16. Which of the following congruencies has NO solution? . A. 24x = 18(mod 39) B. 5x = 4(mod 10) C. 15% = 6(mod 21) D. 15z = 6(mod 36)

Q: Solve the following systems of equations. (a) x = 4(mod 5) and x = 7(mod 11) (b) 3x = 8(mod 10) and…

A: Given: a)  x≡4mod 5 and x≡7mod 11 b)  3x≡8mod  10 and 2x+4≡9mod 11

Q: Which of the following expressions are equivalent to + 6n2 + 12n -? n 18n + 38 A 6n (n+2) 18 (n+2) C…

A:

Q: 9x + 7y = 9(mod 15), The solutions of the following system {5x + 1ly = 13(mod 15), are x = 2(mod 15)…

A:

Q: 3n³ + 20n² + 5 is O(n³)

A: Given: The given expression is 3n3+20n2+5 is 0(n3),

Q: 19. Obtain the eight incongruent solutions (a) 5x+3y = 1 (mod 7) 3x + 2y = 4 (mod 7). (b) 7x + 3y =…

A:

Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: -10- The dlagram shows the locations of Noah and Ben after swimming in different directions from a…

A:

Q: Let s={xEZ:x+2E6(mod 15)}. Then S is *

A: a countable set

Q: If x mod 5 = 2 and y mod 5 = 3, then xy could be D 306 D 843 D 342 O 197

A: See solution below

Q: 7. If 23a+7 = 16a+1, what is the value of a ?

A:

Q: 21 Jlguill The solution of the linear congruence 4x = 5(mod 9) is? %3D 6(mod 9) O 10(mod 9) O 8(mod…

A: We use Euclid division algorithm.

Q: 12 1 If R = and S= 31 0 that R² = 2R+cS. (5 pts) 0 1 find a number c such

A:

Q: (c) 6x mod 11 = 1 (d) x + 2 mod 9 = 0

A: We have to solve the given relation.

Q: 7. Which of the following has the correct solution given for x? Check all the apply. O 3x -3 = 24; x…

A: GIVEN(1)3x-3=243(9)-3=2424=24x=9 is correct solution

Q: Ave the following fancEions contindous FCx)sメーZ メー2 てト=メ 1P 2) FCX)s X 3-5X +7

A:

Q: Q6. Identify the incorrect statement in the following: A. If e* = 2 then x = In 2. B. If In x = 2…

A: To find the incorrect statement we simply use basic properties of natural logarithm function.…

Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 18 2

A:

Q: 6. Solve 11x = 4 (mod 21) (a) 8. (b) 4 (c) 11 (d) has no solution

A: given 11x≡4 mod 21 since gcd11,21=1 thus, we can write 11x=4+21y for some y

Q: If x108 = 1(mod 109) then possible value of x is (а) 108 (b) 218 (c) 109 (d) None c Select one: • bx…

A: Find the possible value of x If x108= 1(mod109).

Q: Solve the following re is correct with a proo a = 3 with a = a -1 +2k for all

A:

Q: given the following: A = {x ∈N : x2 ≤ 50}, B = {x ∈Z : −7 3 ≤ x < 4}, C = {x ∈R : |x| < 2} and D =…

A: Note: There are many subparts in the above question. So I will give the answer of the first four…

Q: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

A:

Q: Solve : ex+ay =4 (mod 13) E 2 2 (mod 13) Using elimination

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Q: Is 12n + 18 equivalent to (2n + 6) (n + 3) ? True O False

A: Answer: True.

Q: 2n if 1sn< 457 | Зп +1 b) {a,} where a, ={ne"* if 457 <n< 2100 4n –1 if n22100 5n+7

A:

Q: Converges or diverges

A:

Q: i need to find the value of m 12 = (m*28)mod 113

A: Solution is given by using Diophantine equation and extended Euclidean algorithm as follows

Q: The solution for x =10(mod11) is: а) 5 b) 6 c) No solution d) 4

A: The objective is to find the solution for x8=10mod 11

Q: 8. A recent survey askec According to the surve for a raise; and of tho raise. If a woman is se a. P…

A: Let the two events be defined as : A and B such that, A = asking for rasieB = got a raise a.…

Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

A:

Q: Given 3 * 4.52 = x(mod 53), Here x is equal

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: (d) utive but no two X's can be consecutive? How many permutations are there, if all three of the…

A:

Q: P= 5 mod 8 show Ps² +byd = I mad 3P has for in teger S,y. ho Solution

A: Given: p≡5mod8 To show that px2+6y2≡1mod(3p) has no solution for x,y ∈ℤ

Q: Solve for x using a =b mod m) iff mlla-b): 8 I lx-19)

A:

Q: 6- The special sotution 5014tion to the र१पच्दं०n . -ya)=x"e? 1 XP A/ Xex Ğ d/other than that

A:

Q: 4. 2x = 3 (mod 5)

A: A congruence ax≡b(mod n) has a solution only if  gcd(a,n) divides b. Also to solve a congruence…

Q: ind the solutions of the following system: x + 2y = 1 (mod 5) 2x + y = 1 (mod 5) + 3y = 1 (mod 5)

A:

Q: 3. Solve the systam using either sab stitetion of ellmattion

A: We solve the given system of equations buy using the substitution method.  Step1 : From the second…

Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 20 30 18 O 60

A:

Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 20 30 18 O 6 0

A:

Q: b. x = 4 (mod 5) x = 2 (mod 3) 2x = 5 (mod 3) 5x + 4 = 5 (mod 7) d.

A:

Q: 5. Let C = {x ∈ Z|x ≡ 7( mod 9)} and D = {x ∈ Z|x ≡ 1( mod 3)}. (a) If C ⊆ D? Justify your…

A:

Q: If S = {"#1; n € N}, then inf S = 0. Select one: OTrue O False

A: The given statement is false. Because inf S=1

Q: Let 38c2 312 3 3104 S = 1+ 3°c + 2! 3! 4! If In S = 2187, then find c. 23 O 7 27 31 47 19

A:

Q: Answer each of the following questions. V ? 1. 23 = 56 mod 4 True 2. 24 = 154 mod 13 False 3. –4 = 4…

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Q: Which of the following is the solution set of In(5x – 7) < In(2x + 8) (5, 00) (-00, 5] (-00, 5) [5,…

A:

Q: 14 - Since x is an odd number, which of the following is an even number? A) (X + 1) +1

A: Answer and explanation is given below..

Q: 4°c2, 4°c3 Let S = 1+4³c+ 2! 412c4 + 4! 3! If In S = 1216, then find c.

A: Here we use exponential series.