Which of the following rational functions is graphed below?
10
- 10
10
tho
A. F(x) =
3
X-7
B. F(x) = x + 3
X-7
C. F(x) =
(x+3)(x-7)
(x+3)(x-7)
D. F(X)
1
(x + 7(x-3)
7\x-
Check the picture out and please help me lol

Which Of The Following Rational Functions Is Graphed Below?10- 1010thoA. F(x) =3X-7B. F(x) = X + 3X-7C.

Answers

Answer 1

Vertical asymptote:

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graphic, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0.

In this graphic:

Dashed vertical lines at: [tex]x = -3, x = 7[/tex], thus, for [tex]x - (-3) = x+3[/tex] and [tex]x - 7[/tex] the denominator is zero.

Thus, the function graphed is:

[tex]F(x) = \frac{1}{(x+3)(x-7)}[/tex]

And the correct answer is given by option C.

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Answer 2

The graph is for the rational function f(x) = 1/(x + 3)(x - 7).

Option C is the correct answer.

We have,

To understand the graph of the function f(x) = 1/((x + 3)(x - 7)).

Vertical Asymptotes:

The function has vertical asymptotes at the values of x for which the denominator becomes zero.

The denominator is (x + 3)(x - 7), so the vertical asymptotes occur at

x = -3 and x = 7.

Horizontal Asymptote:

The highest power of x in the denominator is x², and there is no x² term in the numerator, the function approaches 0 as x goes to positive or negative infinity.

The horizontal asymptote is y = 0.

x-Intercept:

To find the x-intercept, we set y = 0 and solve for x:

0 = 1/((x + 3)(x - 7))

Since the numerator can never be zero, the only way the fraction can be zero is if the denominator is zero:

(x + 3)(x - 7) = 0

Solving for x:

x + 3 = 0

x = -3

x - 7 = 0

x = 7

So, the x-intercepts are (-3, 0) and (7, 0).

y-Intercept:

To find the y-intercept, we set x = 0:

f(0) = 1/((0 + 3)(0 - 7)) = 1/(-3 * -7) = 1/21

The y-intercept is (0, 1/21).

Thus,

The graph is for the rational function f(x) = 1/(x + 3)(x - 7).

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Related Questions

help guys HURRY!!! plsss! :D

Answers

Answer:

B. x+240=425

Step-by-step explanation:

Find the amount that results from a $900 investment invested at 7% interest,
compounded continuously, after 4 years.

Answers

Omg I’m sooooo sooo sorry I don’t know how to calculate I tried soo sorry

What is (are) the x-value(s) that solve the system of equations y = x and y = 2x – 1?

Answers

Answer:

y=1                 x=1

y = 2x – 1

replace y with x

x=2x-1

x-2x =  - 1

-x = -1

x= 1

y=x =1

Given: -3x+y=1. Write the equation In general form Ax + By + C =0.
3x - y = -1
3x = y + 1 = 0
-3x + y -1=0​

Answers

The given equations are 3x + y - 1 = 0 and 6x + 2y - 2 = 0.

So,

Equation I = (3x + y = 1) and

Equation II = (6x + 2y = 2)

= { 2(3x + y) = 2}

= 3x + y = 2/2

= 3x + y = 1

So, The given equations are 3x + y = 1 and 3x + y = 1.

Thus, there is one equation in two variables.

So, the given equations have an infinite number of solutions.

Answer:

1st option; 3x-y=-1

Step-by-step explanation:

-3x + y = 1

we can divide through by -1 so that the 'x' value is positive:

3x - y = -1

Admission to the zoo costs $15 per person. Which graph correctly represents the total cost for a group to visit the zoo? Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (2, 30), (3, 45), (4, 60), (5, 75), (6, 90), and (7, 105). Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (2, 15), (3, 15), (4, 15), (5, 15), (6, 15), and (7, 15). Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (2, 16), (3, 17), (4, 18), (5, 19), (6, 20), and (7, 21). Total Cost of Admission to the Zoo On a coordinate plane, the x-axis is labeled visitors and the y-axis is labeled Dollars. Points are at (1, 15), (1, 30), (1, 45), (1, 60), (1, 75), (1, 90), (1, 105).

Answers

Admission to the zoo costs $15 per person.

The graph y = 15x correctly represents the total cost for a group to visit the zoo.

Given;

Admission to the zoo costs per person = $15

Let:

The total number of people visiting the zoo = x

The total cost for a group to visit the zoo = y

So,  y ∝ x

y = 15x

Therefore, the graph y = 15x correctly represents the total cost for a group to visit the zoo.

Answer:

A

Step-by-step explanation:

solving for G

goal is to isolate the variable by undoing in the reverse of the order of operation.

4=2(3g+2)

Answers

Answer:

g = 0

Step-by-step explanation:

4 = 2(3g + 2) ← divide both sides by 2

2 = 3g + 2 ( subtract 2 from both sides )

0 = 3g , then

g = 0

Mrs bai bought 4 boxes of handkerchief for $31.20. There were 12 handkerchief in the box. Find the cost of the 1 handkerchief​

Answers

Answer:

0.65 cents

Step-by-step explanation:

12x4=48 total

31.20/48 = 0.65 cents each

The original price of a Shirt was $45. In sales, the shirt is reduced to $32.50. Calculate the percentage reduction.

Answers

Answer:

27.8%

Step-by-step explanation:

[tex]\frac{32.5}{45} =0.722[/tex]

0.722 = 72.2%

The % reduction is:

(100-72.2)% = 27.8%

Hope this helps

clothing store sells t shirt in only three colors red blue green the colors are in the ratio of 3:4:5 if the store has a total of 60 how many blue t shirt

Answers

Answer:

Step-by-step explanation:

red/blue = 3/4 and you get blue/green = 4/5

= 60/4 = 15

you have 15 red shirts, 20 blue shirts, and 25 green shirts.

15/20 = 3/4

20/25 = 4/5

if you simplify 15/20, you will see that it is equivalent to 3/4

if you simplify 20/25, you will see that it is equivalent to 4/5.

Find the dimensions of the rectangle with maximum area that can be inscribed in a circle of radius 10.

Answers

Answer:

Step-by-step explanation:

That will be a square with a diagonal of 20

side length of 20sin45

and area of (20sin45)² = 200 units²

prove it you say?

Area of a rectangle is base times height

A = bh

With a radius of 10, the diagonals of any rectangle inscribed will be 20 units

20² = b² + h²

h = [tex]\sqrt{400 - b^2}[/tex]

A = bh

A = b[tex]\sqrt{400 - b^2}[/tex]

Area will be maximized when the derivative is set to zero

           dA/db = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]

                   0 = [tex]\sqrt{400 - b^2}[/tex] - b²/ [tex]\sqrt{400 - b^2}[/tex]

b²/[tex]\sqrt{400 - b^2}[/tex] =  [tex]\sqrt{400 - b^2}[/tex]

                  b² = 400 - b²

                2b² = 400

                  b² = 200

                  b = [tex]\sqrt{200}[/tex]

h = [tex]\sqrt{400 - b^2}[/tex]

h = [tex]\sqrt{400 - \sqrt{200}^2 }[/tex]

h = [tex]\sqrt{200}[/tex]

A = bh

A =  [tex]\sqrt{200}[/tex][tex]\sqrt{200}[/tex]

A = 200 units²


32) Out of 525 people surveyed, 210 answered yes. Estimate how many people would answer yes if 900
people were surveyed.

Answers

Answer:

360 people

Step-by-step explanation:

[tex]\frac{ 210}{525}*900[/tex][tex]=360[/tex]

Hope this helped! :)

Please look at picture for question

Answers

Answer:

a=0.62

b=7/9

c=10/9

3 movie tickets cost 3690$. At this rate, the cost per ticket is $....

Answers

Answer: The cost per ticket is $1,230.

Explanation: 3,690/3 = 1,230.

Answer: The cost for each ticket is $1,230.

Step-by-step explanation:

19. Ram and Rahim are partners in a firm sharing profits in the ratio of 3: 2. Kabir is admitted as a partner for 1/5th share of profits. Machinery would be appreciated by 10% (Book Value of 80,000) and Building would be depreciated by 20% (Book Value of 2,00,000). Unrecorded Debtors of 1,250 would be brought to books. There is a liability of 2,750 included in Sundry Creditors that is not to be paid. What will be the Gain (Proñt Loss on revaluation? (a) Loss of 28,000. (c) Profit 28,000. (6) Loss 40,000. (d) Profit of 40,000.​

Answers

Answer:

make me brainlist

Step-by-step explanation: firm sharing profits and losses in the ratio of 3

2. From Ist April, 2020 they decided to share the future profits equally. On this date, the General Reserve

showed a balance of 1,60,000; Revaluation of fixed assets resulted into a gain of "1,02,000 and stock resulted

to a loss of 22,000. On this date, the goodwill of the firm was valued at $3,60.000

Pas necessary journal entries for the above transactions on reconstitution of the form

Bolutions

What is 29−−√?

What 2 numbers does it fall between when placed on a number line?

Question 5 options:

Between 5 - 5.5


Between 4 - 4.5


Between 4.5 - 5


Between 5.5 - 6

Answers

Between 5 - 5.5
Hope this helps.

A college is selling tickets to the annual battle of the bands
competition. On the first day of ticket sales, the college sold 3
student tickets and 5 adult tickets for a total of $70. On the
second day, the college sold 12 student tickets and 12 adults
tickets for a total of $216.
Use elimination to solve the system of linear equations and
determine the price of each student ticket, x, and each adult
ticket, y. Write your answer as an ordered pair (x,y).

Answers

Answer:

Step-by-step explanation:

Answer:

(10,8)

Step-by-step explanation:

please help will brain list if correct no links please ​

Answers

Answer:

C

Step-by-step explanation:

the angle opposite of it is 30

If y = 6, what is the value of x given 8x + 5y = 62?
Answer:

Answers

The answer: y = 6 ⇔ x = 4

ok done. Thank to me :>

I need a step by step explanation as well as work

Answers

Answer:

  x = 2

  m = 15/4

  a = 5/4

Step-by-step explanation:

When the "base" lines are parallel, all of the triangles are similar. That means corresponding segments are proportional, including corresponding parts of segments.

We see that x corresponds to a partial segment marked 3. That same top-bottom correspondence has another pair of segments marked 2 and 3. That means x=2.

  x/3 = 2/3   ⇒   x = 2

__

The segments marked 'm' and 'a' are "whole side" segments, so we need to put those in proportions with corresponding whole sides. If we use the bottom side, we find ...

  a/3 = 5/(3+6+3) = 5/12   ⇒   a = 5/4 = 1 1/4 . . . . . multiply by 3

and

  m/(6+3) = 5/12   ⇒   m = 15/4 = 3 3/4 . . . . . multiply by 9

__

  x = 2

  m = 15/4

  a = 5/4

Problem Situation: Ben buys a table for $240. He also buys 6 chairs that all cost the same amount. His total cost is $720. What is the price of one chair? Use the drop-down menus to complete parts A and B below.

Answers

The price of one chair Ben bought is $80 and he bought 6 chairs in total.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given,  Ben buys a table for $240. He also buys 6 chairs that all cost the same amount.

Assuming each chair costs $x and his total cost is $720.

240 + 6x = 720.

6x = 720 - 240.

6x = 480.

x = 80

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A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch. How much does it cost to fund 4.5 inches of the construction?

Answers

Answer:

=$114.750

Step-by-step explanation:

Length of new board cast tower=4.5 Inches

Cost of construction(per inch)=$25.50

To find cost=?

                 =25.50x4.5

                 =$114.750

                      ...................................................................................

The required cost of the construction of a 4.5-inch tower is $114.75.

Given that,
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch, how much it cost to fund 4.5 inches of the construction is to be determined.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 × 4.5 = $114.75.

Thus, the required cost of the construction of a 4.5-inch tower is $114.75.

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Please help me it’s due in 12 minutes also pls explain why

Answers

Root 25 is the rational number as it equals 5

A number x is no less than 18

Answers

Answer:

x>18

Step-by-step explanation:

That's the answer if x can't be 18.

Answer:

x ≥ 18

Step-by-step explanation:

I'm not really sure how to explain how it's correct but, the given statement can also be written as " a number, x,  can be equal or more than 18

Solve each equation for x.
a(x-b)+bx+c=a+b

Answers

Answer:

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

Step-by-step explanation:

a(x−b)+bx+c=a+b

Step 1: Add ab to both sides.

−ab+ax+bx+c+ab=a+b+ab

ax+bx+c=ab+a+b

Step 2: Add -c to both sides.

ax+bx+c+−c=ab+a+b+−c

ax+bx=ab+a+b−c

Step 3: Factor out variable x.

x(a+b)=ab+a+b−c

Step 4: Divide both sides by a+b.

[tex]\frac{x(a+b)}{a+b} =\frac{ab+a+b-c}{a+b}[/tex]

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

Hope this helped! :)

The number of gold fish that can live in a small tank is at most 6.
Let g be the number of goldfish that can live in the tank.
Which inequality represents this situation?

g<6 g≥6 g>6 g≤6

Answers

Answer:

g≤6

Step-by-step explanation:

g≤6 inequality represents the given situation of at most.

What is inequality?

" Inequality means an algebraic expression which represents the relation between two situation or values with the sign of > , < , ≥, ≤."

Term used

At most means 'less than to equals to' ( ≤ )

According to the question,

Given'

'g' represents the number of gold fish live in the tank

As per condition of inequality given,

Number of gold fish can live in small tank at most 6

Represent as the  term used we get,

Inequality is

g ≤ 6

Hence, g≤6 inequality represents the given situation of at most.

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Tamika ran 90 meters in 16.1 seconds. Enrique ran 90 meters in 17.0 seconds. Who had the fastest time, Tamika or Enrique? A. Enrique B. Tamika

Answers

The answer is Tamika

How can the equation of a parabola be derived when given the focus and the directrix?


Answers

Answer:

If the focus is to the right of the directrix, then the parabola opens to the right and p>0 . If the focus is to the left of the directrix, then the parabola opens to the left and p<0 .

HOPE ITS HELP

Help help help help help m at h math math

Answers

Answer:X= 6X-14

Step-by-step explanation:

Kevin and Randy Muise have a jar containing 34 coins, all of which are either quarters or
nickels. The total value of the coins in the jar is $5.30. How many of each type of coin do
they have?

Answers

Answer:

20 quarters quarters 14 nickles

A BCC professor decides to grade his class as following: 20 percent for homework assignments, 10 percent for quizzes, 25 percent for a midterm, and 45 percent for the final exam. A student receives 90 for homework, 95 for the quizzes, 85 for the midterm and 84 for the final exam. What will be the student’s class grade?
Class grade: ?

Answers

Answer:

86.55%

Step-by-step explanation:

Basically what you would do is take each percentage and turn it into decimal percent. after that, you multiply it with the respective numbers, like:

90 × 0.20= 18

95 × 0.10= 9.5

85 × 0.25= 21.25

84 × 0.45= 37.8

Adding these numbers together, you could get 86.55, or 86.55%.

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