Given that S'= {e" : 0 € R}, where e® = cos(0) + i sin(@). %3D Use First Isomorphism Theorem to prove that R/Z S'.

Q: 21. -6r - 7x +qx - 12 is divisible by 3x - 4. There is no remainder. Find the value of q. Justify…

A: Use polynomial for finding the value of q.

Q: 23. a) Use the factor theorem to determine the factors of the function f(x) = 10x' +41x +x- 12. b)…

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Q: Let x and y be square matrices of order n a. Show that if x and y are skew symmetric, then x + y is…

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Q: Q.28 Using appropriate identities, factorise the following: (i) 49a? +70ab+25b² (ii) 9a² +6a+1-25b²…

A: Note: as per our guidelines we can solve only 3 sub parts so please repost rest part in other…

Q: "Pu is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was 238…

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Q: Solve the quadratic equation using the quadratic formula.

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Q: What is 10 + 10

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Q: Rocco loves going for a walk. In the past 20, days, he has walked 310, miles. If he walked the same…

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Q: Demonstrate that A A-1 = A-1 A = I

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Q: analyze the graph of the function f(x)=4lx+5l+6 compared to the graph of the absolute value…

A: Given query is to find the transformation performed.

Q: Complete the table.  Interest  Principal  Rate  Time (Days)  P300  P30,000  8%    P450…

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Q: The one-to-one function fis defined below. 8x+5 1+3x -1 Find f (x), wheref is the inverse of f. Also…

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Q: (7) A. How many ways can 7 people line up in a cafeteria line? B. How many ways can five people be…

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Q: Find u - v, 2(u + 3v), and 2v - u. и%3D (6, —8, 5, 3), v = (-2, - -1) (a) u - v = (b) 2(u + 3v) =…

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Q: Determine the value of x given the following equation x²+2x+1=0.

A: x²+2x+1=0 use formula of (x+a)2 = x2 +2ax +a2 (x+1)2 =0 x+1 =0 x =-1

Q: In the equation y able-h) +k how does the value of k affect the graph?

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Q: Evaluate the logarithm. log, 49

A: Given, log749 To Evaluate log749

Q: Suppose that the functions h and g are defined as follows. h (x) = (3+x)(-4+x) g (x) = 1-7x (a) Find…

A: Given functions h(x)= (3+x)(-4+x) g(x) = 1-7x

Q: How should the coefficients a, b, and c be chosen so that the system ax + by – 3z = -23 -2 x – by +…

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Q: Toby and Rocco have 30, toys between them. If Toby has 11 of the toys, how many toys does Rocco…

A: To tell how many toys Rocco have.

Q: If f(x)= Vx and g(x)= 2x+5 , then state the domain of (gof Xx

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Q: 8 The value of the digit in the hundreds place in the number 653,841 is 1 the value 10 of the digit…

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Q: to give to her Father, Breanna had a ba sket OF apples . she de cided away 2 OF her appler plus 1 /2…

A: To find the number of apples that was at the beginning.

Q: 4) Find the sum of first 20 terms of the following series. 2+4 +6 + . a) 380 b) 400 c) 420 d) 440

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Q: The quadratic cquation can be generalized as ax²+bx+c = 0. Show that the value of x in tems of a, b…

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Q: Calculating body-mass index (BMI) is a way to gauge whether a person should lose weight. Doctors…

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Q: TOPIC: APPLICATION OF LINEAR EQUATIONS A gardener can mow a lawn in 3 hours. After 2 hours, it…

A: Let total lawn to be mowed= 1 unit

Q: A electronics retailer list the sales (in thousands) of certain products in three cities for the…

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Q: Suppose that y varies directly with x, and y=20 when x=32. (a) Write a direct variation equation…

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Q: a. Complete the table: Multiples Width of largest shape Width of smallest Width of medium shape…

A: answer is in next step

Q: Consider the following illustration and determine what type of angle is being represented.

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Q: 3. How many groups van can be formed from 8 students taking at least two at a time?

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Q: 490n – 12740 The equation P = represents a computer manufacturer's profit P when n computers are…

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Q: Solve the system of equations 5x – 5y = 130 8x – 2y = 406 by converting to a matrix equation and…

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Q: * 3 = 234, 5

A: Topic = Algebra 23*3=2345

Q: Given that y= -3x + 4. Determine the value of x if y is equal to 10

A: Given equation y = -3x + 4 ,  We have to determine the value of x is y = 10

Q: Individual Practice: 1. Solve for the value of x in vx = 13. 2. Solve the equation vx +7 = 18. %3D

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Q: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the…

A: We will solve the given logarithmic equation and find the value of x.

Q: Consider the following table: Possibilities for a Possibilities for b x -4 Possibilities for c…

A: From the given table

Q: Use the fact that matrices A and B are row-equivalent. 1 2 1 0 2. 5 1 1 A = 3 7 2 2 -2 10 23 7 1 1 0…

A: Show that matrix A and B are row equivalent.

Q: Please solve

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Q: Find B+D and simplify, if possible. Write your answer in exact form. Select "Undefined" if…

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Q: Plot the numbers -2- and on the number line below. -3 -2 -1 0. 1. 2 3

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Q: Find a basis for the nullspace of the matrix. (If there is no basis, enter NONE in any single cell.)…

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Q: 2а + 1 + 1. Solve for b: b 3 II

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Q: A ballpoint pen and a notebook costs 100 pesos. The notebook cost 60 more than a ballpoint pen. What…

A: We can solve this as follows:

Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, –1, 2), (–1, 0, 2, 0),…

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Q: Solve the following logarithmic equation: log2(x – 3) + log2 x – log2(x + 2) = 2. -

A: Use logarithmic property to simplify the equation and solve it then

Q: Problem 3 Let R be any ring with ideals I and J such that J CI Let 1/] = {a +J| a e 1} Prove…

A: NOTE:- AS POSTED MULTIPLE PART OF THE QUESTION, I WILL ANSWER ONLY FIRST THREE PART AS PER BARTLEBY…

Q: Find the solution to the system of equations: x – 2y + z = - 6 y + 2z = – 3 x + y + 3z = 3 Preview y…

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