Which equations arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers? (123, 2347) (Check all that apply.) Check All That Apply 1 = 10 - 3.3 1 = 37.10 - 3. 123 1 = 37.2347-706 - 123 1 = 37.10 -9.41 d d 1 = 36.2347-583 123
Answers
The equations that arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:
1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.
What is the Euclidean algorithm?The Euclidean algorithm is a recursive method for finding the greatest common divisor (GCD) of two positive integers. When we divide the larger number by the smaller number, we obtain the remainder. The smaller number and the remainder are then passed on as input to the next round. The process continues until the remainder is zero, at which point the GCD is obtained.
The solution to the given problem is as follows:
We will use the Euclidean algorithm to compute gcd(123, 2347).
123 ÷ 2347 = 0 remainder 123.2347 ÷ 123 = 19 remainder 106.123 ÷ 106 = 1 remainder 17.106 ÷ 17 = 6 remainder 4.17 ÷ 4 = 4 remainder 1.4 ÷ 1 = 4 remainder 0.The last nonzero remainder we get is 1.
Therefore, the greatest common divisor (GCD)(123, 2347) = 1.
The greatest common divisor of 123 and 2347 can be expressed as a linear combination of the two numbers in the following ways:1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.
Thus, the equations arising when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:
1 = 10 - 3.3,1 = 37.10 - 3.123,1 = 37.2347-706 - 123To know more about the "Euclidean algorithm": https://brainly.com/question/24836675
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Related Questions
Given:
R is the midpoint of QS
Prove: PRQ = TRS
Answers
Answer:
Step-by-step explanation: Hello!
I don't remember all of the postulates to these, but I hope this will help you! Vertical angles are congruent, so both angles SRT and PRQ are congruent. This also means that line segments PQ and ST are congruent. You also know that angles Q and S are congruent which is given. By the ASA Theorem, when two angles and a side are congruent, then the triangles are congruent.
HELPPPPPPPPPPPPPPPPP
Answers
Answer:
I think it's 160 square inches. Try L x W x H (length multiplied by width multiplied by height). So that would mean 4 x 5 = 20 x 8 = 160,
hope this helps!
Answer:
Step-by-step explanation:
if the pile contains only 25 quarters but at least 50 of each other kind of coin, how many collections of 50 coins can be chosen? collections
Answers
The number of collections of 50 coins that can be chosen from this pile is: C(125, 25) = 177,100,565,136,000
This is a very large number, which shows that there are many possible collections of 50 coins that can be chosen from the pile.
If the pile contains only 25 quarters but at least 50 of each other kind of coin, then the total number of coins in the pile must be at least 50 + 50 + 50 = 150. Let's assume that there are 150 coins in the pile, including the 25 quarters.
To choose a collection of 50 coins from this pile, we need to exclude the 25 quarters and choose 25 coins from the remaining 125 coins. We can do this in C(125, 25) ways, which is the number of combinations of 25 items chosen from a set of 125 items.
Therefore, the number of collections of 50 coins that can be chosen from this pile is:
C(125, 25) = 177,100,565,136,000
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There are 351 possible collections of 50 coins that can be chosen, considering the given conditions.
To find the number of collections of 50 coins that can be chosen, we will consider the given conditions:
The pile contains only 25 quarters.
There are at least 50 of each other kind of coin (pennies, nickels, and dimes).
Now, let's break this down step by step:
Determine the minimum number of coins from each kind required to make a collection of 50 coins.
- 25 quarters (as it's the maximum available)
- The remaining 25 coins must be a combination of pennies, nickels, and dimes.
Find the different combinations of pennies, nickels, and dimes that can be chosen to make a collection of 50 coins.
- We need 25 more coins, so we can divide them into three groups:
a) Pennies (P)
b) Nickels (N)
c) Dimes (D)
Calculate the combinations for the remaining 25 coins.
- Using the formula for combinations with repetitions: C(n+r-1, r) = C(n-1, r-1)
Where n is the number of types of coins (3) and r is the number of remaining coins (25)
- C(3+25-1, 25) = C(27, 25) = 27! / (25! * 2!) = 351.
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Which division problem does the number line below best illustrate?
A number line going from 0 to 13. An arrow jumps from 0 to 3, from 3 to 6, from 6 to 9, and from 9 to 12.
12 divided by 3 = 4
9 divided by 3 = 3
12 divided by 2 = 6
16 divided by 4 = 4
Answers
Answer:
12 divided by 3 = 4
. . . . . ....
Answer:
The first one- 12 divided by 3 = 4
Step-by-step explanation:
It is the most Logical answer out of the 4
answer question 13 PLSSSSSSS
Answers
Step-by-step explanation:
By Exterior Angle Theorem,
(x + 40)° + (4x - 5)° = (6x + 20)°
Therefore 5x + 35 = 6x + 20 and x = 15.
Hence angle QPT = (6 * 15 + 20)° = 110°.
what is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
Answers
The probability to get a sample average of 51 or more customers if the manager had not offered the discount is 1.36%
We can use the formula for the standard error of the mean to calculate the standard deviation of the sample means. The standard error of the mean is given by:
standard error of the mean = standard deviation / √(sample size)
In this case, the standard error of the mean is:
standard error of the mean = 10 / √(6) = 4.08
To find the probability of observing a sample mean of 51 or more customers, we need to standardize the sample mean using the standard error of the mean. This gives us the z-score, which we can use to look up the probability in a standard normal distribution table.
The z-score is given by:
z-score = (sample mean - population mean) / standard error of the mean
In this case, the population mean is 42, and the sample mean is 51. Therefore, the z-score is:
z-score = (51 - 42) / 4.08 = 2.21
Using Table 1 (or a calculator or statistical software), we can find that the probability of observing a z-score of 2.21 or higher is approximately 0.0136 or 1.36%.
This means that if the manager had not offered the discount, there would be a 1.36% chance of observing a sample mean of 51 or more customers.
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Complete Question:
A small hair salon in Denver, Colorado, averages about 42 customers on weekdays with a standard deviation of 10. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $4 discount on 6 consecutive weekdays. She reports that her strategy has worked since the sample mean of customers during this 6-weekday period jumps to 51. Use Table 1.
What is the probability to get a sample average of 51 or more customers if the manager had not offered the discount?
What would happen if you subtracted the equation for x from the equation for 10x?
Answers
Answer:
9x
Step-by-step explanation:
If you have 10 x and you subtract one, you get left with 9 x.
Think of it as objects. You have 10 apples and someone takes an apple, what do you have left? 9.
Answer:
9x
Step-by-step explanation:
If you have 10 x and you subtract one, you get left with 9 x.
Think of it as objects. You have 10 apples and someone takes an apple, what do you have left? 9x = 3
Three students that share a townhouse find that their electric bill for October is $5.29 less than the September bill. The total of both bills is $155.93, and each bill is split evenly among the roommates how much they each owe in September?
Answers
We will have the following:
From the problem we will have the following expressions:
\(\begin{gathered} S=x \\ O=x-5.29 \\ S+O=155.93 \\ 2x-5.29=155.93 \end{gathered}\)Now, from this we determine the value for the bill on september:
\(\Rightarrow2x=161.22\Rightarrow x=80.61\)Now, since there are 3 people, the payment for each one is:
\(\frac{80.61}{3}=26.87\)So, the payment for each one is $26.87 in September.
Simplify the expression (2x^2+6x-7)-(9x^2-11)
Answers
2x^2 + 6x - 7 - 9x^2 + 11
(2x^2 - 9x^2) + (6x) + (-7 + 11)
-7x^2 + 6x + 4
Hope this helps!! :)
Answer:
=- 7x^2+6x+4
Step-by-step explanation:
Suppose that the selling price of a company's primary product is 1600−0.25x dollars per unit when x units are sold every week. (a) Write a formula for the total revenue as a function of x R(x)= dollars per week (b) Suppose further that the product has fixed costs of 400 dollars and each units costs 0.7x+1440 dollars per unit to produce, where x is the number of units produced every week. Write a formula for the total cost as a function of x C(x)= dollars per week (c) Find the break-even points. Round each value to at least three decimal places. The larger quantity at which break-even occurs is units per week, with corresponding revenue of dollars per week. The smaller quantity at which break-even occurs is units per week, with corresponding revenue of dollars per week. (d) Write a formula for the profit function. Recall that profit is the difference between revenue and cost. Profit: dollars per week (e) What price will maximize profit? Price dollars per unit
Answers
Assuming that the main product of a business sells for 16000.25x dollars per when x units are sold each week.
The smaller break-even quantity is approximately 15.739 units per week, with corresponding revenue of approximately $25040.559 per week.The larger break-even quantity is approximately 21.053 units per week, with corresponding revenue of approximately $35336.842 per week.The price that maximizes profit is approximately $1378.947 per unit.Here is the explanation :
(a) The formula for total revenue as a function of x can be obtained by multiplying the selling price per unit by the number of units sold:
R(x) = (1600 - 0.25x) * x
(b) The formula for the total cost as a function of x can be obtained by adding the fixed costs to the cost per unit multiplied by the number of units produced:
C(x) = 400 + (0.7x + 1440) * x
(c) To find the break-even points, we need to determine the values of x where the total revenue equals the total cost. In other words, we need to solve the equation R(x) = C(x).
1600x - 0.25x² = 400 + (0.7x + 1440)x
Simplifying the equation:
1600x - 0.25x² = 400 + 0.7x² + 1440x
Rearranging and combining like terms:
0.95x² + 40x - 400 = 0
We can solve this quadratic equation using the quadratic formula:
\(\begin{equation}x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
In this case, a = 0.95, b = 40, and c = -400. Plugging in these values, we can find the break-even points.
Calculating using the quadratic formula, we find:
x ≈ 15.739 and x ≈ -22.739
Since we're dealing with the number of units produced every week, we discard the negative solution. Therefore, the smaller break-even quantity is approximately 15.739 units per week.
Substituting this value of x into the revenue function R(x), we can find the corresponding revenue:
R(15.739) ≈ (1600 - 0.25 * 15.739) * 15.739 ≈ $25040.559
The larger break-even quantity is the maximum value of x, which means it occurs at the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a). In this case, a = 0.95 and b = 40.
\(\begin{equation}x = \frac{-40}{2 \cdot 0.95} \approx 21.053\)
Substituting this value of x into the revenue function R(x), we can find the corresponding revenue:
R(21.053) ≈ (1600 - 0.25 * 21.053) * 21.053 ≈ $35336.842
Therefore, the larger break-even quantity is approximately 21.053 units per week, with corresponding revenue of approximately $35336.842 per week.
(d) The profit function can be obtained by subtracting the total cost function from the total revenue function:
P(x) = R(x) - C(x) = (1600 - 0.25x) * x - (400 + (0.7x + 1440) * x)
Simplifying further:
P(x) = 1600x - 0.25x² - 400 - 0.7x² - 1440x
P(x) = -0.95x² + 1600x - 400
(e) To find the price that maximizes profit, we need to determine the value of x that maximizes the profit function P(x). Since the coefficient of the quadratic term is negative (-0.95), the parabolic function opens downwards and has a maximum value.
The x-coordinate of the vertex of the parabolic
function can be found using the formula \(\begin{equation}x = \frac{-b}{2a}\). In this case, a = -0.95 and b = 1600.
\(\begin{equation}x = \frac{-1600}{2 \cdot -0.95} \approx 842.105\)
Substituting this value of x into the revenue function R(x), we can find the corresponding price:
Price = 1600 - 0.25 * 842.105 ≈ $1378.947
Therefore, the price that maximizes profit is approximately $1378.947 per unit.
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3-12x4-6x²
Expression in standard form:
Leading Coefficient:
Answers
Answer:
Below in bold.
Step-by-step explanation:
Standard form:
-12x⁴ - 6x² + 3.
Leading Coefficient:
-12.
Write FIVE (5) major learnings of yours in media and current event
course. Explain each learning briefly
Answers
Throughout my studies in media and current events, I have gained several major learnings that have shaped my understanding of the subject matter.
These include the importance of media literacy and critical thinking, the power and influence of social media, the role of bias in news reporting, the significance of ethical journalism, and the impact of media on shaping public opinion.
1. Media Literacy and Critical Thinking: One of the most crucial learnings is the importance of media literacy and critical thinking skills. It is essential to analyze and evaluate the information presented by media sources, considering their credibility, bias, and potential agenda. Developing these skills enables individuals to make informed judgments and avoid misinformation or manipulation.
2. Power and Influence of Social Media: Another significant learning is recognizing the power and influence of social media in shaping public opinion and disseminating news. Social media platforms have become prominent sources of information, but they also pose challenges such as the spread of fake news and echo chambers. Understanding the impact of social media is crucial for both media consumers and producers.
3. Role of Bias in News Reporting: Media bias is an important factor to consider when consuming news. I have learned that media outlets may have inherent biases, influenced by their ownership, political affiliations, or target audience. Recognizing these biases allows for a more balanced and critical understanding of news content, and encourages seeking diverse perspectives.
4. Significance of Ethical Journalism: Ethics play a fundamental role in responsible journalism. I have learned about the importance of principles such as accuracy, fairness, and accountability in reporting news. Ethical journalism promotes transparency and ensures the public's trust in the media, contributing to a well-informed society.
5. Impact of Media on Shaping Public Opinion: Lastly, I have learned that the media holds a significant role in shaping public opinion and influencing societal attitudes. Through various forms of media, such as news coverage, documentaries, or entertainment, narratives are constructed that can sway public perception on issues ranging from politics to social matters. Recognizing this influence is crucial for media consumers to engage critically with the information they receive and understand the potential impact it can have on society.
These five major learnings have provided me with a comprehensive understanding of media and current events, enabling me to navigate the vast landscape of information and make more informed judgments about the media I consume. They highlight the importance of media literacy, critical thinking, understanding bias, ethical journalism, and the impact media has on public opinion, ultimately contributing to a more well-rounded and discerning approach to media consumption.
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Write the equation of the line
whose slope is 3 and y-intercept
is (0,7).
The equations should be written
in y-mx+b form.
Answers
Answer:
y = 3x+7
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = 3x+7
2 point
1) What is mZWXY?
WS
K
60°
40°
20"
40"
60°
100
Answers
The regular polygon has the following measures.
a = 2√3 yd
s = 4 yd
Segment a is drawn from the center of the polygon
perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.
Show all your work.
Answers
The vocabulary for the segment a is the apothem
The area of the polygon is about 41.6 yd²
What is the area of a regular figure?The area of a regular figure is the extent of the planer space the figure occupies.
The length of each side of the regular polygon, s = 4 yd
The length of the segment a = 2·√3
The vocabulary term for the segment a drawn from from the center of the polygon and perpendicular to one of its sides is the apothem
Therefore, the vocabulary term for segment a is the apothem
The polygon is a hexagon.
The area of a hexagon is; A = ((3·√3)/2) × s²
Therefore, the area of the polygon is; A = ((3·√3)/2) × (4)² = 24·√3 ≈ 41.6
The area of the polygon is about 41.6 yd²
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8. Mystery Number: a number is multiplied by 5. The product is then added to 11. The square root of that sum is equal to 9. Find the number. Show your work or steps.
Answers
Answer:
14
Step-by-step explanation:
14x5=70
70+11=81
√81=9
One of the altitudes of the parallelogram shown is the square root of 22.5. What is the other altitude?
Answers
Answer:
Step-by-step explanation:
4x+3y=2 solve for y pls help omg i cant
Answers
Answer: 3 y = 2 − 4 x
Step-by-step explanation: 3 y = 2 − 4 x
how do you slove the eqaution 4x=3y-7
Answers
The given equation can be solved for the value of x and y
i.e. x = (3y - 7)/4 & y = (4x + 7)/3.
What is the linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We have,
The equation 4x=3y-7
So, here we can solve this equation for the x as well as y equals,
Firstly we will solve for x:
4x = 3y - 7
dividing the whole equation by 4 we get,
4x/4 = (3y - 7)/4
x = (3y - 7)/4
Similarly, we will solve for y:
4x = 3y - 7
3y = 4x + 7
dividing the whole equation by 3 we get,
3y/3 = (4x + 7)/3
y = (4x + 7)/3
Hence, the given equation can be solved for the value of x and y
i.e. x = (3y - 7)/4 & y = (4x + 7)/3
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What number is 26% of 752
Answers
Answer:
195.52
Step-by-step explanation:
26% of 752 is 195.52
✓3 correct to 5 decimal places
Answers
Answer:
1,73205
Step-by-step explanation:
First, count out the five decimal places, and then look at the sixth place:
\(\sqrt{3}\) ≈ 1,73205 | 0807...
The sixth decimal is less than 5, so we round to the smaller side.
BERE
Which function represents exponential decay?
o
f(x) = {
f(x) = (-)
o pux) = 4(-3)
Of(x) = 4
Answers
Step-by-step explanation:
Sorry I don't kNkw the amswer
10x - 4 = 16
What does x equal to?
Answers
Answer:
x = 2
Step-by-step explanation:
First isolate the variable:
10x - 4 = 16
+4 +4
10x = 20
Then get x by itself:
10x = 20
x = 20/10
x = 10
Researching the average earnings by major and by career can help you determine the _____ of an institute of higher education.
a) net cost
b) sticker price
c) available scholarships
d) return on investment
Answers
Researching the average earnings by major and by career can help you determine the return on investment of an institute of higher education.
How to Calculate Return on Investment (ROI)?The primary indicator of the profit made from any venture is return on investment (ROI). A gain or loss from an investment in relation to its cost is compared using this ratio. Whether you are assessing the success of your stock portfolio, taking into account a company investment, or choosing whether to start a new project, it is helpful in evaluating the current or projected return on an investment.ROI and other cash flow indicators, including internal rate of return (IRR) and net present value (NPV), are important metrics that are used in business research to assess and prioritize the attractiveness of various investment options.Despite the fact that ROI is a ratio, it is usually stated as a percentage.It's crucial to keep a few things in mind when assessing ROI figures. First off, because it is inherently simpler to understand than a ratio, ROI is frequently represented as a percentage. Second, because investment returns can be either positive or negative, the ROI calculation includes the net return in the numerator.To learn more about return on investment, refer to
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Find the total surface area of this cuboid. 4 cm 5 cm 2 cm
Answers
Answer:40
Step-by-step explanation:
Width x length x height
4 x 2 = 8 x 5 = 40
Idenify the terms and the coefficient of the expression?
1. 5x + 2v - 5
Answers
Answer:
The expression is:
5x + 2v - 5
The terms in this expression are:
5x, with a coefficient of 5
2v, with a coefficient of 2
-5, with a coefficient of -5
So the coefficients are 5, 2, and -5 respectively.
Which of the following observations based on the graph is correct?
The cost of maintaining the machine is constantly rising.
No - "Constantly rising" means that there is never but an upward trend, but there is a flat spot and downward trend from 4 to 6 years.
For the first 3 years, it cost $300 to maintain the machine.
No - If true, the graph would be flat in the first 3 years, but it is rising. Only the 3rd years is the cost $300. The average rate of change between year 1 and year 4 is $500-$100/4 years = $400/year
No - The change in time from year 1 to year 4 is 3 years, not 4. And the $400/400 is $100/year.
The average rate of change between year 1 and year 4 is $500-
$100/(4-1) years = $400/3 years = $133.33 per year
Yes - Divide the change in wage by the change in time.
Answers
The average rate of change between year 1 and year 4 is $500-$100/(4-1) years = $400/3 years = $133.33 per year. This statement accurately calculates the average rate of change in cost.
To determine the correctness of the observations based on the graph, we need to carefully analyze the information presented.
Observation 1 states that the cost of maintaining the machine is constantly rising. However, this statement is incorrect as there is a flat spot and a downward trend from 4 to 6 years, indicating a decrease in maintenance costs during that period.
Observation 2 claims that the cost of maintenance is $300 for the first 3 years. This statement is also incorrect since the graph shows a rising trend in the cost during the first 3 years, and it is only in the third year that the cost reaches $300. The cost is not constant for the entire period.
Observation 3 states that the average rate of change between year 1 and year 4 is $400/400 = $100/year. This statement is incorrect because the change in time from year 1 to year 4 is actually 3 years, not 4. Therefore, the correct calculation would be $400/3 years, which is approximately $133.33 per year.
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4. construct a geometric figure that illustrates why a line in lr2 not through the origin is not closed under vector addition.
Answers
In LR2 (two-dimensional Euclidean space), a line passing through the origin is closed under vector addition, meaning that if you take any two vectors on that line, their sum will also lie on the same line.
However, a line not passing through the origin is not closed under vector addition.
To illustrate this, let's consider a line L in LR2 that does not pass through the origin. We can represent this line as a straight line segment starting from a point A and ending at a point B. The line segment AB represents the line L.
Now, consider two vectors represented by two line segments starting from the origin O and ending at points C and D, respectively. These vectors can be represented as OC and OD. Since the line L does not pass through the origin, OC and OD will not lie on line L.
If we try to add these two vectors, we construct the parallelogram OBCD, where BC represents the vector addition OC + OD. Since OC and OD do not lie on line L, their sum BC will also not lie on line L. This violates the closure property, where the sum of two vectors on a line should also be on the same line.
the geometric figure, in this case, would consist of a line L not passing through the origin, two vectors OC and OD not lying on line L, and the resulting vector BC (sum of OC and OD) not lying on line L. This figure demonstrates that a line in LR2 not passing through the origin is not closed under vector addition.
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The price for calculating the price to deliver a parcel of mass m kg is price ($) = 7 + 3.5m
What is the mass, in kg, of a parcel with a delivery price of $70?
Answers
Answer:
18 Kg
Step-by-step explanation:
We can use algebra to solve for the mass, m, given the delivery price, $70.
Starting with the formula:
price ($) = 7 + 3.5m
We can substitute $70 for price ($) and solve for m:
$70 = 7 + 3.5m
Subtracting 7 from both sides:
$63 = 3.5m
Dividing both sides by 3.5:
m = 18
Therefore, the mass of the parcel is 18 kg.
Write the transformation function for the following tranformation. Black is pre image
T<_____>(x,y)
Answers
Answer:
See the attached worksheet
Step-by-step explanation:
The function is transformed by subtracting 3 from both the x and y values. I'm uncertain how this is expressed in a functional form.
