Answers
By algebra properties, the factor form of polynomials are listed below:
(a + b) · (a - b) (a + b) · (a² - a · b + b²) (a - b) · (a² + a · b + b²) (x² + 6) · (x + √6) · (x - √6) (4 · c + 1) · (16 · c² - 4 · c + 1) (k - 3) · (k² + 3 · k + 9) (∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²] 3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n) a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1) y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²) 9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²] (w - 4) · (w - 9) p · (p + 12) · (p - 7)How to factor polynomials
In this problem we need to factor 13 cases of polynomials, whose results must be derived by algebra properties. The factor form of the polynomial is:
Case 1:
a² - b²
(a + b) · (a - b)
Case 2:
a³ + b³
(a + b) · (a² - a · b + b²)
Case 3:
a³ - b³
(a - b) · (a² + a · b + b²)
Case 4:
x⁴ - 36
(x² + 6) · (x² - 6)
(x² + 6) · (x + √6) · (x - √6)
Case 5:
64 · c³ + 1
(4 · c + 1) · (16 · c² - 4 · c + 1)
Case 6:
k³ - 27
(k - 3) · (k² + 3 · k + 9)
Case 7:
54 · x³ + 250 · y³
(∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²]
Case 8:
3 · m⁴ - 48 · n²
(√3 · m² - 4√3 · n) · (√3 · m² + 4√3 · n)
3 · (m² - 4 · n) · (m² + 4 · n)
3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n)
Case 9:
a⁷ · b² - a · b²
a · b² · (a⁶ - 1)
a · b² · (a³ + 1) · (a³ - 1)
a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1)
Case 10:
x³ · y² - 343 · y⁵
y² · (x³ - 343 · y³)
y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²)
Case 11:
9 · y⁷ - 144 · y
y · (9 · y⁶ - 144)
y · (3 · y³ - 12) · (3 · y³ + 12)
9 · y · (y³ - 4) · (y³ + 4)
9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²]
Case 12:
w² - 13 · w + 36
(w - 4) · (w - 9)
Case 13:
p³ + 5 · p² - 84 · p
p · (p² + 5 · p - 84)
p · (p + 12) · (p - 7)
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Related Questions
Kayak rental company A charges an initial fee of $12 plus $3.25 for every hour spent kayaking. Kayak rental company B charges $9.25 for every hour spent kayaking. A customer finds that after h hours, the kayak rental companies will cost the same. Which equation represents this situation? Responses 3.25h+12=9.25h , 3.25 h plus 12 equals 9.25 h, 9.25h+3.25h=12 , 9.25 h plus 3.25 h equals 12, 9.25h=12−3.75h , 9.25 h equals 12 minus 3.75 h, 3.25h=12+9.25h
Answers
Answer: 3.25h + 12= 9.25
Step-by-step explanation:
12 is the initial fee which we will just add to our answer
3.25 is the rate per hour, it is being multiplied by the number of hours.
the number of hour it took to reach the same cost is not told so we will just put a variable.
Austin invested $92,000 in an account paying an interest rate of [tex]5\frac{7}{8}[/tex]
% compounded daily. Josiah invested $92,000 in an account paying an interest rate of [tex]5\frac{3}{4}[/tex] % compounded continuously. After 17 years, how much more money would Austin have in his account than Josiah, to the nearest dollar?
Answers
Austin would have approximately $2,108 more than Josiah.
What is approximately?Approximately means "nearly" or "close to" an exact amount or number. It is often used to describe a quantity that is not exact, but can be estimated or rounded off. For example, "There were approximately 25 people in the room" means that the number was close to 25, but not necessarily exactly 25.
Using the formula A = P(1 + r/n)^nt, where P is the principal amount, r is the interest rate, n is the number of times compounded, and t is the number of years, we can calculate the amount of money Austin and Josiah would have in 17 years.
For Austin: A = $92,000(1 + 5.875/365)^365*17 = $120,308.05
For Josiah: A = $92,000(1 + 0.0575)^17 = $118,200.43
Therefore, Austin would have approximately $2,108 more than Josiah.
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HELP PLS DUE TDAY
STRESSING
Answers
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Please quick, mark brainy and 20 points
Answers
The answer is d
because you're waiting too long.
Answer:
0.81,74%,5/8,31/50
Step-by-step explanation:
74% means 74/100 which equals to 0.74, and 5/8 is 0.625, and lastly 32/50 is 0.62 so it leaves us with 0.81 as the greatest so we can start ordering them
0.81,74%(0.74),5/8(0.625), 31/50(0.62)
Determine the area of the parallelogram with vertices(−7,7,6),(−4,9,5),(−10,6,6), and(−7,8,5). Use the square root symbol "∇" where needed to give an exact value for your answer. Area =0
Answers
The area of the parallelogram is ∇19.
To determine the area of the parallelogram, we will use the formula: Area = ||u x v||, where u and v are vectors representing two sides of the parallelogram.
First, we need to find the vectors u and v. We can do this by subtracting the coordinates of two adjacent vertices:
u = (−4,9,5) - (−7,7,6) = (3,2,-1)
v = (−10,6,6) - (−7,7,6) = (-3,-1,0)
Next, we need to find the cross product of u and v:
u x v = [(2)(0) - (-1)(-1), (-1)(-3) - (3)(0), (3)(-1) - (2)(-3)] = [-1, 3, -3]
Finally, we need to find the magnitude of the cross product, which will give us the area of the parallelogram:
Area = ||u x v|| = ∇((-1)^2 + (3)^2 + (-3)^2) = ∇(1 + 9 + 9) = ∇19
Therefore, the area of the parallelogram is ∇19.
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In the same year, at the Avondale golf club, there are 12 women and 56 men members. Write the ratio of women: men, in its simplest form.
Answers
Answer:
3:14
for every 3 women, there is 14 men
Step-by-step explanation:
What is the highest number of degrees (as a whole number) an image can rotate without returning to it's exact original position?
please answer in __°!
Answers
Answer:
359°
Step-by-step explanation:
When an image is rotated by a multiple of 360 degrees, it returns to its original position because it has completed one full revolution. However, if the image is rotated by any angle less than 360 degrees, it will not return to its exact original position.
For example, if an image is rotated by 45 degrees, it will not return to its exact original position, but will instead be in a new and unique position. If the image is then rotated by another 45 degrees, it will again be in a new and unique position, and so on.
Therefore, the highest number of degrees an image can rotate without returning to its exact original position is 359 degrees.
Answer: 359 degrees
Step-by-step explanation:
If you rotate any object exactly 360 degrees, it returns to it's original position. Remember that phrase "360 no-scope?" It involves spinning until you're back where you started; try doing it right now. You'll be back where you were. But this question wants to know how far you can rotate an object without it being back where it was. I would usually say 359.999999999, but it's a whole number answer, so we'll stick with 359. Hope this helps!
f(x,y) = x^2 + 3y^(2) is equivalent to f′(x,y)= x^2 + 4xy + 7y^(2)
Answers
The two functions are not equivalent.
The given functions f(x,y) = x^2 + 3y^2 and f′(x,y) = x^2 + 4xy + 7y^2 are not equivalent.
To determine if two functions are equivalent, we can compare their equations and see if they are the same. In this case, the equations of the two functions are different. The first function, f(x,y), has a term of 3y^2, while the second function, f′(x,y), has a term of 4xy and a term of 7y^2.
Therefore, the two functions are not equivalent.
It is important to note that two functions can have different equations but still be equivalent if they produce the same output for any given input. However, in this case, the two functions will produce different outputs for the same input, so they are not equivalent.
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Interior angles measured as A \( 51^{\circ} 22^{\prime} 30^{\prime \prime} \) B \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \) C \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \) D \( 124^{\prime} 46^
Answers
The measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).
The interior angles of a quadrilateral are measured as A \( 51^{\circ} 22^{\prime} 30^{\prime \prime} \), B \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \), C \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \), and D \( 124^{\prime} 46^{\prime \prime} \).
To find the measure of angle D, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.
Add the measures of angles A, B, and C:
\( 51^{\circ} 22^{\prime} 30^{\prime \prime} \) + \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \) + \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \) = \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \)
Subtract the sum of angles A, B, and C from 360 degrees to find the measure of angle D:
360^{\circ} - \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \) = \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \)
Therefore, the measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).
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d the product of the following two matrices. [[-2,0],[1,-1]][[-1,0,5,1,0],[1,-1,3,1,-1]]
Answers
[[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]]
The product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
To calculate the product of two matrices, multiply each row of the first matrix with each column of the second matrix. Begin by multiplying the first row of the first matrix [-2, 0] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values -2, 0, 10, 2, 0 which will be the first row of the product matrix.
Next, multiply the second row of the first matrix [1, -1] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values 1, -1, 9, 2, -1 which will be the second row of the product matrix.
Therefore, the product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
The given matrices are:
[[-2, 0],
[1, -1]]
[[-1, 0, 5, 1, 0],
[1, -1, 3, 1, -1]]
To find the product of two matrices, we need to follow a few steps:
Multiply the first row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the first row of the first matrix by the second column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the second column of the second matrix, and then add the results.
By following these steps, we can obtain the product of the matrices. So, we can proceed as follows:
-2×(-1) + 0×1 = 2
-2×0 + 0×(-1) = 0
1×(-1) + (-1)×1 = -2
1×0 + (-1)×(-1) = 1
Hence, the product of the given two matrices is:
[[2,0,10,2,0],
[-2,2,-8,-2,2]]
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The graphs below have the same shape. What is the equation of the red
graph?
g(x)=_
A. g(x) = (x+3)²
B. g(x) = (x-3)²
C. g(x) = x²+3
D.g (x) = x2-3
Answers
The equation of the red graph is g(x) = x² + 3.
Option C.
What is the equation of the red graph?
The equation of the red graph can be determined by considering upscaling or transformation on the x - axis.
Since the equation focuses on the function g(x) and not on upscaling in the y-axis, any changes should not affect the x-axis. Therefore, we can eliminate (x - 3)² and (x + 3)² from the options given, since they involve modifying the x-axis.
In conclusion, as the transformation involves increasing the y-values along the y-axis, the correct choice is x² + 3 rather than x² - 3.
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HELP!!
One cubic foot of water is equivalent to 7.48 gallons. If the capacity of the fish tank is 100 gallons, find the maximum possible height for the fish tank. Round your answer to the nearest thousandth of an inch.
Show your work.
Answers
The height of the fish tank should be approximately 1.981 feet which is also equivalent to 23.772 inches.
What is the maximum possible height for the fish tank?As desired capacity of the fish tank is 100 gallons, and 7.48 gallons of water are equivalent to 1 cubic foot, the desired volume of the fish tank is (100 / 7.48) cubic feet, or approximately 13.369 cubic feet.
The desired volume is stated as a number of cubic feet so the known dimensions of the fish tank must be converted from inches to feet.
length = 54 inches = 4.5 feet
width = 18 inches = 1.5 feet
The formula for the volume V of a rectangular prism with length l, width w, and height h is V = lwh. We will substitute the known dimensions into the formula and solve for h.
V = ℓwh
13.369 ≈ 4.5 × 1.5 × h
13.369 ≈ 6.75h
h ≈ 13.369 / 6.75
h ≈ 1.981
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Use the associative property to
write an equivalent expression.
9 x (2 x 5) =
Answers
Answer: 90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
5) A decade of inflation
a) Suppose the annual inflation rate was 3% for 10 years in a row. What was the inflation rate for that decade?
b) Find the inflation rate for the decade from 1960 to 1970. If the inflation rate had been the same for each year in that decade, what would that annual rate have been? The answer to part a) will help you with this problem. This might be difficult depending on your math background, but try to be creative.
Answers
The inflation rate for that decade will be 34.39%. If the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.
a) If the annual inflation rate was 3% for 10 years in a row, the inflation rate for that decade would be 34.39%. This is calculated by using the formula (1 + annual inflation rate)^number of years - 1. So in this case, it would be (1 + 0.03)^10 - 1 = 0.3439 or 34.39%.
b) To find the inflation rate for the decade from 1960 to 1970, we need to know the Consumer Price Index (CPI) for both years. The CPI for 1960 was 29.6 and the CPI for 1970 was 38.8.
We can use the formula (CPI in later year/CPI in earlier year)^(1/number of years) - 1 to find the annual inflation rate.
So in this case, it would be (38.8/29.6)^(1/10) - 1 = 0.0279 or 2.79%. Therefore, if the inflation rate had been the same for each year in that decade, the annual rate would have been 2.79%.
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Which describes the translation of the graph of f (x ) = e^x to create the graph of f (x )= e^x+ 2 - 9?
Answers
Answer:
B. Left 2 units, down 9 units
Step-by-step explanation:
You would determine the x value by making the equation for x equal to 0. In this case we have x + 2 = 0. Subtract 2 from both sides to get x = -2. Determine the y value by the last digit which is -9. You now have the coordinate -2, -9, which is left 2 units and down 9 units.
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
Answers
We can state this by responding to the provided question Each friend's equation portion of the tab and the tip is represented by the equation x = 60.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
The circumstance, where x is the cost of the groceries, is represented by the equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction. As the lunch cost and the gratuity were shared equally among the eight companions, this equation accurately depicts the total sum that each of them paid.
The scenario is represented by the equation 8 (x + 16) = 76, where x is the cost of the groceries. This calculation is incorrect since it includes the tip and includes the total amount paid by all 8 friends rather than just the cost of the meal.
Each friend's portion of the tab and the tip is represented by the equation x = 60.
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Factor the following polynomial with a negative coefficient. -5x^(6)+15x^(4)+20x^(3)
Answers
The factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).
To factor the polynomial with a negative coefficient, -5x^(6)+15x^(4)+20x^(3), we can use the content loaded factor method. This method involves factoring out the greatest common factor (GCF) of all the terms in the polynomial.
The GCF of -5x^(6), 15x^(4), and 20x^(3) is 5x^(3). So, we can factor out 5x^(3) from each term:
-5x^(6) = -(5x^(3))(x^(3))
15x^(4) = (5x^(3))(3x)
20x^(3) = (5x^(3))(4)
Now, we can rewrite the polynomial as:
-5x^(6)+15x^(4)+20x^(3) = (5x^(3))(-x^(3)+3x+4)
So, the factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).
In summary, the polynomial -5x^(6)+15x^(4)+20x^(3) can be factored as (5x^(3))(-x^(3)+3x+4) using the content loaded factor method.
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Solve everything in this page please
Answers
Answer:
19. Angelique=0.3, Jamila=0.1 20.15.2
Step-by-step explanation:
19 Angelique=0.3
Jamila=0.1
20.
[tex]x^{2} =8.7^{2}+12.5^{2} \\x^{2} =231.94\\x=15.229...\\x=15.2[/tex]
Alex spent One Hour Twenty Minutes less than Lane Reading Last Week Lane spent Fifty Minutes less than Pete pete spent Three Hours Reading How Long did Alex spend Reading
Answers
Using unitary method, we can find out that Alex spent 50 minutes reading.
Unitary Method: What is it?By using the unitary technique, we can determine both the value of many units from the value of a single unit as well as the value of multiple units from the value of a single unit.
The worth of many things is supplied in the unitary technique, and we must either determine the value of more or fewer items. To do that, we must first determine the value of a single item by division and then determine the value of further or other items by multiplication.
Given in the question,
Alex spent 1 hour 20 minutes less than Lane.
Lane spent 50 minutes less than Pete.
Pete spent 3 hours reading.
Since, Pete spent 3 hours.
So, Lane spent:
= 3 hours or (180 minutes) - 50 minutes
= 2 hours 10 minutes.
Now, Alex spent:
= 2 hrs 10 minutes - 1 hour 20 minutes
= 50 minutes
Therefore, Alex spent 50 minutes reading.
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Given a line and a point, not on the line, there is one and only _____ line which passes through the given point and______ is to the given line.
A. one, parallel
B. one, perpendicular
C. two, parallel
D. two, perpendicular
Answers
Given a line and a point, not on the line, there is one and only one line which passes through the given point and is perpendicular to the given line. The correct answer is B.
A line and a point not on the line are given. We are asked to find the one and only line that passes through the given point and is perpendicular to the given line. The line that passes through the given point and is perpendicular to the given line is known as the perpendicular bisector.
The perpendicular bisector passes through the midpoint of the line segment formed by the two endpoints of the given line. Therefore, the answer is B. There is one and only one line that passes through the given point and is perpendicular to the given line. Therefore the correct answer of this question is option B
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Which formula can be used to determine the n ^ (th) term of the arithmetic sequence 6, 15, 24, 33, 42;
A f(n) = - 3 - 9n;
B f(n) = - 3 + 9n;
C f(n) = 6 - 9n;
D f(n) = 6 + 9n
Answers
The formula for the nth term of the arithmetic sequence is 3(3n-1) or -3+9n(option B)
What is arithmetic sequence?An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.
The nth term of a n arithmetic sequence is given as:
a(n) = a+(n-1)d
where a is the first term and d is the common difference
a = 6
d = 15-6 = 9
a(n) = 6+( n-1) 9
= 6+9n -9
a(n) = 9n-3
a(n) = 3(3n-1)
therefore the formula for the nth term of the sequence is 3(3n-1)
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Parallel Sort using Multiple Processes and Threads Goal In this assignment, you will implement a parallel version of the Bubble Sort algorithm to sort a bunch of numbers using first multiple processes and then multiple threads. You will learn about working with multiple processes, concurrency, race conditions, and simple inter-process and inter-thread synchronization. Part A: Sequential Bubble Sort 1. Learn the following concepts a. The bubble sort algorithm b. fork() system call c. pipe() system call d. pthread_create() and pthread_join() e. shmget(), shmat(), shmdt(), and shmctl() system calls. f. gettimeofday() to time the sorting performance. 2. Study, compile, and run this sequential bubble sort program. It takes an integer argument N, generates a set of N random integers, sorts them in ascending order using bubble sort, and prints the sorted list to standard output. $ seq_bubble 4 Generating 20 10 15 2 Sorted sequence is as follows: 2 10 15 20 3. Now study, compile, and run this even-odd pass variant of sequential bubble sort. You will find this version more amenable to a parallel implementation. 4. Test the above programs with hundreds, thousands, or millions of numbers. Adjust MAX_NUM and MAX_COUNT in the code as needed. 5. You can redirect very large output to a file using the operator to examine later. 6. Use gettimeofday () to measure and print the sorting time for different values of N. . Requirements for parts B and C below. - Use only the C language and glibc, so that you can understand low-level behavior or your code. No other languages, libraries or packages are necessary/allowed. - Do not use any pre-existing bubble-sort implem tions/libraries other than the provided in this assignment. - Implement only a parallel version of bubble sort, NOT any other sorting algorithm, even though there may be other (possibly better) parallel sorting algorithms, such as parallel nes . merge sort .
Answers
To test with hundreds, thousands, or millions of numbers, MAX_NUM and MAX_COUNT should be adjusted in the code as needed.
The Bubble Sort algorithm is a simple sorting algorithm that repeatedly steps through a given array, comparing elements and swapping them if they are in the wrong order. The sequential Bubble Sort algorithm can be implemented using a for loop that iterates through the array and swaps the elements if they are in the wrong order. The even-odd pass variant of the Sequential Bubble Sort adds two for loops, one for even elements and one for odd elements, which makes it more amenable to a parallel implementation.
Using multiple processes and threads to implement a parallel version of the Bubble Sort algorithm involves using system calls such as fork(), pipe(), pthread_create() and pthread_join(), and shmget(), shmat(), shmdt(), and shmctl() system calls. When implementing this parallel version of the Bubble Sort algorithm, care must be taken to avoid race conditions by properly synchronizing processes and threads.
To test the sequential and even-odd pass variants of the Bubble Sort algorithm, one should use the gettimeofday() function to measure and print the sorting time for different values of N. To test with hundreds, thousands, or millions of numbers, MAX_NUM and MAX_COUNT should be adjusted in the code as needed, and very large output can be redirected to a file using the operator.
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In the figure shown, lines f and g are parallel. Select all angles that are congruent to angle 1.
Answers
Answer:
Step-by-step explanation:
I can't see anything.
The trinomial x^(2)+7x-18 factors into and x^(2)-7x-18 factors into The signs in each binomial are
Answers
The trinomial [tex]x^(2)+7x-18[/tex] factors into (x+9)(x-2), and the trinomial [tex]x^(2)-7x-18[/tex] factors into (x-9)(x+2). The signs in each binomial are opposite.
In the first trinomial, the signs are positive and negative, while in the second trinomial, the signs are negative and positive. This is because the signs in the binomials are determined by the signs of the constant term and the coefficient of the linear term in the trinomial.
For the first trinomial, the constant term is -18 and the coefficient of the linear term is 7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to 7. The numbers 9 and -2 satisfy this condition, so the trinomial factors into (x+9)(x-2).
For the second trinomial, the constant term is -18 and the coefficient of the linear term is -7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to -7. The numbers -9 and 2 satisfy this condition, so the trinomial factors into (x-9)(x+2).
In both cases, the signs in the binomials are opposite because one of the numbers is positive and the other is negative.
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I am unsure how to solve problems H through L and it's due by Friday!!! pls help! (solve for variable listed on paper from equation)
Answers
Step-by-step explanation:
steps are in the image above
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Law of Sines and Law of Cosine Quiz
Date 03/1/23
State the number of possible triangles that can be formed using the given measurements.
1) In APQR, mLQ = 78°, p = 12, q = 13
2) In ADEF, mLD = 135°, f = 27, d = 13
Solve each triangle. Round your answers to the nearest tenth.
3) mA = 123°, c = 15, a = 43
5) In AKHP, mLK = 139°, p = 10 cm, k = 47 cm
Find the area of each triangle to the nearest tenth.
6)
6 in
H
B
P
74°
C
er
27 m 102°
10.8 in
Solve each triangle. Round your answers to the nearest tenth.
7)
8)
5m
2
30 m
9) In APKH, h = 26, k=28, m/P = 109°
R
K
reserved.
A
Find the area of each triangle to the nearest tenth.
10)
11 m
13 m
4) m/C= 110°, mA = 47°, c = 36
P
A
15 km
17 km
B
C
14 km
Answers
There are three possible triangles that can be formed using the given measurements.
What is measurement?Measurement is the process of quantifying or comparing the amount, size, or extent of something. It is an important concept for scientists, engineers, and other professionals in order to compare and understand the world around them. Measurement involves the use of physical tools, such as rulers, scales, and protractors, and mathematical equations, such as formulas and equations.
We can use the Law of Cosines to solve for the missing side:
[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 43^2 + 15^2 - 2(43)(15)\cos(123^\circ)$\\$b^2 \approx 799.5$\\$b \approx 28.3$[/tex]
Now we can use the Law of Sines to solve for the remaining angles:
[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.977$\\$A \approx 79.4^\circ$\\$B \approx 23.6^\circ$[/tex]
So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=79.4^\circ$[/tex], [tex]$B=23.6^\circ$[/tex], [tex]$C=77^\circ$[/tex], [tex]$a=43$[/tex], [tex]$b\approx 28.3$[/tex] , and [tex]$c=15$[/tex].
We can use the Law of Cosines to solve for the missing side:
[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 36^2 + 47^2 - 2(36)(47)\cos(47^\circ)$\\$b^2 \approx 1666.5$\\$b \approx 40.8$[/tex]
Now we can use the Law of Sines to solve for the remaining angles:
[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.647$\\$A \approx 40.9^\circ$\\$C \approx 92.1^\circ$[/tex]
So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=40.9^\circ$[/tex], [tex]$B=47^\circ$[/tex], [tex]C\approx 92.1^\circ, a\ =36$[/tex], [tex]$b\approx 40.8$[/tex],
We can use the Law of Cosines to solve for the missing side:
[tex]h^2 = k^2 + p^2 - 2kp\cos(K)\\$h^2 = 47^2 + 10^2 - 2(47)(10)\cos(139^\circ)$\\$h^2 \approx 2363.7$\\$h \approx 48.6$[/tex]
Now we can use the Law of Sines to solve for the remaining angles:
So the triangle is [tex]$\triangle KHP$[/tex] were [tex]$K=139^\circ$[/tex], [tex]$H\approx 56.5^\circ$[/tex], [tex]$P\approx 124.5^\circ$[/tex], [tex]$k=47$[/tex], [tex]$h\approx 48.6$[/tex], and [tex]$p=10$[/tex].
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Which is the correct answer?
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The best possible equation of the line of best fit would be →
y = 8.6x + 10.5.
What is scatter plot?A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data
Given is a scatter plot as shown in the image.
For the given graph the correlation is positive. So, we can write the slope of the line of the best fit as positive. So, we can write the equation of the line of best fit as → y = 8.6x + 10.5.
Therefore, the best possible equation of the line of best fit would be →
y = 8.6x + 10.5.
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Eric bought a truck in 2015 for $43,500. By 2020, the truck was worth $36,500.
Part A. What function type could model the given situation?
Part B. What is the rate of change in the truck's worth per year?
Part C. Which model describes this situation?
Answers
A function type that could model the given situation is a linear function.
The rate of change in the truck's worth per year is -1400.
A model that describes this situation is y = -1400x + 43500
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (36,500 - 43,500)/(2020 - 2015)
Slope (m) = -7,000/5
Slope (m) = 1,400.
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The cost for an 8th grade party isv$450 for a room rental, entertainment, and decorations, plus $20 per person for food. Tickets for the party are sold $25. What is the break-even point?
Answers
The break-even point is 45 tickets.
Describe Algebraic Expression?Algebraic expressions can include one or more variables, which are typically represented by letters, such as x, y, or z. These variables can be used to represent unknown quantities or to express relationships between different quantities in a problem.
Algebraic expressions can also include constants, which are fixed numbers, and coefficients, which are the numbers that multiply the variables in the expression. For example, in the algebraic expression 3x + 2y, the constants are 3 and 2, and the coefficients are 3 and 2, respectively.
To find the break-even point, we need to determine the number of tickets that need to be sold in order to cover the costs of the party.
Let's start by setting up an equation to represent the total cost of the party as a function of the number of tickets sold:
Total Cost = Room Rental + Entertainment + Decorations + Food Cost - Ticket Sales Revenue
Total Cost = 450 + 20n - 25n
where n is the number of tickets sold.
Simplifying this equation, we get:
Total Cost = 450 - 5n + 20n
Total Cost = 15n + 450
Now, we need to set the total cost equal to the revenue from ticket sales:
15n + 450 = 25n
Subtracting 15n from both sides, we get:
450 = 10n
Dividing both sides by 10, we get:
n = 45
Therefore, the break-even point is 45 tickets. If the organizers sell 45 tickets, the revenue from ticket sales will cover the total cost of the party, including the room rental, entertainment, decorations, and food cost.
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what is 8 3/4 + 1 1/2 - 1/4
Answers
Answer:
10
Step-by-step explanation:
Answer:
good morning i hope your day is going well so far
Step-by-step explanation:
the answer to your question is 10
i hope this helps!!!