Given System of equation has multiple solution.
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given a system of equation:
-1 = 2x - y and 8x - 4y = -4
From equation 1
-1 = 2x - y
y = 2x + 1
Substitute this value on equation 2
8x - 4y = -4
8x - 4(2x + 1) = -4
-4 = -4
An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.
Thus, Given System of equation has multiple solution.
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A 90-day, 10% note for $10,000 dated March 15 is received from a customer on account. The face value of the note is:
A. $10,250
B. $10,000
C. $9,000
D. $9,750.
A 90-day, 10% note for $10,000 dated March 15 is received from a customer on account. The face value of the note is $10,250
What is meant by face value?A digit's face value is its actual value as part of a number. We multiply the digit value by the numerical value of a number to obtain its place value. For instance, since 5 is in the tens place and is present in the number 452, its place value is (5 10) = 50. A digit's face value is the actual number.The par value is the notional value of a share, bond, or other comparable security on the date of issuance. The terms "par value" and "face value" are frequently used interchangeably. A bond's face value, or the amount of principal the issuer is required to repay at the conclusion of the bond's term, is its par value.
Face value = $10,000×10/100×3/12 =$10,250
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Question 7
Find the measure of each angle indicated
Answer:
<Q = 93
Step-by-step explanation:
The sum of the angles of a triangle is 180
<Q + <P + < R = 180
<Q + 51+36 = 180
<Q+87=180
<Q = 180-87
<Q = 93
Find the volume of the rectangular prism.
Answer: V=LWH
Step-by-step explanation:
Let x and y be functions of time t such that the sum of x and twice y is constant. Which of the followingequations describes the relationship between the rate of change of with respect to time and the rate ofchange of with respect to time?A) dx/dt=2dy/dtB) dx/dt=-2dy/dtC) 2dx/dt+dy/dt=0D) dx/dt + 2dy/dt=K, where K is a function of t
The equation describes the relationship between the rate of change of with respect to time and the rate of change of with respect to time is dx/dt -2 dy/dt
What are functions?In mathematics, a function is an expression, rule, or law that establishes the relationship between two variables (the dependent variable). Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships. One input results in one output when using a function, which is a type of rule. by Alex Federspiel, the photo's author. Here, y=x2 serves as an illustration. A single output for y results from any input for x. Since x is the input value, we would state that y is a function of x.Well x + 2y = k (constant)
differentiate through wrt t
dx/dt + 2 dy/dt = 0
so dx/dt -2 dy/dt (so B)
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has a normal distribution with mean 7.5 and standard deviation 2.5. for which of the following is the probability equal to 0 ?
Using the normal probability distribution, it is found that P(X = 8) is equal to zero.
In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z = \frac{X-mean }{S.D.}[/tex]
It measures how many standard deviations the measure is from the mean.After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.As in any continuous distribution, the probability of an exact value, that is, P(X = x), is 0.Hence, from the last bullet point, it is found that P(X = 8) is equal to zero.
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1. (05.01 LC) Which data set could be represented by the boxplot shown? (1 point) boxplot with the minimum of 6, lower quartile value of 7, median of 9, upper quartile of 13, and maximum of 14. {6, 6, 8, 8, 9, 12, 13, 13, 14} {6, 6, 7, 9, 9, 12, 13, 14, 16} {6, 7, 8, 9, 10, 11, 12, 13, 14} {6, 7, 9, 9, 9, 12, 13, 14, 14}
A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.
What is a box-and-whisker plot?In Mathematics, a boxplot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:
Minimum = 6.First quartile = 7.Median = 9.Third quartile = 13.Maximum = 14.By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that it correctly represents this data set {6, 6, 8, 8, 9, 12, 13, 13, 14}.
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I need help could someone figure out the two blank spots for me
The two numbers that correctly complete the chart based on the proportions are
How to calculate the new amounts of ingredients needed?This can be calculated by using the original recipe:
Batch 1:
This batch requires 1 blue paint rather than 1/2 or half, which shows you need to multiply by 2 the ingredients, based on this the correct number for the yellow paint is 1/2 as 1/4 x 2 = 1/2.
Batch 2:
This batch requires two yellow gallons rather than 1/4, which shows you should multiply the ingredients by 8. Based on this, the number for batch 2 is 4 as 0.5 or 1/2 x 8 = 4
Note: Below you can find the complete chart
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In 2007, a principal of $4700 was invested at 5.25% Interest, compounded annually.
Let t be the number of years since 2007. Let y be the value of the investment, in dollars.
Write an exponential function showing the relationship between y and t.
The formula for calculating the future value of an investment compounded annually is:
FV = P(1 + r)^t
where:
FV = future value of the investment
P = principal or initial investment
r = annual interest rate as a decimal
t = number of years the investment is held
In this problem, the principal is given as $4700, the annual interest rate is given as 5.25%, and the time is measured in years since 2007.
So we can write the function as:
y = 4700(1 + 0.0525)^t
In this function, y represents the future value of the investment (in dollars) and t represents the number of years since 2007.
The above function can be written in the form A or A B , where A and B are constants or variable expressions that have no variables in common.
A = 4700
B = 1 + 0.0525
y = A*B^t
So the exponential function for the problem is:
y = 4700*(1+0.0525)^t
(10^4)^2 in index form
Answer:(10^4) ^2=10^4•2=10^8=100000000
a) The transportation cost of 35 kg of potatoes is Rs 105. (i) What is the transportation cost of 2.5 quintals of potatoes at the same rate for the same distance? (ii) How many quintals of potatoes can be transported for Rs 1,500 at the same rate for the same distance?
(i) 1 quintal = 100 kg
2.5 quintals = 2.5100 = 250 kg
Transportation cost of 250 kg of potatoes = 105(250/35) = Rs 750
we are asked to find the transportation cost of 2.5 quintals (250 kg) of potatoes at the same rate as 35 kg of potatoes. We know that the transportation cost for 35 kg is Rs 105.
To find the cost for 250 kg, we use the proportion of 35/105 = x/750. By cross multiplying we get x= 250*105/35= 750. So the transportation cost for 250 kg of potatoes is Rs 750.
(ii) Transportation cost of 1 quintal of potatoes = 105*(100/35) = Rs 300
Transportation cost of 1 quintal of potatoes = Rs 1500 / Rs 300 = 5 quintals.
we are asked to find how many quintals of potatoes can be transported for Rs 1,500 at the same rate as 35 kg of potatoes. We first find the transportation cost of 1 quintal of potatoes by using the proportion of 35/105 = x/300.
So x = 100, thus the transportation cost of 1 quintal of potatoes is Rs 300. So we can transport 1 quintal of potatoes for Rs 300. Dividing 1500 by 300, we get 5 quintals.
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help would be appreciated!
Complete the equation describing how
x and y are related.
0 1 2 3
4 5
y 0 1 2 3 4 5
y = [? ]x
Enter the answer that belongs in [?].
Answer:56
Step-by-step explanation:
What length of 2-in. by 4-in. material will be required to make six bench legs each 28 1/4 in. long?
Material will be required to make six bench legs each 28 1/4 inch is 169.5 inches.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is Decimal?
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
The simple solution is to convert 28 1/4 to a decimal and be cautious about converting it back to a fraction if necessary.
28 1/4=28.25
You need Six of them.
1 leg measures28.25 inches.
6 legs = x
Cross multiply 1/6 = 28.25 / x
x = 6* 28.25
x equals 169.5 inches
How many feet is that exactly? To calculate the amount of feet, divide by 169.5 /6=28.25 feet.
2 by 4s are typically 6 feet long. Unfortunately, you will need two of these for two more for 6 feet.
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gathered a random sample of bags of potato chips from a popular company. she calculated data on different variables. for one of the variables that she collected, she constructed a
The correct option is (4) Flavor of potato chips. she uses Histogram to show the data collected from the sample of bags of Potato chips.
A histogram is a graphical representation of the distribution of a dataset, it shows how the data is spread out across different ranges of values. It is used to show the frequency of observations within each range of values, also known as a bin.
The bin is a range of values, and the height of each bar represents the number of observations within that range of values. The x-axis represents the range of values and the y-axis represents the frequency of observations.
When you construct a histogram, you will first need to decide on the number of bins to use and the range of values that each bin will cover. This is known as binning. It is important to choose the appropriate number of bins and range of values to effectively display the distribution of the data.
Question:
Anya gathered a random sample of bags of potato chips from a popular company. She calculated data on different variables. For one data that she collected, she constructed a circle graph. Which of the following variables did she use?
Price of bag of potato chipsNumber of chips in the bag of potato chipsWeight of bag of potato chipsFlavor of potato chipsTo know more about Histogram:
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how would you graph functions like these in a graph?
Answer:
Step-by-step explanation:
f(x) is basically another term for y, and you already have your x values, so you can just plot the points and draw lines through them :)
For drawing graphs we have two points (x-axis and y-axis ) to loacte exact location on the graph.
X-axis point to locate on the graph parallel distance from y-axis.
Y-axis point to locate on the graph parallel distance from x-axis.
Take the y-coordinates as the f(x) and points of x-coordinates as the value of x.
1.Write down the coordinates of x-axis and y-axis
y=-3x+1
(X-axis,Y-axis)=A(-2,7),B(-1,4),C(0,1),D(1,-2),E(2,-5)
2.Write down the coordinates of x-axis and y-axis
y=-x²+5
(X-axis,Y-axis)=A(-2,1),B(-1,4),C(0,5),D(1,4),E(2,1)
3.Write down the coordinates of x-axis and y-axis
y=[tex]2^{x}[/tex]
(X-axis,Y-axis)=A(-2,0.25),B(-1,0.5),C(0,1),D(1,2),E(2,4)
These are the graphs linke images
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N(t) = 25t + 150 for 0<=t<6, (200 + 80t)/(2 + 0.05t) for t>=8The number of fish in a pond at time t years is modeled by the function N defined above, where f is a continuous function such that f(0)=80.a) Find limt→[infinity]N(t). Explain the meaning of limt→[infinity]N(t) in the context of the problem.
a) limit→[infinity]N(t) = limit→[infinity](200 + 80t)/(2 + 0.05t) = 200.
What is a limit in plain English?
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.
This means that as the number of years (t) approaches infinity, the number of fish in the pond (N(t)) approaches a limit of 200. In other words, as t gets larger and larger, the number of fish in the pond will get closer and closer to 200, but will never exceed 200. In the context of the problem, this means that the pond has a carrying capacity of 200 fish and that the population of fish in the pond will eventually stabilize at this level, regardless of the initial population.
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describe all the x -values at a distance of 15 or less from the number 6 . enter your answer in interval notation.
The set of all x-values at a distance of 15 or less from the number 6 can be represented in interval notation as (-9, 21).
Interval notation is a way of expressing a set of numbers in a concise and easily readable format. In this case, we are looking for all the x-values that are a distance of 15 or less from the number 6. To find these values, we need to consider the range of numbers that are 15 units away from 6 in both the positive and negative directions.
On the negative side, 6 - 15 = -9, so any x-value that is greater than -9 and less than 6 is within the desired range.On the positive side, 6 + 15 = 21, so any x-value that is greater than 6 and less than 21 is also within the desired range.So, in interval notation, the set of all x-values at a distance of 15 or less from 6 is written as (-9, 21) which means all the values between -9 and 21 (not including -9 and 21)
Key points:
Interval notation uses parentheses to indicate that the endpoint is not included in the interval, and square brackets to indicate that the endpoint is included.The interval is always written in increasing order, with the lower endpoint first and the upper endpoint second.Interval notation is commonly used in mathematics, particularly in calculus and analysis, to describe the domain or range of a function.Learn more about Interval notation here:
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Which of the following shows 8x³y + x² - 14z - 2 + 5y2x written in standard form?
-14z + 8x³y + 5y²x - 2 + x²
8x³y + 5y²x + x² - 14z - 2
8x³y + x² + 5y²x - 14z - 2
x²-2-14z + 5y²x + 8x²y
Answer:
The correct answer is 8x³y + 5y²x + x² - 14z - 2.
Step-by-step explanation:
This is in standard form because it is a polynomial with the terms arranged in descending order of their exponents, with the coefficient of each term being positive.
The exponent of x is 3, the exponent of y is 2, the exponent of z is 1, and the constant is -2.
A teacher has a goal of displaying the names of 2 students selected at random from a group of 30 students in a classroom. Any possible pair of students should be equally likely to be selected. Which of the following algorithms can be used to accomplish the teacher's goal?
Answer:
Step-by-step explanation:
The teacher can use a random sample size number generator to select two numbers between 1 and 30. The numbers generated correspond to the indices of the list of student names, thus selecting two students at random. This ensures that any possible pair of students is equally likely to be selected.
1. Create a list of 30 student names.
2. Create a random number generator that generates two numbers between 1 and 30.
3. Use the random number generator to generate two numbers.
4. Use the two numbers generated to select two student names from the list using the numbers as indices.
5. Display the two student names selected.
The teacher's goal of randomly selecting two students from a group of 30 can be accomplished by using a random number generator. This generator can be used to generate two numbers between 1 and 30, which correspond to the indices of the list of student names. By selecting two numbers at random, the teacher is able to ensure that any possible pair of students is equally likely to be selected. This can be done by first creating a list of 30 student names and then using the random number generator to generate two numbers. The numbers generated can then be used to select two student names from the list using the numbers as indices. Finally, the two student names selected can be displayed.
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How many terms does the following expression contain?
5yz^2-z-24y+77
According to the question, there are five terms in the expression 5yz^2-z-24y+77.
What is expression?Expression is the representation of an idea or feeling in a creative way. It is the manifestation of someone's thoughts, emotions, and desires through an artistic form. Expression can take on many forms including writing, music, painting, sculpting, and dancing. Expression allows us to communicate our innermost feelings and beliefs to the outside world. It can be used to reach out to those who may be feeling isolated, to inspire and empower others, or to simply bring joy to those who experience it. Expression is a unique way of conveying our ideas and is an important part of the human experience.
The first term is 5yz^2, the second term is -z, the third term is -24y, the fourth term is +77, and the fifth term is the constant 77.
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Which input in this table is incorrect?
siete veces un número en expresión algebraica
In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.
What is the formula for algebraic expressions?An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)
A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).
If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.
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Complete question -
Seven times a number in algebraic expression
Which of the following is a correct interpretation of the expression
−
4
−
(
−
7
)
−4−(−7)minus, 4, minus, left parenthesis, minus, 7, right parenthesis?
A correct interpretation of the expression -4 - (-7) include the following: D. the number that is 7 to the right of -4 on the number line.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In this context, the expression -4 - (-7) equals to 3 and it simply means that you would start at -4 on the number line and move 7 places to the right;
x = -4 - (-7)
x = -4 + 7
x = 3.
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by evaluating first and second derivatives using differential calculus (and not a purely graphical solution), show that the molar entropy of mixing is maximized for a specific value for nne and determine this value as well as the corresponding maximized change in molar entropy upon mixing (in j/mol-k).
The molar entropy of mixing is given by the equation S_mix = R(x1lnx1+x2lnx2).
To maximize the molar entropy of mixing, we need to find the value of x1 and x2 that will produce the maximum value of S_mix. Differentiating S_mix with respect to x1 and x2 and setting the derivatives equal to 0 will yield the critical points. The critical points can then be tested to see which one produces the maximum value of S_mix. After differentiating, we get x1 = x2 = 1/2. This implies that the molar entropy of mixing is maximized when the mole fraction of each component is 0.5. The corresponding maximized change in molar entropy upon mixing is Rln2 which is equal to 2.30258509299405 j/mol-k.
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A parabolic tunnel has a width of 20 feet and a height of 12 feet at the center. Find the cross-sectional area of the parabolic tunnel.
A. Illustrate the parabolic tunnel. Show the measurements.
A parabolic tunnel has the shape of a parabola in cross-section, with one axis being symmetric (the width) and the other axis being the height at the center. To find the cross-sectional area of the parabolic tunnel, we can use the formula for the area of a parabola:
Area = (1/2) x Width x Height
Given that the width of the parabolic tunnel is 20 feet and the height at the center is 12 feet, we can substitute these values into the formula:
Area = (1/2) x 20 x 12 = 120 square feet.
So the cross-sectional area of the parabolic tunnel is 120 square feet.
consider a small ferry that can accommodate cars and buses. the toll for cars is $3 and the toll for buses is $10. let x and y denote the number of cars and buses, respectively, carried on a single trip. suppose the x and y are independent and have the following probability distributions:
The probability of the ferry carrying x cars and y buses is given by the joint probability distribution for x and y. The expected toll for this trip is 3x + 10y.
The probability of the ferry carrying x cars and y buses can be found using the joint probability distribution for x and y. This joint probability distribution is the product of the individual probability distributions for the number of cars and buses. The expected toll for this trip is 3x + 10y, which indicates that each car carries a toll of $3 and each bus carries a toll of $10. The joint probability distribution for x and y can be used to calculate the probability of the ferry carrying x cars and y buses. For example, if the probability of the ferry carrying 3 cars and 2 buses is 0.2 then the expected toll for this trip would be
3x + 10y = 3(3) + 10(2) = $36.
Thus, the joint probability distribution for x and y can be used to calculate the probability of the ferry carrying a given number of cars and buses, as well as the expected toll for this trip.
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Please really need help on these
Answer:
2. True
3. Maximum
4. [tex]2(m-9)^2[/tex]
Step-by-step explanation:
Question 2:
Yes, it is the vertex formula used to calculate the vertex of a quadratic funtion.
Question 3:
Since the first term of the equation has a negative coefficient, the parabola turns upside down, which opens down. Therefore the equation has a maximum.
Question 4:
[tex]2m^2-36m+162\\[/tex]
Find the GCF:
[tex]2(m^2-18m+81)[/tex]
Find the perfect square binomial:
[tex]81*1=81\\\\(-9*-9)\\\\-9*-9=81\\\\-9-9=-18[/tex]
Therefore this equation can be written as a perfect square binomial.
[tex]2(m-9)^2[/tex]
5. An association of coffee producers has estimated that 50% of adult workers drink coffee at least occasionally while on the job. Given this estimate:
a) For a randomly selected group of 4 adult workers, what is the probability that no more than 3 of them drink coffee at least occasionally while on the job?
For a randomly selected group of 4 adult workers, the probability that no more than 3 drink coffee at least occasionally while on the job is 37.5%.
What is the probability?Probability refers to the chance, odds, or likelihood that an expected outcome is obtained when there are many possible events.
Probability may be 100% certain, depicted as 1, or 100% uncertain, expressed as zero.
Other values of probability lie between one and zero as fractional values that can be depicted as percentages, decimals, or fractions.
The estimated percentage of adults who at least occasionally drink coffee = 50%
Random sample = 4
The number of adult workers from 4 who occasionally drink coffee on the job = 3
The probability of 3 out of 4 workers drinking coffee on the job = 37.5% (3/4 x 50%)
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A sports reporter records the number of touchdowns scored each week during the football season. What statistical question could the reporter ask about the data?
Answer:
There are a lot of questions the reporter could ask.
Step-by-step explanation:
There are several statistical questions that a sports reporter could ask about the data on the number of touchdowns scored each week during the football season, depending on their focus and the information they want to gather. Some examples could be:
What is the mean number of touchdowns scored per week?
What is the median number of touchdowns scored per week?
What is the mode of number of touchdowns scored per week?
What is the range of the number of touchdowns scored per week?
What is the standard deviation of the number of touchdowns scored per week?
Is there a trend or pattern to the number of touchdowns scored per week?
Is there a difference in the number of touchdowns scored per week between home and away games?
What factors are associated with the number of touchdowns scored per week?
What is the probability of scoring a certain number of touchdowns per week?
Are the number of touchdowns scored per week follow a normal distribution?
These are just a few examples of the questions that a sports reporter could ask about the data. The specific question will depend on the goals of the analysis and what the reporter wants to convey to their audience.
Compute the perimeter of the shape shown.
A) 17 cm
B) 19 cm
C) 13 cm
D) 15 cm
Answer:
D. 15
Step-by-step explanation:
4+5+6=
4+5=9..
9+6=
15.
Thus, Answer is D. 15
Answer:
Your answer is: D)15cm
Step-by-step explanation:
To find the perimeter add all of the side together.
6+4+5=15
Given the vectors A =2.00 i^ +6.00 j^ and B =3.00 i^ −2.00 j^
. (a) Draw the vector sum C = A+ B and vector difference D = A − B . (b) Calculate C and D in terms of unit vector. (c) Calculate C and D in terms of polar coordinates with angles measured with respect to the positive x axis.
The magnitude of D is √(-1^2 + 8^2) = √65 = 8.06, and the angle is arctan(8/-1) = 126.87°.
(a) The vector sum C = A+ B is shown in the figure below, and the vector difference D = A − B is shown below that.
(b) C = (5i^ + 4j^) and D = (-1i^ + 8j^).
(c) The polar coordinates of C = (5, 53.13°) and D = (-1, 126.87°). To calculate these, I used the formulas for converting from Cartesian to polar coordinates, where r is the magnitude of the vector and θ is the angle with respect to the x-axis. The magnitude of C is √(5^2 + 4^2) = √41 = 6.4, and the angle is arctan(4/5) = 53.13°. The magnitude of D is √(-1^2 + 8^2) = √65 = 8.06, and the angle is arctan(8/-1) = 126.87°.
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