F(x)=5x+1 independent variable
Answer:
Step-by-step explanation:
In 2021, Madison Square Garden employed 8,900 people. For a basketball game at the garden, there are seats for 19,812 fans. What is the number of fans per employee during a basketball game? Round to the nearest tenth.
Answer:
There are 2.2 fans per employee.
Step-by-step explanation:
19812/8900 = 2.2 Rounded.
Helping in the name of Jesus.
A new homeowner is purchasing a living room set for $2,784 and must decide between two financing offers. Offer 1: $225 down payment, 24.90% interest rate, compounded monthly, for 3 years. Offer 2: $450 down payment, 22.90% interest rate, compounded monthly, for 4 years. Part A: What is the total cost of offer 1? Explain which technology you used to solve and each step of your process. (3 points) Part B: What is the total cost of offer 2? Explain which technology you used to solve and each step of your process. (3 points) Part C: Which financing offer should the new homeowner choose? Explain your reasoning.
Therefore , the solution of the given problem of interest comes out to be Offer 1 should be selected by the new homeowner since it has a reduced overall cost.
What exactly does the word interest mean?Divide the sum by the funding cost, the remaining time, and other factors to determine the simple interest rate. Principal loan repayment hours is the marketing plan with the simplest return. The simplest way to determine involvement is through this technique. In most instances, income is calculated as a percentage of the starting sum.
Here,
Part A: To start, we must divide the yearly interest rate by 12 to determine the monthly interest rate:
Monthly interest rate equals 24.90% divided by 12 equals 0.0249 per month.
=> Monthly payment = (P * r) / (1 - (1 + r)⁻ⁿ
=> Monthly payment = $104.23 per month
=> (2784 * 0.0249 / (1 - (1 + 0.0249)(-36)).
Taking the entire number of months (36) into account, we get:
Cost of the whole deal 1 = 36 * $104.23 = $3,751.28
As a result, offer 1's overall price is $3,751.28.
Part B:
First, we figure out the interest rate per month:
Monthly interest rate = 22.90% / 12 = 0.0229 / month.
=> Monthly payment = (P * r) / (1 - (1 + r)⁻ⁿ
=> Monthly payout
=> (1 - (1 + 0.0229)(-48)) / (2784 * 0.0229) ≈ $82.12/month
Using the entire number of months (48) as a multiplier, we obtain:
Cost of the whole deal 2 = 48 * $82.12 = $3,938.56
Part C:
Offer 1 costs $3,751.28 in total, while Offer 2 costs $3,938.56 in total.
Offer 1 should be selected by the new homeowner since it has a reduced overall cost.
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If Big Bun won 5 out of 25 matches, what percent did he win? A 25% B 20% C 15% D 10%
Answer:20%
Step-by-step explanation:
5(100)/25=20
You want to create a simulation of the following scenario:
In country x 50% of people have blood type O, 25% have blood type A, 12.5% have blood type B, and 12.5% have blood type AB.
In country y, 60% have blood type O, 20% have type A, 10% have type B and 10% have type AB.
What is the best way to assign values for a simulation using random digits table?
Choose answer from photo below! A, B, C, or D : this is the answer I want, not just an explanation please, thank you so much! 100 points!
Thank you :)
Answer: click thanks if you like my answer. have a good day <:
The best way to assign values for a simulation using a random digits table is to first identify the possible outcomes and assign a number or range of numbers to each outcome. Then, using the random digits table, randomly select digits and match them to the assigned outcomes.
For example, in the given scenarios for blood types in different countries, each blood type is assigned a specific number or range of numbers. Using the random digits table, the assigned numbers can be matched to the digits in the table to simulate the occurrence of each blood type in the population.
To answer the questions:
1.What is the purpose of assigning values for a simulation using a random digits table?
The purpose of assigning values for a simulation using a random digits table is to create a simulated scenario that reflects the likelihood of different outcomes based on assigned probabilities. This can help in making predictions and decisions in various fields such as medicine, finance, and social sciences.
2.In which scenario are blood types represented with the fewest number of digits?
Blood types are represented with the fewest number of digits in the third scenario for both Country X and Country Y. Blood type O is represented with 0, blood type A with 1, blood type B with 3, and blood type AB with 4, while all other digits are ignored.
3.In which scenario are blood types represented with the most number of digits?
Blood types are represented with the most number of digits in the first scenario for Country X, where blood type O is represented with 0, 1, 2, 3, 4, and 5, blood type A with 6 and 7, blood type B with 8, and blood type AB with 9. The same applies to Country Y in the first scenario.
Step-by-step explanation:
hope its help <:
Increase the number 15/16 by 3/5 of it of it. Then increase the resulting number by 3/5 of it
The resulting number is 12/5
What are arithmetical operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it
So, performing the operations,
15/16+15/16×3/5
= 15/16(1+3/5)
= 15/16(8/5)
= 120/80
= 3/2
Now,
3/2+3/2×3/5
= 3/2(1+3/5)
= 3/2(8/5)
= 24/10
= 12/5
Hence, the resulting number is 12/5
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Ava is going on holiday with Fly Away airlines. The maximum weight her suitcase can be is 2020 kg.
When empty her suitcase weighs 33 kg.
The clothes she plans on taking have a combined weight of 55 kg.
Her electrical accessories have a combined weight of 44 kg.
She is also taking 55 hardback books, which each weigh 720720 g.
Finally, the toiletries she is taking have a combined weight of 46004600 g.
How much over the maximum weight will Ava's suitcase be? Give your answer in grams.
As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.
What exactly is weight?Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.
First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.
Maximum weight limit = 2020 kg = 2020000 g
Weight of empty suitcase = 33 kg = 33000 g
Weight of clothes = 55 kg = 55000 g
Weight of electrical accessories = 44 kg = 44000 g
Weight of 55 hardback books = 55 x 720720 g = 39639600 g
Weight of toiletries = 46004600 g
Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g
Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g
Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.
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Derrick invested some money at 2.25% simple interest and $1000 less than twice this amount at 1.5%. His total income from the interest was $510. How much was invested at each rate?
Derrick invested $23,306.28 at 2.25% and $462.79 at 1.5%.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". For example, 50% means 50 out of 100 or 0.5 as a decimal.
Let's start by assigning variables to the unknown quantities in the problem. Let x be the amount Derrick invested at 2.25% and y be the amount he invested at 1.5%.
According to the problem, Derrick invested "1000 less than twice" the amount he invested at 2.25% at 1.5%. This means:
y = 2(0.0225x - 1000) = 0.045x - 2000
Now we can set up an equation based on the total income from the interest:
0.0225x + 0.015y = 510
Substituting the expression for y from the first equation, we get:
0.0225x + 0.015(0.045x - 2000) = 510
Simplifying and solving for x, we get:
0.0225x + 0.000675x - 30 = 510
0.023175x = 540
x = 23306.28
So Derrick invested approximately $23,306.28 at 2.25%. To find the amount he invested at 1.5%, we can substitute this value for x in the equation for y:
y = 0.045x - 2000 = 0.045(23306.28) - 2000 = 462.7856
So Derrick invested approximately $462.79 at 1.5%.
Therefore, Derrick invested $23,306.28 at 2.25% and $462.79 at 1.5%.
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The Revenue and Cost equations for a company are known to be polynomials of order 1 and 2 respectively. It is also known that the graphs of the two equations meet at points A(1,1) and B(5,9) while the third point of the cost function is C(2,0), obtain the following:
a) The Revenue equation and the cost equation
b) What do the common solutions to the two equations signify?
Answer: a) We know that the Revenue equation is a polynomial of order 1, so we can write it in the form:
R(x) = ax + b
where a and b are constants to be determined. We also know that R(1) = 1 and R(5) = 9, so we have two equations:
a(1) + b = 1
a(5) + b = 9
Solving these equations simultaneously, we get:
a = 2, b = -1
Therefore, the Revenue equation is:
R(x) = 2x - 1
Similarly, the Cost equation is a polynomial of order 2, so we can write it in the form:
C(x) = ax^2 + bx + c
where a, b, and c are constants to be determined. We know that C(1) = R(1) = 1 and C(5) = R(5) = 9, so we have two equations:
a(1)^2 + b(1) + c = 1
a(5)^2 + b(5) + c = 9
We also know that C(2) = 0, so we have a third equation:
a(2)^2 + b(2) + c = 0
Solving these equations simultaneously, we get:
a = 1, b = -4, c = 4
Therefore, the Cost equation is:
C(x) = x^2 - 4x + 4
b) The common solutions to the Revenue and Cost equations represent the production level(s) at which the company makes a profit, since the Revenue equation represents the amount of money the company earns and the Cost equation represents the amount of money the company spends. In other words, the common solutions are the values of x for which R(x) - C(x) > 0. At these production levels, the company's revenue is greater than its cost, resulting in a profit. At production levels where R(x) - C(x) < 0, the company is making a loss. At production levels where R(x) - C(x) = 0, the company is breaking even. Therefore, the common solutions to the two equations signify the production levels at which the company makes a profit or breaks even.
Step-by-step explanation:
please hep me with these 4 questions in math!!
for the first question, the simplest way I solve reflections is by making negatives positive and positives negative.
question 2:
pi is the irrational number as it does not end
question 3:
Slope is equal to -1/2 or -0.5
as it takes 2 units right to go down by 1 unit
Question 4:
C: $11
Dan is training for a bike race. He wants to bike 300 miles over the next couples of weeks. Dan biked 29 miles a day for 3 days. Then, he biked 32 miles a day for 4 days. How many more miles does he still have to bike to get to his goal of 300 miles?
A. Sara estimated that Dan would need to bike about 80 more miles to get to his goal of 300 miles. Is this a reasonable estimate? Why or why not?
B. Write an equation for this problem with a letter standing for the unknown quantity.
C. Solve the problem. Show your work.
Answer:
Step-by-step explanation:
a. Sara's estimate is reasonable because:
Dan has biked for 7 days so far, 29 miles for 3 days and 32 miles for 4 days.
If you round 29 and 32 up and down respectively to 30, then Dan will of have ridden about 30 * 7, or 120 miles so far. 300-120 is 80, so that is a good estimate.
b. If x stands for the miles Dan still needs to bike, then:
(29*3) + (32*4) + x = 300
c. 87 + 128 + x = 300
x = 85
Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
The volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.
What is area?Area is a measure of the size of a given space or the amount of a given surface. It can be measured in square feet, square meters, acres, hectares, and other units. Area can be used to describe the size of a two-dimensional shape or the surface area of a three-dimensional object. Area can also be used to calculate the amount of material needed to cover a given space, such as for a roof, carpet, or other covering.
To find the volume of the solid, we will use the following formula:
V=∫baπ(y2−(x−1)2)dx
Where b is the upper bound of the integral, a is the lower bound of the integral and y is the height of the solid.
Since the region R is the base of the solid, we can set a = 0 and b = 2, since this is the x-value at which the two functions intersect. Additionally, we can set y = ln(x) + 1 since this is the height of the solid.
Therefore, the volume of the solid is:
V = ∫02π(ln(x)2 + 12 − (x−1)2)dx
Calculating the integral, we get:
V = [π(xln(x)2 + x − 2xln(x) − x + 1)]02
Substituting the bounds of the integral, we get:
V = [π(22ln(2)2 + 2 − 4ln(2) − 2 + 1)] − [π(02ln(0)2 + 0 − 2ln(0) − 0 + 1)]
Simplifying the equation, we get:
V = π(ln(2)2 + 1 − 2ln(2))
Finally, substituting the value of ln(2) into the equation, we get:
V = 3.14159 (2.386294 + 1 − 4.772188) ≈ 7.58 thousandths
Therefore, the volume of the solid is 7.58 thousandths when rounded to the nearest thousandth.
In conclusion, the volume of the solid whose base is the region R and each cross section perpendicular to the a-axis is a semicircle is 7.58 thousandths when rounded to the nearest thousandth. This was calculated by integrating the equation V=∫baπ(y2−(x−1)2)dx with the bounds of integration a=0 and b=2 and the height of the solid y=ln(x)+1.
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F(x)=x 2 what is f(2)
we input the value 2 into the function, it will output the value 4.
What is Function?Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively. Initially, functions represented the idealized relationship between two variable quantities.
The function F(x) = x^2 represents a quadratic function, where the input value (x) is squared to produce the output value (F(x)).
To find the value of F(2), we simply need to substitute 2 in place of x in the equation:
F(2) = (2)^2 = 4
This means that when we input the value 2 into the function, it will output the value 4.
In other words, F(2) represents the value of the quadratic function at the point where x is equal to 2.
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Complete question:
If F(x)=x^2 then what is f(2).
A(-4,4) B(2,7) C(2,1) where is the orthocenter
Answer:
Step-by-step explanation:
(1\2, 4) = (0.5, 4)
11 Sabina travels from London to Telford.
A ticket from London to Telford normally costs £65.25
Sabina gets off the cost of the ticket.
Amir travels by train from London to Coventry and then from Coventry to Telford.
The ticket from London to Coventry costs £23.75
The ticket from Coventry to Telford costs £14.95
Work out the difference between the cost of Sabina's journey and the cost of
Amir's journey.
"I have to say a lot of people have been asking this question. No, really. A lot of people come up to me and they ask me. They say, 'What's 2+2?' And I tell them look, we know what 2+2 is. We've had almost eight years of the worst kind of math you can imagine. Oh my god, I can't believe it. Addition and subtraction of the 1s the 2s and the 3s. Its terrible. Its just terrible. Look, if you want to know what 2+2 is, do you want to know what 2+2 is? I'll tell you. First of all the number 2, by the way I love the number 2. It's probably my favorite number, no it is my favorite number. You know what, it's probably more like the number two but with a lot of zeros behind it. A lot. If I'm being honest, I mean, if I'm being honest. I like a lot of zeros. Except for Marco Rubio, now he's a zero that I don't like. Though, I probably shouldn't say that. He's a nice guy but he's like, '10101000101', on and on, like that. He's like a computer! You know what I mean? He's like a computer. I don't know. I mean, you know. So, we have all these numbers and we can add them and subtract them and add them. TIMES them even. Did you know that? We can times them OR divide them, they don't tell you that, and I'll tell you, no one is better at the order of operations than me. You wouldn't believe it. That I can tell you. So, we're gonna be the best on 2+2, believe me. OK? Alright. Thank you." Reporter 1: "But what actually is 2+2?" Trump: "Siddown. No, siddown. I've already answered your question. Haven't I already answered your question. This is what we get from news reporters, folks. Give me a nice question. Yes - you." Reporter 2: "Is your name Donald Trump?" Trump: "Now that's a nice question, folks. That's what I want."
The difference between the cost of Sabina's journey and the cost of Amir's journey is -£38.70.
We have,
The cost of Sabina's journey is £65.25.
Since she gets off the cost of the ticket, her journey is free, so the cost is £0.
Amir's journey consists of two segments:
London to Coventry and Coventry to Telford.
The cost of the London to Coventry ticket is £23.75, and the cost of the Coventry to Telford ticket is £14.95.
Difference = Sabina's Journey Cost - Amir's Journey Cost
Difference = £0 - (£23.75 + £14.95)
Difference = £0 - £38.70
Difference = -£38.70
This means that Amir's journey is £38.70 more expensive than Sabina's journey.
Therefore,
The difference between the cost of Sabina's journey and the cost of Amir's journey is -£38.70.
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100 Points!!! Algebra graphing question. Describe the reflection in the function as it relates to the parent graph. Then graph the function. Y=-|x| Photo attached. Thank you!!
The graph of the function y = -|x| is the graph of the function y = |x| reflected across the x-axis
How to describe the graph of the function y = |x|The function given in the question is
y = -|x|
The above function is an absolute value function graph
And the parent function of an absolute graph is
y = |x|
When y = |x| and y = -|x| compared, we have the transformation to be
A reflection across the x-axis
This means that the graph of y = |x| is reflected across the x-axis to create y = -|x|
See attachment for the graph of the function
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please help me find the area
The calculated area of the composite figure is 129 square units
Calculating the area of the composite figureGiven that we have
A composite figure
To find the area of a composite figure, you can break it down into smaller, simpler shapes whose areas you can calculate. Then you can add up the areas of these shapes to get the total area of the composite figure.
The area is then calculated as
Area = Trapezoid + Rectangle + Parallelogram + Triangle
Using the dimensions from the graph, we have
Area = 1/2 * (12 + 6) * 4 + 6 * 10 + 3 * 7 + 1/2 * 6 * 4
Evaluate
Area = 129
Hence, the area is 129 square units
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All of these are valid ways to earn money in Microworkers, except
All of the given options are valid ways to earn money in Microworkers, except for submitting a review for a service you have not used. The correct option is "Submitting a review for a service you have not used."
Testing an app, translating a document, and data mining for a gardening company are all tasks that can be completed for compensation through the Microworkers platform.
However, submitting a review for a service you have not used is considered fraudulent and goes against the principles of the Microworkers community. It is important to maintain ethical practices when completing tasks for compensation in order to preserve the integrity of the platform. Therefore, "Submitting a review for a service you have not used." option is correct.
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The probable question may be:
All of these are valid ways to earn money in Microworkers, except
Testing an app
Submitting a review for a service you have not used
Translating a document
Data Mining for a gardening company
100 POINTSS PLEASEEEE HELP BRAINLIEST
The missing component in this equation is an alpha particle (He), which has a mass number of 4 and an atomic number of 2. Therefore, the balanced nuclear equation for this alpha decay would be:
^45/20Ca -> ^45/21Sc + ^4/2He
Answer: ^45/20Ca -> ^45/21Sc + ^4/2He
You deposit $3400 in an account with an annual interest of 3.3% for 10 years.
The amount of money you'll have at the end of 10 years is $
(Type an integer or a decimal.)
Answer: 3.3= .033 percentage. .033 times 34000=1112 times (t) time (10 years) equals 11120
Step-by-step explanation:
14 yd
21 yd find the area of the triangle
Answer:
147
Step-by-step explanation:
A= h^b b=21*14= 147
You roll a number cube labeled 1 through 6, one time.What is the probability that you roll a number that is less than 5?
HURRY!
Answer:
66.67%
Step-by-step explanation:
To find the probability, divide 4 by 6, since there are 4 numbers less than 5, out of 6 in total.
4/6
= 0.6667
So, the probability is approximately 66.67%
help pls, i am struggling
The correct graph would be the one with a normal distribution curve centered at 0, with two tails shaded on either side, representing the lowest and highest 4% of scores So option C is correct.
What is standard normal distribution ?
The standard normal distribution is a special case of the normal distribution in which the mean is 0 and the standard deviation is 1. It is also known as the "Z-distribution" because the scores are expressed in terms of their z-scores, which are the number of standard deviations above or below the mean.
The standard normal distribution is a bell-shaped curve that is symmetric around the mean of 0. It is used in statistics as a reference distribution for calculating probabilities and making statistical inferences.
To convert a normal distribution with a given mean and standard deviation to a standard normal distribution, we use the formula:
z = (x - μ) / σ
According to the question:
To find the bone density test scores that can be used as cutoff values separating the lowest 4% and highest 4%, we need to find the z-scores that correspond to the 4th and 96th percentiles of the standard normal distribution.
Using a standard normal table, we find that the z-score corresponding to the 4th percentile is approximately -1.75, and the z-score corresponding to the 96th percentile is approximately 1.75.
Therefore, the bone density test scores that can be used as cutoff values separating the lowest 4% and highest 4% are approximately -1.75 and 1.75, respectively.
To sketch the region containing the lowest 4% and highest 4%, we need to shade the area under the normal curve to the left of -1.75 and to the right of 1.75.
The shaded regions represent the lowest 4% and highest 4% of bone density test scores, respectively. The correct graph would be the one with a normal distribution curve centered at 0, with two tails shaded on either side, representing the lowest and highest 4% of scores.
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I need help due tomorrow so please help I’ve been trying for a while so can I get some help?
Answer:
It will be same as angle x because they are on the same line and are alternative angles
So, measurement of angle u will be u=152
Step-by-step explanation:
Hope this helps:)
Good luck
what should target charge for a package of paper plates if they want to make a 75% profit on the plates that originally cost $9.00
Answer:
$15.75
Step-by-step explanation:
the area of a rectangle is 14 square units. it has the side length of x and y. given each value for x, find y.
1. x = 4 and 1/5
2. x = 2 and 1/3
3. x = 7/6
Answer:
1. y = 3 1/3
2. y = 6
3. y = 12
Step-by-step explanation:
A = xy => xy = 14 => y = 14/x
1. x = 4 1/5 = 21/5
y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3
2. x = 2 1/3 = 7/3
y = 14/x = 14/(7/3) = (3 x 14)/7 = 6
3. x = 7/6
y = 14/x = 14/(7/6) = (6 x 14)/7 = 12
what led to the development of the aviation industry
a. the development of texas’ wwII aircraft training facilities
b. the placement of the johnson space center
c. the petrochemicals industry
d. texas’ location and climate
Texas' location and climate led to the development of the aviation industry.
What is the significance of Texas in the development of the aviation industry?
The development of the aviation industry in Texas can be attributed to its favorable geographical location and climate. Texas is located in the southern part of the United States, making it a strategic location for air travel between the east and west coasts of the country. Additionally, its warm and dry climate provided ideal conditions for flight testing and training.
Reason what led to the development of the aviation industry :
Texas has a long history of aviation, with the Wright brothers conducting one of their earliest flight demonstrations in the state in 1910. The establishment of military bases during World War II and the subsequent development of aircraft training facilities in Texas further fueled the growth of the aviation industry in the state. Additionally, the placement of the Johnson Space Center in Houston helped to establish Texas as a hub for aerospace research and development. However, it is Texas' favorable location and climate that truly made it a prime location for the aviation industry. Its central location made it a strategic location for air travel and logistics, while its warm and dry climate provided ideal conditions for flight testing and training. Today, Texas remains one of the top states for aviation and aerospace industries, with major airports, aircraft manufacturers, and research institutions located throughout the state.
Therefore, option (d) is correct.
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Are the fractions 2/2 and 8/8 equivalent fractions
Answer:
Step-by-step explanation:
yes since they are both divisible by their denominators and equal the same thing
Answer:
yes, they are equivalent
Step-by-step explanation:
2/2 = (2/2)x(4/4) = 8/8 = 1
Given f(x)=5-3x, if f(x)=-19, find x.
Need help will give brainliest and 5 star rating!
The polynomial function f(x) which produced the graph shown is f(x) = -6(x - 1/2)²(x + 1)²(x - 2).
What is a polynomial graph?In Mathematics and Geometry, a polynomial graph touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.
By critically observing the graph of the polynomial function shown above, we can logically deduce that its x-intercepts include the following;
x = -1 ⇒ x + 1 = 0.
x = 2 ⇒ x - 2 = 0.
Also, the graph has a zero of multiplicity 2 at x = 1/2;
x = 1/2 ⇒ x - 1/2 = 0.
(x - 1/2)²
In this context, an equation that represent the polynomial function is given by:
f(x) = a(x - 1/2)²(x + 1)²(x - 2)
By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, 3), we have;
3 = a(0 - 1/2)²(0 + 1)²(0 - 2)
3 = a(1/4)(-2)
3 = -a/2
a = -6.
Therefore, the required polynomial function is given by:
f(x) = -6(x - 1/2)²(x + 1)²(x - 2)
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