the center of the singapore flyer is located at (0, 0) on a coordinate grid, and the radius lies on the x-axis. Write an equation of a circle for your Ferris wheel, and sketch an image of what your Ferris wheel would look like on the grid. Now graph a circle that is similar to the Ferris Wheel. Discuss the transformations needed to show that both circles on your graph are similar

Answers

The equation of the Ferris wheel is x² + y² = 25, and the transformation that shows that the circles are similar is the dilation transformation

How to determine the equation of the Ferris wheel?

From the question, we have the following parameters:

Center (a,b) = (0,0)Radius, r = 5

The equation of a circle is represented as:

(x - a)² + (y - b)² = r²

So, we have:

(x - 0)² + (y - 0)² = 5²

Evaluate

x² + y² = 25

Hence, the equation of the Ferris wheel is x² + y² = 25

See attachment for the image of the Ferris wheel

Transformation to a similar circle

Assume that the similar circle has the following parameters:

Center (a,b) = (0,0)Radius, r = 10

The equation of the circle would be:

(x - 0)² + (y - 0)² = 10²

Evaluate

x² + y² = 100

Since both circles have the same center, the transformation that shows that they are similar is the dilation transformation

Read more about circle equations at:

https://brainly.com/question/1559324

If f(3) = 3^x and g(x) = 7^x then the graph of g(x) will be — the graph of f(x) when x<0.

Answers

Using the given exponential functions, it is found that the graph of g(x) will be less than than the graph of f(x) when x < 0.

What are the exponential functions?

The given exponential functions, f(x) and g(x), are respectively given by:

[tex]f(x) = 3^x[/tex][tex]g(x) = 7^x[/tex]

When x < 0, one possible value is x = -1, hence evaluating the functions at these values:

[tex]f(-1) = 3^{-1} = \frac{1}{3}[/tex]

[tex]g(-1) = 7^{-1} = \frac{1}{7}[/tex]

[tex]\frac{1}{3} > \frac{1}{7}[/tex], hence, the graph of g(x) will be less than than the graph of f(x) when x < 0.

More can be learned about exponential functions at https://brainly.com/question/25537936

what two numbers multiply to get -8 and add to get 4?

Answers

Answer:

 -2-2√3, -2+2√3

Step-by-step explanation:

Let x and y be two numbers.

Let x represent one of the numbers. Then the other number is -4-x. We want the product to be -8:

 x(-4-x) = -8

 -4x -x^2 = -8 . . . . . eliminate parentheses

 x^2 +4x = 8 . . . . . . multiply by -1

 x^2 +4x +4 = 12 . . . add 4 to complete the square

 (x +2)^2 = 12

 x +2 = ±√12 = ±2√3

 x = -2±2√3

Suppose a city with population 100,000 has been growing at a rate of 5% per year. If this rate​ continues, find the population of this city in 21 years.

Answers

Answer:

205,000

Step-by-step explanation:

(100,000*0.05) *21 +100,000

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