The graph shown here is the graph of which of the following rational
functions?
-10
10
FOO
10
O A. F(X) = (2+1)(²-3)
B. F(x) = (z+1)(x-2)(z-3)
D-2
O C. F(x) = (2-1)(x+3)

The Graph Shown Here Is The Graph Of Which Of The Following Rationalfunctions?-1010FOO10O A. F(X) = (2+1)(-3)B.

Answers

Answer 1

According to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.

What is vertical asymptote?

At the margins of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of such a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function never traverse a vertical asymptote. A graph's vertical asymptote is a vertical line with the equation x=a, where the graph tends to positive or negative infinity as the inputs go closer to a.

For the given graph we can see that the vertical asymptotes are -1 and 3, and there is no horizontal asymptote.

In option A:

[tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex]

The horizontal asymptote is none.

The vertical asymptote is -1 and 3.

Hence, this is the correct option.

Option B:

[tex]F(x) = \frac{1}{(x-2)(x+1 )(x-3)}[/tex]

The horizontal asymptote is 0.

The vertical asymptote is 2, -1 , and 3.

Hence, option B is incorrect.

Option C:

[tex]F(x) = \frac{x-2}{(x-1 )(x+3)}[/tex]

The horizontal asymptote is none.

The vertical asymptote is 1 and -3.

Hence, option C is incorrect.

Hence, according to the graph the rational function represented in the graph is [tex]F(x) = \frac{x-2}{(x+1 )(x-3)}[/tex], and option A is correct answer.

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Related Questions

three quantities, the results of measurements, are to be added. they are 2.0800, 2.677, and 1.67. what is their sum to the correct number of significant figures?

Answers

Sum to the correct number of significant figures is 6.43

Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.

Significant figures are used to establish the number which is presented in the form of digits. These digits carry a meaningful representation of numbers. The term significant digits are also used often instead of figures. We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.

Since the least precise measurement 1.67 is correct to only two decimal place.

  2.0800

+ 2.677

+  1.67          

  6.427

Therefore, the final result should be rounded off to 6.43 where Significant Figures: 3, Decimals: 2.

The arithmetic addition of given numbers to the correct number of significant figures is 6.43.

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on Wednesday evening sonto spent one ½ doing doing homework 45 minutes doing housework 1 hour visiting friends and 1 hour ½ watching television . write information in a ratio

Answers

If on Wednesday evening sonto spent one ½ doing doing homework 45 minutes doing housework 1 hour visiting friends and 1 hour ½ watching television .This  information in a ratio is: 2: 3 : 4 :6.

How to find the ratio?

We need to first analyze the details  before determining the ratio.

​1 hour = 60 minutes

1/2 h = 30 minutes

1 1/2 = 90 minutes

So,

30 : 45 = 60 :90

Reduce the above minutes  to ratio

2: 3 : 4 :6

Therefore the ratio of the information is 2: 3 : 4 :6.

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Sal received an 8% raise. He now earns $66960. How much did he earn previously? Hint: number only, no symbols, no units​

Answers

Answer:

Sal previously earned $61640.

Answer:

$62,000.00

Step-by-step explanation:

x + .08x = 66960  Combine like terms

1.08 x = 66960  Divide both sides by 1.08

[tex]\frac{1.08x}{1.08}[/tex] = [tex]\frac{66960}{1.08}[/tex]

x = 62000

I don’t understand how to do this.

Answers

Answer:

6000

Step-by-step explanation:

Interest of 3% a year of principal of 200,000 = 6000

monthly payment of 843 also includes a portion of amortization of the principal itself, which you can ignore cause the question only asked for the interest portion.

this is an unclear question cause it didn't say PER YEAR interest paid.  you only need to remember interest% * principal = ANNUAL interest payment $.  Then you can divide that over 12 months, which is 500$ per month.

rosie says she could solve 24*25 with the arry above. do you agree with her why or why not.

Answers

She could only solve 24 * 25 if the array has 24 rows and 25 columns or vice versa

How to determine the true statement

From the question, we have the following parameters that can be used in our computation:

Product expression = 24 * 25

An array is a set of items that has rows and columns

The array is not given

However, the true statement is that: for Rosie to evaluate the expression using an array, then the array must be a 24 x 25 array or 25 x 24 array

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an automobile manufacturer claims that their car has a 55.7 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this car. after testing 91 cars they found a mean mpg of 55.2 with a variance of 3.24 mpg. is there sufficient evidence at the 0.05 level that the cars underperform the manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.

Answers

For the given case the Null hypothesis is The mean mpg of the 91 cars tested is equal to the manufacturer's mpg rating of 55.7 and the  Alternative hypothesis is The mean mpg of the 91 cars tested is less than the manufacturer's mpg rating of 55.7.

In order to determine whether the cars underperform the manufacturer's mpg rating, the independent testing firm would need to perform a hypothesis test. To do this, they would need to compare their sample mean of 55.2 mpg with the manufacturer's mpg rating of 55.7. They would also need to know the standard deviation of the sample, which is 3.24.

The independent testing firm would then calculate the z-score by subtracting the manufacturer's rating from the sample mean, and dividing it by the standard deviation. If the z-score is greater than the critical value for a 0.05 level of significance, then there is sufficient evidence to reject the null hypothesis.

In this case, the z-score is -1.51. Since the critical value for a 0.05 level of significance is 1.96, the z-score is less than the critical value. Therefore, there is not sufficient evidence to reject the null hypothesis, and we cannot conclude that the cars underperform the manufacturer's mpg rating.

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mary divides a circle into sectors. the central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. what is the degree measure of the smallest possible sector angle?

Answers

The measure of the smallest possible sector angle possible is 8°.

Let [tex]$a_1$[/tex] be the first term of the arithmetic progression and [tex]$a_{12}$[/tex] be the last term of the arithmetic progression.

From the formula of the sum of an arithmetic progression, we have -

[tex]$12*\frac{a_1+a_{12}}{2}=360$[/tex]

simplifying we get,

[tex]$a_1 + a_{12} = 60$[/tex]

[tex]$a_{12}$[/tex]  is the largest term of the progression and it can also be expressed as-

[tex]a_{12} = $a_1+11d$[/tex]

where d is a common difference.

Since each angle measure must be an integer, d should also be an integer.

[tex]$a_{12}-a_1=a_1+11d-a_1=11d$[/tex]

Since d is an integer, the difference between the first and last terms, 11d, must be divisible by 11.

Since the total difference should be less than 60, let's start checking multiples of 11 less than 60 for the total difference between [tex]$a_1$[/tex] and [tex]$a_{12}$[/tex].

Let us take the largest multiple because the maximum difference will give us the minimum value of the first term.

If the difference is 55, [tex]$a_1=\frac{60-55}{2}=2.5$[/tex], is not an integer.

If the difference is 44, [tex]$a_1=\frac{60-44}{2}= 8[/tex] . It satisfies the given conditions.

Hence, the measure of the smallest possible sector angle possible = 8°.

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If I Got 7 "(tokens or whatever you prefer) a minute for 9 hours/ 540 minutes, how many tokens would I have

Answers

Answer:

If you get 7 tokens a minute and you work for 9 hours, or 540 minutes, then you would have:

7 tokens/minute * 540 minutes = 3780 tokens

You would have 3780 tokens in total.

Answer:

3,780

Step-by-step explanation:

7* 540= 3780

because you get 7 every minute and there are 540 minutes

How many solutions does the equation 6x + 12 = 2(3x + 6)

Answers

Answer: Infinite, or unsolvable

Step-by-step explanation:

6x + 12 = 2(3x+6)

6x + 12 = 6x + 12 <-- opening up the bracket

Because both sides of the equation are the same, the answer is either that there are an infinite amount of solutions for x, or that the equation is unsolvable.

Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.

Answers

Answer:

AAA similarity

Step-by-step explanation:

Similar triangles:

      In ΔECD,

            ∠E + ∠D + ∠ECD = 180°   {Angle sum property}

            ∠E + 36 + 123       = 180°

                      ∠E + 159     = 180

                                   ∠E = 180 - 159

                                  ∠E = 21°

In ΔACB,

           ∠A + ∠B + ∠ACB = 180°   {Angle sum property}

            ∠ACB + 36 + 21       = 180°

                      ∠ACB + 57    = 180

                                   ∠ACB = 180 - 57

                                  ∠ACB= 123°

    In ΔECD & ΔBCA,

               ∠A ≅ ∠D

              ∠B ≅ ∠A

           ∠BCA ≅ ∠ECA

ΔECD ~ ΔBCA by Angle Angle Angle similarity.

A towns population is expected to grow between 5% and 8% per year for the next 10yr. if the current population is 50,000, write an inequality for the expected population, p, next year.

Answers

Answer: An inequality for the expected population, p, next year can be written using the information provided. Since the population is expected to grow between 5% and 8% per year, we can represent that as a range of growth rates: 0.05 <= growth rate <= 0.08

To find the expected population next year, we can use the formula:

p = population * (1 + growth rate)

where "population" is the current population of 50,000 and "growth rate" is the percentage increase. Since the growth rate is expected to be between 0.05 and 0.08, we can write the inequality as:

50,000 * (1 + 0.05) <= p <= 50,000 * (1 + 0.08)

This inequality represents the expected range of population next year, with the lower bound being the population if it grows by 5% and the upper bound being the population if it grows by 8%.

Simplifying the inequality:

52,500 <= p <= 54,000

So the expected population next year, p, is between 52,500 and 54,000.

Step-by-step explanation:

Explain your work please.

Answers

Refer to the attached image. Comment any questions you have!

In bags of Happy Trail Mix, the number of raisins is skewed left with a mean of 33. 6 and a standard deviation of 8. 4, while in bags of a generic trail mix, the number of raisins is skewed right with a mean of 28. 8 and a standard deviation of 12. 7. What is the probability in a sample of 17 randomly selected Happy Trail Mix bags and a sample of 17 randomly selected generic bags that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix?

Answers

The probability that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix is 9.7%.

To solve this problem, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a sample size of 17, we can approximate the distribution of the sample means as normal.

Let's call the mean of the Happy Trail Mix sample x and the mean of the generic mix sample y.

Using the formula for the mean of a normal distribution, we can find the mean of x and y:

μx = μ = 33.6

μy = μ = 28.8

Using the formula for the standard deviation of the sample mean, we can find the standard deviation of x and y:

σx = σ/√n = 8.4/√17 = 2.04

σy = σ/√n = 12.7/√17 = 3.08

Now that we have the mean and standard deviation of x and y, we can use a normal distribution calculator or a z-score table to find the probability that x > y.

The z-score is given by:

z = (x - y - μ)/σ = (33.6 - 28.8)/(√(2.04^2 + 3.08^2)) = 1.30

Using a standard normal table, we find that the probability of a z-score being greater than 1.30 is 0.097, or 9.7%.

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evaluate the function f (x) = -3x + 4 when x = -6

Answers

Answer:

x=−3⋅−6+4=x=22

Step-by-step explanation:

Please anwser this...

Answers

Check the picture below.

To describe a sequence of transformation that maps triangle ABC onto triangle a”b”c” a student starts with a reflection over x-axis

Answers

We can write the coordinates after reflection as -

A (x₁, y₁) → A" (x₁, - y₁)

B (x₂, y₂) → B" (x₂, - y₂)

C (x₃, y₃) → C" (x₃, - y₃)

What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each other.

Given is that to describe a sequence of transformation that maps triangle ΔABC onto triangle ΔA”B”C” a student starts with a reflection over x - axis.

Assume the coordinates of a triangle are -

A (x₁, y₁)

B (x₂, y₂)

C (x₃, y₃)

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.The reflection of point (x, y) across the x-axis is (x, -y).

So after the reflection over the {x} axis, we can write the coordinates as -

A" (x₁, - y₁)

B" (x₂, - y₂)

C" (x₃, - y₃)

Therefore, we can write the coordinates after reflection as -

A (x₁, y₁) → A" (x₁, - y₁)

B (x₂, y₂) → B" (x₂, - y₂)

C (x₃, y₃) → C" (x₃, - y₃)

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Does 4x - 8 = 3x +13 have one solution, no solution or infinite solutions

Answers

Answer:

only one solution

Step-by-step explanation:

4x - 8 = 3x + 13

x = 21

Hey there!

Given:

[tex]4x-8=3x+13[/tex]

Solution(s):

One Solution; [tex]x=21[/tex]

Hope this helps!

help pls and thanks

Answers

An equation of a circle which represents the picture include the following: A. (x)² + (y)² = 25.

What is the equation of a circle?

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²  

Where:

h and k represents the coordinates at the center of a circle.r represents the radius of a circle.

From the information provided above, we have the following points on this circle:

P(–5, 0)Q(0, 5)R(5, 0)S(0, –5).Radius of the circle (r) = 5 units.Center of the circle (h, k) = (0, 0)

Substituting the given points into the equation of a circle, we have the following;

(x - 0)² + (y - 0)² = 5²  

(x)² + (y)² = 25.

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PLS HELP

What is in decimal form?
16
O 0.3125
O 0.6875
O 1.45
OI don't know.

Answers

Answer:

decimal form is limited of 3 numbers after the point only.

so it will be 1.45

I hope I help you in this ans and tq.

For the shape below, if side BD = 29 and side AC = 3x - 4, find x.

Answers

x=11
since sides BD and AC are congruent, then the equation would be 29=3x-4

Answer:

x = 11

Step-by-step explanation:

We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)

Determine whether the pairs of triangles are congruent.
~Circle yes, no, or not enough information. Explain your choice.

Answers

The answer should be yes.

Both triangles have the same angles. Congruent triangles are congruent when triangles have the same exact sides and angles.

I need help in this problem

Answers

Answer:

b

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

2x + 1 + 5x + 5 + 90 = 180

7x + 96 = 180 ( subtract 96 from both sides )

7x = 84 ( divide both sides by 7 )

x = 12

A. Sketch a cube and label its side length as 4cm (this will be Cube A).
B. Sketch a cube with sides that are twice as long as Cube A and label its side length (this will be Cube B).
C. Find the volumes of Cube A and Cube B.

Answers

Answer:

see attached

Step-by-step explanation:

parallelogram has sides of lengths 35 inches and 75 inches. One angle has measure of140°. Find the length of each diagonal.

Answers

The length of diagonal of a parallelogram is 2546 inches.

What is a parallelogram?

A quadrilateral with equal pairs of opposing sides and angles is referred to as a parallelogram. It has a pair of opposing sides that are parallel to one another. The inner angles are supplementary in nature, meaning that the sum of them equals 180 degrees. A parallelogram's diagonals are bisected by one another, or divided into two equal portions. A parallelogram's internal angles add up to 360 degrees.

The diagonals of parallelogram are given by:

x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)

Given the two sides are 35 and 75 inches.

We also know that the adjacent angles of parallelogram are supplementary:

∠A + ∠B = 180

140 + ∠B = 180

∠B = 40

Substitute the value of sides and angle in the equation:

x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)

x = √((35)^2 + (72)^2 + 2(35)(72) cos 140)

x = 1225 + 5184 + (5040)(-0.766)

x = 1225 + 5184 - 3860

x = 2546 inches

Hence, the length of diagonal is 2546 inches.

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what is WD?

what is AB + DC

what is the perimeter of the trapezoid?

Answers

Perimeter (P) = AB + BC + CD + DA.

What is perimeter of trapezoid?

The perimeter of a trapezoid is the sum of the lengths of each side of the trapezoid. A trapezoid is a quadrilateral that has two sides parallel to each other and two non-parallel sides termed as bases and legs respectively. Let us learn how to calculate the perimeter of the trapezoid in this article.

perimeter of the trapezoid=sum of 4 side

                                            =AB+BC+CD+DA

Perimeter (P) = AB + BC + CD + DA.

It can also be written as a sum of lengths of parallel sides and the sum of lengths of non-parallel sides where AB and CD are the parallel sides and AD and BC are the non-parallel sides.

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The area of the cross section of the prism is 30 cm2.

The length of the prism is 25 cm.

Work out the volume of the prism?

Answers

The required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.

Area of cross section of the prism = 30 cm²

Length of the prism = 25 cm

Volume of the prism = ?

A prism is a polyhedron consisting of an n-sided polygon base. The relation between volume, base area and height of the prism is mathematically given as,

V = B H

where, B is Base area

H is Height of prism

V = 30 × 25 = 750 cm³

Thus, the required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.

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write the expanded form of the expression
4(3x-5)
4 (3x-5)=​

Answers

One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation. So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.

How do you write in a more detailed format?

One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation.

It is also possible to create a mathematical expression using integers that have been divided into distinct place values and decimal places.

5,000 + 300 + 20 + 5 = 5,325 is the expanded notation for the number.

Expanded form of the given expression.

1) We can expand the given term by the direct formula of the algebra

(A-B)³ = A³-B³-3AB(A-B)2)

We have (3x-5)³on comparing with the formula:

A = 3x

B = 5

(3x-5)³

(3x)³-5³-3×3x×5(3x-5)

27x³-125-45x(3x-5)  27x³-125-135x²+225x

So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.

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Find the balance in the account after the given period. $2,600 deposit earning 4.2% compounded monthly, after 3 years. The balance after 3 years will be $ (Round to the nearest cent as needed.)​

Answers

To find the balance of the account after 3 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the initial principal is $2,600, the interest rate is 4.2% (expressed as a decimal), the number of times the interest is compounded per year is 12 (monthly), and the number of years is 3.

So, we can plug these values into the formula:

A = 2600(1 + 0.042/12)^(12*3)

A = 2600(1.0035)^36

A = 2600 * 3.876

A = 10,049.6

The balance of the account after 3 years is $10,049.6.

Question 4(Multiple Choice Worth 2 points)
(Slope MC)

A linear relationship is given in the table.


x −2 −1 0 1 2
y −13 −9 −5 −1 3


What is the slope of the relationship?
one fourth
negative one fourth
4
−4

Answers

The slope of the relationship is equal to; C. 4.

How to calculate the slope of a line?

In Mathematics, the slope of any straight line can be calculated by using this mathematical expression;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points on the line:

Points on x-axis = (-2, -1).Points on y-axis = (-13, -9).

Substituting the given points into the slope formula, we have;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-9 + 13)/(-1 - (-2))

Slope (m) = 4/1

Slope (m) = 4

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A car travels down the road at a constant speed of 120 meters in 5 seconds. What is the velocity of the car

Answers

Answer: 17 m/s

Step-by-step explanation:  

the answer is 17 meters per second!
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Summarize each piece of EVIDENCE.Scientists have measured much more nickel and iron in carbonaceous chondrites than they have found in Earths surface rocks and magma.Scientists have observed magnetic minerals in rocks along the Mid-Atlantic Ridge are aligned with Earths magnetic field. Scientists observed rocks on both sides of the ridge form identical patterns. Every few million years, the alignment of these minerals reverses. Carbonaceous chondrites (a special type of meteorite) and Earth formed from the same cloud of gas and dust. They should have the same composition, including the same amounts of nickel and iron.Summarize each piece of Reasoning.Because Earth was very hot after it formed, it completely melted. Scientists deduce that most of Earths iron and nickel sunk to its core at this time in Earths history. Convection occurs in the outer core. Cool, dense matter sinks while warm, less dense matter rises. The flow of this liquid iron creates electric currents, which produce our magnetic fields. Periodically, the flow of fluid changes which results in a reversal of our magnetic field. Select the 2 fractions that are equivalent to 1 nursing students are reviewing information about various types of skin lesions. the students demonstrate understanding of the information when they identify which as a vascular lesion? supreme court deals major blow to 2nd amendment for millionsHow has the Supreme Court changed its stance on the meaning of the Second Amendment? Why is the Illiad important to the study of the Bronze Age? CARBOHYDRATES WORKSHOP choose the set of keywords that would be most effective in searching for results on the research question below: boolean which of the following is/are true about cancer cells? select all that apply. check all that apply disregard their genetic programmingdisregard their genetic programming receive the correct signals for cell growthreceive the correct signals for cell growth lose their specializationlose their specialization divide uncontrollablydivide uncontrollably it is important for nurses and patients to communicate in the same language because a common language ensures cultural understanding. 1. Mr. Gewanter, whose mass is 60 kg, is doing a physics demonstration in the front of the classroom. A. How much gravitational force does he exert on 55 kg Martha in the front row, 1.5 m away? B. How much force does he exert on 65 kg Lester in the back row, 4.0 m away? 2. A 400 kg weather satellite is about to launched into orbit. A. When the satellite is still on Earth, what is the gravitational force on it? (The mass of the Earth is 5.98x1024 kg and the radius of the Earth is 6.37x106 m) B. What radius of orbit does the satellite need to experience half this force? heparin is a common anti-coagulant. to prepare an iv containing heparin and buffers, you acquire a large mixing tank. for this problem, assume a simplified system in which there are three inlet streams and one outlet stream. in mixing the solution, you keep track of two constituents: heparin and bicarbonate. streams 1, 2, and 3 enter the mixer; stream 4 leaves the mixer. stream 1 contains 300 mm heparin in water. stream 2 contains 200 mm bicarbonate in water. stream 3 contains water with no heparin or bicarbonate. the overall mass flow rate in stream 4 is 1000 g/min. the outlet stream contains 60 mm heparin, 30 mm bicarbonate, and water. assume that the density of every stream is 1.0 g/cm3 . which of the following commands would invoke a windows update to happen on the computer immediately?