400 square feet of carpet area for $240 is the best deal among the given option.
What is Area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
Detailed explanation:The carpets were sold for the following prices:
1) $67 for 100 square feet.
2) $130 for 200 square feet.
3) $240 for 400 square feet
4) $504 for 800 square feet.
Calculation:
For each of them, we would calculate the unit cost per square foot. It develops
1) The price per square foot is 67÷100 = $0.67
2) The price per square foot is 130÷200 = $0.65.
3) The price per square foot is 240÷400 = $0.6.
4) The price per square foot is 504÷800 = $0.63.
Comparing the unit costs per square foot the best deal costs $0.6 per square foot per unit, which is 400 square feet of carpet for $240.
400 square feet of carpet area for $240 is the best deal among the given option.
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you invested $20680 part of it in a stock that paid 12% annual interest. However the rest of the money suffered a 5% loss. if the total annual income from both investments was $2026 how much was invested at each rate?
Select all the equations that have g=5 as the solution.
Select all that apply.
A. g-1=4
B. 34+g=50
C. g-1=15
D. g+5=15
A
5-1=4
34+5=39
5-1=4
5+5=10
Answer:
[tex]A)g-1=4\\g=4+1\\g=5[/tex]
Step-by-step explanation:
[tex]A)g-1=4\\g=4+1\\g=5\\\\B)34+g=50\\g=50-34\\g=16\\\\C)g-1=15\\g=15+1\\g=16\\\\\\D)g+5=15\\g=15-5\\g=10\\So the only Option remaining is A) which the correct answer[/tex]
13. A contractor is building a new subdivision. A rectangular piece of land for a new
house and yard is 60 feet wide. The length of the land is longer than the width by a
distance of n feet. Which equation represents the area of the land?
Answer:
Area = (60 + n) * 60 = 3600 + 60n
Step-by-step explanation:
The length of the land is 60 + n feet. The area of the land is the product of the length and width, so the equation representing the area of the land is:
Area = (60 + n) * 60 = 3600 + 60n
This equation represents the area of the land in square feet.
Rosemary works two part-time jobs while attending college. During the day she works at the college bookstore and earns $8.25 per hour. In the evening she delivers pizza for Papa Gino's, earning $9.25 per hour. If Rosemary earned $247 last week from working a total of 28 hours, find how many hours she worked at Papa Gino's last week.
Answer: 16 hours
Step-by-step explanation:
We will write a system of equations to help us solve. Let x be equal to the number of hours worked at the college bookstore, and y be equal to the number of hours worked at Papa Gino's.
First, we will write an equation for the money earned. Then, we will write one for the hours worked.
8.25x + 9.25y = 247
x + y = 28
Now, we will will substitute the second equation into the first and solve for the hours worked at Papa Gino's last week, equal to y.
x + y = 28 ➜ x = -y + 28
8.25x + 9.25y = 247
8.25(-y + 28) + 9.25y = 247
-8.25y + 231 + 9.25y = 247
y + 231 = 247
y = 16
Rosemary worked 16 hours at Papa Gino's last week.
The cost of a new home is $90,000 and the bank requires a 8.8% down payment.
What is the amount that will need to be borrowed from the bank after the down payment is paid?
The mortgage amount will be____.
To find the amount of the down payment, we need to multiply the cost of the home by the down payment percentage: $90,000 * 8.8% = $7,920.
This means that the total amount that will need to be borrowed from the bank is $90,000 - $7,920 = $82,080.
The mortgage amount will be $82,080. This is the amount that will need to be borrowed from the bank after the down payment of $7,920 is paid. The down payment is calculated by multiplying the cost of the home by the required down payment percentage: $90,000 * 8.8% = $7,920. The mortgage amount is then calculated by subtracting the down payment from the cost of the home: $90,000 - $7,920 = $82,080.
Stock Market Worksheet 1
You need to show your work in order to receive full credit.
Business Organization
1. James invests $10,000 in a partnership with 3 other people. One of those people also invested
$10,000 and the other two invested $90,000 each. What percent of the business does James
own?
James owns on owns only 5 percent of the business capital.
How to calculate percentage?We should know that percentage deals with number of ratios as a fraction of 100
James = $10,000
One partner = $10,000
Other two partners = ($90,000+90,000)=$180,000
Total capital invested = $)10000+10000+90000+90000)
Total investment = $200,000
James proportion= [tex]\frac{10,000}{200,000} *\frac{100}{1}[/tex]
Simplifying this to have James percentage of investment as 5 percent
James =5%
In conclusion James has only 5% of the business investment
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Suppose that the length of a confidence interval is 0.06 when the sample size is 400. Determine how the sample size must change to decrease the length of the confidence interval to 0.03 (Use decimal notation. Give your answer as a whole number:) new sample size:
We use Z-Distribution for large sample sizes, The reduced sample size is 200.
What do you mean by probability distribution?A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.
What do you mean by Z-distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
confidence interval = 0.06
Sample size= 400
new interval of confidence = 0.03
new sample size = 400/0.06 * 0.03
=200
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Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Question 8 options:
Tim is building a brick wall that will be 4 feet
high and 57 feet long. It takes 7 bricks to build
1 square foot of wall.
(Area = length x width)
The approximate number of bricks he will use for the entire building is; 1596 bricks
How to find the area of the building?We are given that;
- Tim is building a brick wall that will be 4 feet high and 57 feet long.
- It takes 7 bricks to build 1 square foot of the wall.
The area of the building is gotten by applying the area of a rectangle which is;
Area of building = Length * Width
Thus;
Area = 4 * 57
Area = 228 square foot
Now, we are told that it takes 7 bricks to build one square foot of wall. Thus;
Number of bricks required here is;
N = 228 * 7
N = 1596 bricks
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The complete question is;
Tim is building a brick wall that will be 4 feet
high and 57 feet long. It takes 7 brick to build 1 square foot of wall
(Area = Length x Width)
Approximately how many bricks will he use for the entire building?
Why is authoritarianism a coexistence problem?
It can be said that authoritarianism has been a coexistence problem because it is based on domination and violates many norms and rights.
¿How does authoritarianism impact coexistence?Without a doubt, authoritarianism has a negative impact on coexistence, because it focuses on many behaviors and thoughts that go against many values and good principles.
Let's keep in mind that authoritarianism is a type of behavior where an individual places his will above others, this undoubtedly generates a conflict in coexistence.
¡Hope this helped!
Authoritarianism is a form of government characterized by strong central power and limited political freedoms.
It is a coexistence problem because it often leads to the suppression of individual rights, freedoms, and diversity of opinion.
In an authoritarian regime, the government exercises strict control over all aspects of society, including the media, education, and civil society organizations.
This can result in the suppression of dissenting voices and the persecution of those who express views that are critical of the government.
Find all relative extrema in the function h(x)=cos((2π/3)x) on the interval [0, 2]
Find all ABSOLUTE extrema in the function h(x)=cos((2π/3)x) on the interval [0, 2]
HELP!!!
a) The relative extrema of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:
Local minimum: (1.5, -1).Local maximum: (0,1).b) The absolute extremas of the function h(x)=cos((2π/3)x) on the interval [0, 2] are given as follows:
Minimum: (1.5, -1).Maximum: (0,1).What are relative extrema and absolute extrema?Relative extrema are all the turning points on the graph of a function, which are the points in which the derivative of the function is zero, hence the function behavior's may change from increasing to decreasing or vice versa.
From the graph given by the image at the end of the answer, the extremas of the function are given as follows:
Local maximum: (0,1), as the function changes from increasing to decreasing.Local minimum: (1.5, -1), as the function changes from decreasing to increasing.These are also the absolute extremas, as there are only one minimum extrema and one maximum.
If there were multiple extremas, we would have that:
The absolute minimum is the local minimum with the lowest value of y.The absolute maximum is the local maximum with the highest value of y.More can be learned about relative and absolute extrema at https://brainly.com/question/13602432
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Algebra HELP PLS
The ceiling of Victoria's living room is a square that is 15√2 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Victoria can buy rolls that each contain 30 ft of crepe paper. what is the minimum number of rolls she should buy?
pls show your work
Answer:
Minimum 5 rolls---------------------------------------
Total length we need is the sum of the perimeter and two diagonals of the square.
Perimeter:
P = 4s P = 4(15√2) = 60√2 ≈ 85 ft (rounded up to the whole number)Diagonals:
2d = 2s√2 = 2(15√2)(√2) = 30*2 = 60 ftTotal length:
85 + 60 = 145 ftNumber of rolls:
145/30 ≈ 5 (rounded up to the whole number)If angle EBC is congruent to angle ECB, then ? is congruent to ?
By using the property of angle, it can be calculated that [tex]\angle EBA \cong \angle ECD[/tex]
What are angles?
Angles are a way of measuring the amount of turn between two lines or three or more planes. An angle is formed when two lines intersect or when two planes meet. It is measured in degrees, with a full circle being 360 degrees. The angle is measured in terms of the amount of turn between the two lines or planes. Angles are typically used to describe the orientation of objects in space, such as the corners of a triangle, the angle of a flight path, or the angle of the sun’s rays. Angles are also used to measure the size of an angle and the distance between two points. Angles are important in mathematics because they help to analyze the size and shape of objects, and also to help solve problems.
Here,
It is given that
[tex]\angle EBC \cong \angle ECB[/tex]
Now,
[tex]180-\angle EBC \cong 180-\angle ECB[/tex] [Angle on a straight line]
[tex]\angle EBA \cong \angle ECD[/tex]
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Eileen takes a student loan of 10,000 with simple interest to pay back after 10 years. If the estimated payment is 22,000, what is the interest rate on this loan?
The interest rate on this loan will be 5%.
How to calculate the interest?Given that Eileen takes a student loan of 10,000 with simple interest to pay back after 10 years. If the estimated payment is 22,000.
The interest on the loan will be:
= $22000 - $11000
= $11000
The interest rate on this loan will be:
Rate = Interest / Principal × Time
Rate = 11000 / (22000 × 10)
Rate = 11000 / 220000
Rate = 5%
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Regional Rent-A-Car is interested in studying how weight of a vehicle is related to the fuel efficiency for
several of its rental vehicles.
A random sample of 13 vehicles from Regional Rent-A-Car yielded the data in the table.
Weight (in pounds)
2000
3123
3775
2287
4000
2485
2114
2433
2525
2889
3186
3258
3622
Fuel Efficiency (in miles per gallon)
32.7
22.8
18.6
26.1
18.4
26.2
33.1
28.3
26.2
22.5
20.9
21.3
18.1
Answer:
Step-by-step explanation:
SolutionFinal answers are given below.
Back-up Theory and Details of calculations follow at the end.
Part (a)
Estimate of the slope for the least-squares regression line = - 0.0073 Answer 1
InterpretationFor every increase of 1 pound in car’s weight, the fuel efficiency would reduce by 0.0073 mpg. Answer 2
Part (b)
Correlation coefficient, r = - 0.9438 Answer 3
Interpretation An r-value of - 0.9438 indicates that there is a strong inverse linear relation between car’s weight and fuel efficiency.
Negative sign implies that as car’s weight increases, the fuel efficiency would come down.Answer 4
Part (c) The estimated regression equation is: Fuel efficiency = 45.4705 – 0.0073 x car’s weight. Substituting car’s weight = 2684 in the above equation, the estimated fuel efficiency = 25.83.So, residual = 24.5 – 25.84 = - 1.23.
Thus, Residual for a car weighing 2684 pounds and having an average fuel efficiency of 24.5 mpg= - 1.23 Answer 5
Part (d)
Substituting fuel efficiency = 20.2 in the above regression equation, the estimated car’s weight = 3461Estimate of the weight of a car whose fuel efficiency is 20.2 mpg = 3461 pounds Answer 6
Solve each equation by completing the square:
0.1²-0.6x+0.9=0
2x²-12x+18=0
Answer:
-3
3
Step-by-step explanation:
0.1x^2-0.6x+0.9=0
(1/10)(x^2+6x+9)=0
(1/10)(x+3)^2=0
x=-3
2x^2-12x+18=0
2(x^2-6x+9)=0
2(x-3)^2=0
x=3
The solution of the equation 0.1x²-0.6x+0.9=0 is -3 and 2x²-12x+18=0 is 3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given the system of equation as;
0.1x²-0.6x+0.9=0
2x²-12x+18=0
Solving by completing the square:
0.1x²-0.6x+0.9=0
(1/10)(x²+6x+9)=0
(1/10)(x+3)²=0
x=-3
2x²-12x+18=0
2(x²-6x+9)=0
2(x-3)²=0
x=3
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what part of 72 is 36a
Answer: 2
Step-by-step explanation: hope it helps
the number that comes up when a die, loaded so that one comes up twice as often as each of the other five sides, is rolled
When a die is loaded so that the probability of one side appears twice as often as the other five, the number "1" will be the most frequent result when the die is rolled.
When a die is loaded so that one side appears twice as often as the other five, the number that comes up most often when the die is rolled is "1". This is because the loaded die has an unequal probability of rolling each number, with one side being twice as likely to come up as any of the other five sides. This means that the chances of rolling this particular number are twice as great as the chances of rolling any of the other five numbers. For this reason, the number "1" will be the most frequent result when the die is rolled.The probability of rolling the number "1" is 2/7, while the probability of rolling any of the other five numbers is 1/7. Therefore, the number "1" is twice as likely to come up as any of the other five numbers when the die is rolled.
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This table represents a linear function?
X o 5
Y5 15
The greater unit of the two
The greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
From the given table, (0, 5) and (5, 15)
Here, slope(m)=(y2-y1)/(x2-x1) =(15-5)/(5-0)
= 10/5
= 2
Substitute m=2, (x, y)=(0, 5) in y=mx+c, we get
5=2(0)+c
c=5
Substitute m=2, c=5 in y=mx+c, we get
y=2x+5 --------(I)
From the graph, (-4, 0) and (0, 6)
Here, slope(m)=(6-0)/(0+4)
= 3/2
= 1.5
Substitute m=1.5, (x, y)=(0, 6) in y=mx+c, we get
6=1.5(0)+c
c=6
Substitute m=1.5, c=6 in y=mx+c, we get
y=1.5x+6 --------(II)
Therefore, the greater unit rate of the two functions is 2. The greater y-intercept of two functions is 6.
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Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year. The employee was just promoted and received a 15% raise. What is the new yearly salary
The new yearly salary will be $31,694.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
Given that;
Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.
And, The employee was just promoted and received a 15% raise.
Now,
Since, Employee c is paid an hourly rate of 13.25 per hour and works 2,080 hours per year.
And, The employee was just promoted and received a 15% raise.
Hence, The salary for 13.25 hours = 13.25 × 2080
= $27,560
And, The employee was just promoted and received a 15% raise.
Hence, The new salary = $27,560 + 15% of 27,560
= 27,560 + 4134
= $31,694
Thus, The new salary = $31,694
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When graphing the line y = x - 1. how do you
move from one point to another on the line?
A. 2 units up. 1 unit to the right
B. 2 units up. 1 unit to the left
C. 1 unit down. 2 units to the right
D. 1 unit up. 2 units to the right
Answer: C. 1 unit down. 2 units to the right
Step-by-step explanation:
Kayla saves $110 to purchase a new outfit. She decides to buy a skirt for $29.65, a sweater for $38.32, and a purse for $31.00.
Question 1
Which choice is the total amount for the 3 items?
Responses
A $87.43$87.43
B $92.41$92.41
C $98.97$98.97
D $107.12$107.12
Question 2
Which amount of money will Kayla have left after the purchase?
Responses
A $11.03$11.03
B $9.74$9.74
C $6.92$6.92
D $7.15
The choice that is the total amount for the 3 items is C. $98.97.
The amount of money that Kayla have left after the purchase is A. $11.03.
How to calculate the amount?From the information, Kayla saves $110 to purchase a new outfit. She decides to buy a skirt for $29.65, a sweater for $38.32, and a purse for $31.00.
The cost of the items will be:
= Skirt + Sweater + Purse
= $29.65 - $38.32 + $31.00
= $98.97
The amount of money that Kayla have left after the purchase is:
= $110 - $98.97
= $11.03
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Answer:
c and a
Step-by-step explanation:
Player First
Round Final
Round
Golfer 11 72 72
Golfer 12 72 70
Golfer 13 70 73
Golfer 14 70 77
Golfer 15 68 70
Golfer 16 68 66
Golfer 17 71 70
Golfer 18 70 68
Golfer 19 69 68
Golfer 20 67 71
Suppose you would like to determine if the mean score for the first round of a golf tournament event is significantly different than the mean score for the fourth and final round. Does the pressure of playing in the final round cause scores to go up? Or does the increased player concentration cause scores to come down?
(a) Use α = 0.10 to test for a statistically significantly difference between the population means for first- and fourth-round scores. State the null and alternative hypotheses. (Use μd = mean score first round − mean score fourth round.
Calculate the value of the test statistic. (Round your answer to three decimal places.)
Calculate the p-value. (Round your answer to four decimal places.)
p-value =
(b) What is the point estimate of the difference between the two population means? (Use mean score first round − mean score fourth round.)
The difference between the two population means is estimated at -1.05.
What is meant by Null Hypothesis?Null Hypothesis: The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.
The information presented here represents the golfers' first and final round scores.
a. α= 0.10 is the significance level.
The following hypothesis test can be created:
Hypothesis of nullity H₀ μₐ= 0
This suggests that the population means of the first round and final round are identical.
Alternative formulation: Hₐ μₐ≠0
This suggests that the population means of the first round and final round are different.
The test statistic is now:
t=(d-meanₐ)[tex]\sqrt{n}[/tex]/sₐ
Excel can be used to determine the test statistic.
This will result in: 0.10<P<0.20.
b. The 90% confidence level is the primary margin of error. This indicates that there is no discernible difference, and the result is -1.05.
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Triangle Congruence: Question 1
In the accompanying proof, what is reason (5)?
Given: A B║DC
AB=DC
Prove: m ∠DAC= m ∠BCA
Select one:
SSS
SAS
SSA
ASA
In the accompanying proof, the reason (5) is SAS theorem.
In the given question,
Given: AB || DC
AB=DC
Prove: m∠DAC = m∠BCA
The statement used to prove this conditions are:
Statement Reason
AB || DC (1) Using the Quadrilateral Rule
AB=DC (2) Opposite sides are equal
m∠BAC = m∠DCA (3) Alternate interior angles Theorem
AC=AC (4) Common Side
∆ADC≅∆CBA (5) SAS Theorem
m∠DAC = m∠BCA (6) Alternate interior angles Theorem
We have to explain in the accompanying proof, what is reason (5).
So, in the accompanying proof, the reason (5) is SAS theorem.
In the proving we first prove one side equal, then angle equal and at last again one side equal.
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In how may ways can the letters of the word 'SEMESTER' be arranged such that at least two vowels are together. Show ALL your work step by step to get credit. Final answers MUST be provided in decimal form
In 720 ways the letters of the word 'SEMESTER' be arranged such that at least two vowels are together.
Arrangement in probability
A number of topics like statistics and probability are closely interrelated to the topic of permutation and combination. Permutation and combination is about making arrangements and making selections on the basic of certain formulas.Given that:
In SEMESTER there are 8 letters.
Which include 3 vowels (E) and 5 consonants (S, M, T , R )
Take 3 vowels as one letter, we have 6 letters
arranged in 6[tex]p_{6}[/tex] = 6! ways E can be taken together in 1! ways
Number of words = 6! × 1!
= 6 × 5 × 4 × 3 × 2 × 1
= 720 ways
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Consider the equation a + b = c − d/2 when solved for each variable. Choose all that are correct.
A. d = 2a + 2b - 2c
B. b = 1/2(-2a + c - d)
C. c = a + b + d/2
D. a = 1/2(-2b + 2c - d)
The equations that are correct are a = 1/2(-2b + 2c -d) and c = a + b + d/2. The correct options are C. c = a + b + d/2 and D. a = 1/2(-2b + 2c -d)
Solving equationFrom the question, we are to solve the equation for each variable
The given equation is
a + b = c - d/2
Solving for a
a + b = c - d/2
a = -b + c -d/2
Multiply through by 2
2a = -2b + 2c -d
By multiplying both sides by 1/2, this can be written as
a = 1/2(-2b + 2c -d)
Solving for b
a + b = c - d/2
b = -a + c - d/2
Multiply through by 2
2b = -2a + 2c - d
By multiplying both sides by 1/2, this can be written as
b = 1/2(-2a + 2c - d)
Solving for c
a + b = c - d/2
a + b + d/2 = c
Therefore,
c = a + b + d/2
Solving for d
a + b = c - d/2
Multiply through by 2
2a + 2b = 2c - d
d = 2c - 2a - 2b
d = -2a - 2b + 2c
Hence, a = 1/2(-2b + 2c -d) and c = a + b + d/2 are correct
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592x43 using standard algorithm showing answers
Answer:
25,456
Step-by-step explanation:
592 2 x 3 = 6 9 x 3 = 27 (You put the 7 in the tens place)
x 43 (And add 2 to the hundreds after multiplication)
______ 5 x 3 = 15 15 + 2= 17 (So you add 1 to the thousand place)
1776 Which would be 1776
2368
Now we do the same thing but with 4 this time, and we wont use the ones place because were putting the numbers in the tens place to start with since it's 40 2 x 4 = 8 (Goes in tens place)
9 x 4 = 36 (6 goes in hundreds place and 3 to thousands place)
5 x 4 = 20 (So 2 goes into the ten thousands place, and 3 to thousands place)
So it would be 2368
Write a quadratic function with the given zero. 3 + i
Answer:
[tex]x^2 - 6x + 10[/tex] or in general: [tex]a(x^2 - 6x + 10)[/tex] where "a" is any constant real number except zero.
Step-by-step explanation:
Complex Conjugate Root Theorem:If we're given a complex root of a polynomial to be: [tex](a+bi)\text{ or }(a-bi)[/tex], then we know that its conjugate is also a root of the polynomial: [tex](a-bi)\text{ or }(a+bi)[/tex].
So since we're given the root: [tex](3+i)[/tex], then we know that its conjugate: [tex](3-i)[/tex] is also a root. Thus we have two roots so far.
Fundamental Theorem of Algebra:The Fundamental Theorem of Algebra simply states that any polynomial, with degree "n", will have "n" roots, which can consist of both real and imaginary solutions.
So let's say I have a polynomial: [tex]x^6+3x+2=0[/tex], this has 6 roots, according to the Fundamental Theorem of Algebra, since the degree of the polynomial is 6 (remember the degree is simply the variable with the highest degree)
Since we already have two roots, and a quadratic function has a degree of two, we know that these are all the roots the quadratic has, since the Fundamental Theorem of Algebra states that a quadratic will only have 2 roots.
Factored Form:We can generally express any polynomial in factored form, that is: [tex]a(x-b)(x-c)(x-d)...=y[/tex]
where "b", "c", and "d", and so on... are zeros of the function. This aligns with the behavior of zeros, since if we plug any of them into the function, then one of the factors will become zero, and since zero times anything is zero, well the entire thing is zero.
For example if I plug in "b", which is zero we get: [tex]a(b-b)(b-c)(b-d)...=y\implies a(0)(b-c)(b-d)=y\implies 0=y[/tex]
this is since plugging in zero, makes the factor: [tex]x-b[/tex] equal to zero, making the entire thing zero.
One last thing to mention is the "a" value in front which just generally determines the stretch/compression of the polynomial.
So with this information, we can write a polynomial:
[tex]a(x-(3+i))(x-(3-i))[/tex]
From here let's distribute the negative sign:
[tex]a(x-3-i)(x-3+i)[/tex]
Now this may look a bit tough to distribute, but you may notice a pattern here, we have a difference of squares. It may not be obvious, but if we make one substitution, let's say: [tex]u=x-3[/tex], then we get the equation
[tex]a(u-i)(u+i)[/tex]
The difference of squares is expressed as: [tex]a^2 - b^2 = (a-b)(a+b)[/tex], so our expression will expand out into:
[tex]a(u^2 - i^2)[/tex]
The substitution was just to make things a bit more clear, but let's just substitute x-3 back into the equation.
[tex]a((x-3)^2 - i^2)[/tex]
From here, we know that i^2 is simply -1, since: [tex]\sqrt{-1} = i, \text{ so }i^2 = -1[/tex]
We can also easily expand out the polynomial using FOIL
[tex]a((x^2 - 6x + 9) -(-1))\\a(x^2 - 6x + 9 + 1)\\a(x^2 - 6x + 10)[/tex]
You may notice the "a value, and that's just a constant, which determines the stretch/compression of the polynomial, and can be any real number, except for zero since that will make the entire thing zero regardless of what x is. For the sake of simplicity, let's just write this to be 1.
The quotient of 5 and a number, k ? Write the algebraic expression
Answer: [tex]\frac{5}{k}[/tex]
Step-by-step explanation:
To write an algebraic expression that represents this situation, we need to know that a quotient will involve division.
We will write the quotient of 5 and a number, k. also written as 5 divided by k, as;
[tex]\displaystyle \frac{5}{k}[/tex]
You can read more about writing algebraic expressions involving division here: https://brainly.com/question/17552845
The algebraic expression is - [tex]\frac{5}{k}[/tex]
If one number is divided by another number, the answer obtained is called the quotient.
In mathematics, a number that divides another number is called a divisor.
The number which is to be divided by the divisor is called a dividend.
In arithmetic, if we divide one integer by another, the 'leftover' portion is called the remainder.
In this case, 5 is the dividend, and k is the divisor, which is representing an unknown number.
We can not get an actual number, but we can use an algebraic equation to express the quotient as follows:
The quotient of 5 and k = [tex]\frac{5}{k}[/tex]
The algebraic expression is - [tex]\frac{5}{k}[/tex]
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select each of the equations that represent a line segment between the points (1,5) and (3,13). a. x
On solving the provided question the equation of line segment is [tex]3y = x+11 OR y = 1/3x + 11/3[/tex]
What is equation?An equation in algebra is a condition on a variable. Only for a certain value of the variable does it satisfy. This indicates that the equation 2x - 5 = 13 can only be met when x = 9. Polynomial equations and linear equations are two significant kinds of equations that are taken into account in algebra. One-variable polynomial equations can be expressed as P(x) = 0, where P is a polynomial and ax + b = 0 is the standard form for linear equations. Here, the variables a and b are used.
Let y=m x + c be the slope intercept form of the equation.
Here, the slope m and the y-intercept c are unknown.
What is known is that this goes through (x 1, y 1) and (x 2, y 2), two coordinate pairs.
Consequently, we have three equations.
[tex]y=mx+c.........1\\ y1=mx1+c....2\\ y2=mx2+c ......3[/tex]
now let's delete m and c using these.
subtracting (2) from (1), we get [tex](y-y1)=m(x-x1) ......(4)[/tex]
and subtracting (2) from (3), we get[tex](y-2-y1)=m(x2-x1) ......(5)[/tex]
[tex]\frac{y-y1}{y2-y1} = \frac{x-x1}{x2-x1} \\\\\frac{y-3}{4-3} = \frac{x+2}{1+2} \\\\y-3 = \frac{x+2}{3}\\ 3y-9 = x+2\\3y = x+11\\OR\\y = 1/3x + 11/3[/tex]
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