Do the graphs of all rational functions have at least one asymptote or hole? Explain why or why not
A. No, a function may have neither asymptotes nor holes.
B. Yes, the function will have both a vertical asymptote and hole for any values that cause the denominator to be equal to zero.
C. Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero
D. Yes, the function will have either a horizontal asymptote or hole for any values that cause the denominator to be equal to zero.
Answer:
C. Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero
Step-by-step explanation:
We want to see if all rational functions always have at least one asymptote or hole.
The answer is C:
" Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero"
A rational function is something like:
[tex]f(x) = \frac{q(x)}{p(x)}[/tex]
Where q(x) and p(x) are polynomials.
The asymptotes or holes happen when the denominator is equal to zero and the numerator don't.
Now, in the cases where the numerator and denominator become zero for the same value of x, it means that we can factorize the polynomials and remove the common factor. So there we do not have a hole nor asymptote.
Now, because the denominator becomes equal to zero, this means that we are dividing by a reallly small value, then the quotient will tend to infinity or negative infinity, this means that we will have a vertical asymptote.
Then the correct option is C:
Yes, the function will have either a vertical asymptote or hole for any values that cause the denominator to be equal to zero
If you want to learn more, you can read:
https://brainly.com/question/4084552
which is a point 5 units to the left of 2
Answer:
1.5
Step-by-step explanation:
Q.3] Formula of (a - b)3 is
9.
&(3f + 12) +f
ASAP need help pls ⬆️
Answer:
4f+12
Step-by-step explanation:
Combine Like Terms:
=3f+12+f
=(3f+f)+(12)
=4f+12
Simplify.
[tex] {2}^{9} \times {2}^{5} = {2}^{?} [/tex]
Enter the missing exponent.
i need help who knows the answer to this You start a new job. After w weeks, you have (10w+120) dollars in your savings account and (45w+25) dollars in your checking account. Write an expression in simplest form that represents the total in both accounts.
solve -8(n+5)=-44-8n
Answer:
there are no solutions
Step-by-step explanation:
HERE ARE THE STEPS IN CASE U NEED EM :)
Step 1: Simplify both sides of the equation.
−8(n+5)=−44−8n
(−8)(n)+(−8)(5)=−44+−8n(Distribute)
−8n+−40=−44+−8n
−8n−40=−8n−44
Step 2: Add 8n to both sides.
−8n−40+8n=−8n−44+8n
−40=−44
Step 3: Add 40 to both sides.
−40+40=−44+40
0=−4
One cell phone company offers a plan that costs $26.99 and includes unlimited night and weekend minutes. Another company offers a plan that costs $18.99 and charges $0.35 per minute during nights and weekends. For what numbers of night and weekend minutes does the second company's plan cost more than the first company's plan? Starting at minutes, the second company's plan will cost more than the first company's plan.
Given :
One cell phone company offers a plan that costs $26.99 and includes unlimited night and weekend minutes.
Another company offers a plan that costs $18.99 and charges $0.35 per minute during nights and weekends.
To Find :
For what numbers of night and weekend minutes does the second company's plan cost more than the first company's plan.
Solution :
Let, after n number of nights and weekends second plan is most costly.
So,
[tex]18.99+0.35x > 26.99\\\\0.35x > 8\\\\x>22.85[/tex]
Therefore, after 22 night and weekends second plan is most costly.
Hence, this is the required solution.
Anique’s favorite store to shop at is Zara in Manhattan, New York. Her mother put $50 on her debit card to purchase a new dress for picture day. Anique spent $30 on a dress, $30 on shoes, $20 on a necklace/bracelet set, and $20 for her lunch.
Answer
Step-by-step explanation:
Find the percent increase. Round to the nearest percent.
From 84 books to 162 books
Answer:
93%
Step-by-step explanation:
Answer:
1.45 x 5 is the answer but i want you to do some work for it and if its wrong im sorry but thats what i calculated it as
Step-by-step explanation:
When finding the volume of the volleyball, Erica used 3.14 in the formula. What type of measurement accuracy is used?
A) Exact
B) Approximation
C) Estimation
Answer:
c
Step-by-step explanation:
you would have to estimate bc you won't get an exact measurement . hope this helpssss. brainliest?
A new amusement park ride that last one minute can have up to 1,200 Riders per hour. How many riders can ride per minute.
Pls help
Answer:
20
Step-by-step explanation:
1 hour = 60 minutes
1200 riders = 60 minutes: divide by sixty to set equal to 1
20 riders = 1 minute
Just divide 1,200 by 60 because there are 60 minutes in 1 hour.
Just think about it this way: If you eat 1 banana a minute, you eat 60 bananas an hour. The amusement park ride goes around once a minute. In one hour it goes around 60 times. Each time it carries the same amount of people.
1,200 divided by 60 is...
20!
The ride can carry 20 riders each ride, and each ride lasts a minute.
if 3x-8= -2,find the value of x -6
Answer:
error
Step-by-step explanation:
you have a defined value by not having a Y so you basically can not put x=-6 because x actually equals 2!
Each driver is paid 8.65 per hour, if the field trip is going to lost 9.6 hours, how much will it cost to pay all of bus drivers?
Answer:
83.04
Step-by-step explanation:
First, you need to know how many drivers there are. But if the question doesn't tell you how many drivers then the answer would be 83.04 for one bus driver. If you forgot to add how many drivers then you can just multiply 83.04 to how many bus drivers then you get your answer.
Tom makes $214.40 in 4 days. How much does he make in 2 days
Answer:107.2
Step-by-step explanation:
So u know how much he gets in 4 days so u subtract 4 days by 2 and u get 2 so then divide 214.40 by 2 and u get 107.2
Please help me, I really dont want to get an F :((( (The Graph Is In The Image)
The graph shows the data for the time it takes Jerome to bike to school, based on his average biking speed for that trip. Which sentence describes the association?
A.The speed he bikes at affects the time it take him to get to school, but it is unclear if the time increases or decreases.
B. As the average speed increases, the time he takes to get to school decreases.
C. The speed he bikes at does not affect the time it takes him to get to school.
D. As the average speed increases, so does the time he takes to get to school.
Answer:
B: As the average speed increases, the time he takes to get to school decreases.
Step-by-step explanation:
On the graph, it showed that the plotted points are decreasing as the average speed is increasing. Also, I took the test and B was the correct answer.
Please simplify!!
[tex]x+18\geq 50[/tex]
Answer:
x ≥ 32
Step-by-step explanation:
x + 18 ≥ 50
subtract 18 from both sides.
x ≥ 50 - 18
x ≥ 32
2x^2+8−3=0 Complete the square
Answer:
- 5/4 or - 1 1/4
Step-by-step explanation:
Step 1:
2x² + 8 - 3 = 0 Equation
Step 2:
4x + 8 - 3 = 0 Exponents
Step 3:
4x + 5 = 0 Combine Like Terms
Step 4:
4x = - 5 Subtract 5 on both sides
Step 5:
x = - 5 ÷ 4 Divide
Answer:
x = - 5/4 or - 1 1/4
Hope This Helps :)
find the slope of this graph
Answer:
-3
Step-by-step explanation:
Pls help I need these by midnight
Maria is buying ping pong balls online. Website A charges $6 per box of ping pong
balls, plus an $8 service charge. Website B charges $5 per box, along with a shipping
and handling fee of $10. How many boxes does Maria need to buy for the cost of
both websites to be the same?
18 boxes
2 boxes
6 boxes
1 box
Answer:
2 boxes
Step-by-step explanation:
im sorry this is a bit late but this is for other people
Find the value of this triangle!
Answer:
x=35
y=145
z=25
Step-by-step explanation:
(do first)x:
55 + 90 = 145
180-145=35
(do last)y:
25+10=35
180-35=145
(do second)z:
65+90=155
180-155=25
Answer:
x = 35, y = 145, z = 25
Step-by-step explanation:
All triangles' angles have a sum of 180°. Because we know this, we can solve the first triangle easily.
180 = x + 90 + 55
180 = x + 145
35 = x
Angles x and y are what we call suplementary angles. This means they have a sum of 180°.
180 = 35 + y
145 = y
Once again, we know that triangles have a sum of 180°. So the next triangle should now be easy to solve.
180 = 10 + 145 + z
180 = 155 + z
25 = z
A toy box contains eight green balls and four purple balls. Suppose you choose a ball at random and then replace it by putting it back in the toy box. You then choose a second ball. What is the probability that you have selected a green ball and then a purple ball?
Answer:
okay now I know this for absolute sure the answer is 2 over 9 aka 2/9
Step-by-step explanation:
7 is a solution to the equation 3n + 9 = 33.
The sum of negative five plus three times a number equals twenty-eight.
The sum of three and a number times negative five gives twenty-eight.
The product of three times a number equals twenty-eight.
The product of negative three and a number plus five equals twenty-eight.
??????
Answer:
Step-by-step explanation:
1. 7 is not the solution of 3n+9 because if you do 7*3 and add 9 you will get 30.
2.
-5+3n=28
-5+5+3n= 28+5
3n=33
n= 11
3. 3n= 28
n= 28/3 or 9.333333
4. -3+n+5=28
n+2= 28
n+2-2= 28-2
n= 26
Answer:
it's d
Step-by-step explanation:
i got it right and the pic above :)
A Muffin Recipe needs 3/5 pound of butter to make 12 muffins, how much butter does the recipe need for 1 muffin
Answer:
1/15
Step-by-step explanation:
Hope it helps
Find the distance between the two points in simplest radical form.
(0, –4) and (-3,-1)
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (- 3, - 1)
d = [tex]\sqrt{(-3-0)^2+(-1+4)^2}[/tex]
= [tex]\sqrt{(-3)^2+3^2}[/tex]
= [tex]\sqrt{9+9}[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Hey there!
Given;
The points are;(0,-4) and (-3,-1).
Use formula for distance between the two points.
[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]
Put all values.
[tex]d = \sqrt{( { - 3 - 0)}^{2} + ( { - 1 + 4)}^{2} } [/tex]
Simplify to get answer.
[tex]d = \sqrt{9 + 9} [/tex]
[tex]d = \sqrt{18} [/tex]
[tex]d = 3 \sqrt{2} [/tex]
Therefore, the distance is 3√(2) units or 4.24 units.
Hope it helps...
5.
(plz helppp)
Mrs. Thompson’s class measured the rainfall at their school for four weeks.
Week 1:
Week 2: 3.2 inches
Week 3:
Week 4: ?
How much rain fell in week 4 if the total rainfall for the four weeks was 7 inches?
Answer: 1.26 inches
explanation :
because if you subtract 7 by 3.2 you'll get
3.8, 3.8 will be the total of rain if you add week 1 2 4 , then youll have to find the average by dividing 3.8 by 3 youll get 1.26 . so that means the average lenth of the rain for 1 2 4 is 1.26 inches
Select equivalent or not equivalent for each pair of expressions
Answer:
1: equivalent
2: equivalent
3: not equivalent
Step-by-step explanation:
for 1 & 2, you just switch the terms, but for 3, the 6z is not negative in the first expression, but it is in the second.
Sorry I just asked another question a few minutes ago
The photo cut off the word equation
Answer:
x=1
Multiply both sides by 10 (13)10-0.5(2x-6)*10+2x(10)=17*10Refine 130-5(2x-6)+20x=170Subtract 300 from both sidesSimplify -5(2x-6)+20x=40Expand 10x+30=40Subtract 30 from both sidesSimplify 10x=10Divide both sides by 10Simplify x=1:) Hope you enjoy this :)what is the value of n for the equation 1/3n=9
Answer: n = 27
Step-by-step explanation: n in (-oo:+oo)
(1/3)*n = 9 // - 9
(1/3)*n-9 = 0
1/3*n-9 = 0 // + 9
1/3*n = 9 // : 1/3
n = 9/1/3
n = 27
A pipe cleaner lay across a wire shelf. The wires that make up the shelf are parallel, and the pipe cleaner is a transversal. The parallel wires are labeled a, b, and, c, and the angles are labeled with numbers. Parallel lines a, b, and c are cut by a pipe cleaner transversal. All angles are described clockwise, from uppercase left. Where line a intersects with the pipe cleaner, the angles are: 1, 2, 4, 3. Where line b intersects with the pipe cleaner, the angles are 5, 6, 8, 7. Where line c intersects with the pipe cleaner, the angles are: 9, 130 degrees, 12, 11. The measure of one angle is 130°. Which statement is true regarding the 130° angle and angle 3? They are same-side interior angles, so angle 3 measures 50°. They are alternate interior angles, so angle 3 also measures 130°. They are corresponding angles, so angle 3 also measures 130°. They are alternate exterior angles, so angle 3 measures 50°.
Answer:
B. They are alternate interior angles, so angle 3 also measures 130°.
Explanation: This is the correct answer on Edge 2021, just took the unit test. Hope this helps ^-^.
They are alternate interior angles, so angle 3 also measures 130°. The correct option is B.
What are alternate interior angles?The angle formed by the line intersecting two parallel lines is called the alternate interior angle. These two angles are equal in magnitude.
Here, according to the given figure, lines a and c are parallel lines and pipe cleaner is a transversal that is passing through these parallel lines.
Therefore, by the property of parallel lines, the corresponding and alternative exterior or interior angles made by the common transversal ( pipe cleaner) on lines a and c must be equal, and here ∠3 and 130° are alternative interior angles by lines a and c with the same transversal, So, they must be equal.
The complete question is given below:-
A pipe cleaner lay across a wire shelf. The wires that make up the shelf are parallel, and the pipe cleaner is a transversal. The parallel wires are labeled a, b, and, c, and the angles are labeled with numbers. The measure of one angle is 130°. Which statement is true regarding the 130° angle and angle 3?
A. They are same-side interior angles, so angle 3 measures 50°.
B. They are alternate interior angles, so angle 3 also measures 130°.
C. They are corresponding angles, so angle 3 also measures 130°.
D. They are alternate exterior angles, so angle 3 measures 50°.
To know more about alternate interior angles follow
https://brainly.com/question/24839702
#SPJ2
