2) Which expression is a factor of n2 + 3n 54? A) n+ 6 B) n+9 C) n² +9 D) n-9

Q: what is 7n+2=4n+17

A: Given,  7n + 2 = 4n + 17

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate ?(x)

A: given , expression :- 32x+7 we have to prove that given expression is divisible by 4 .

Q: What can you conclude about the numbers m and n if X " = 7 and r is an even number and m and n are…

A: The number that is divisible by 2 is called the even number and the number that is not divisible by…

Q: Is the statement true or false? If an odd number is less than 15, then it is prime. False Give a…

A: We have to check

Q: 8. If * is defined as a*b = 3a+b where a and b are real numbers, what is 4*3?

A: Given operation is a*b = 3a+b

Q: Prove that 5 does not divide 5n+3 for any integer n.

A:

Q: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

A:

Q: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

Q: Identify the property of integers being illustrated in 1[2( 4)] = (1 • 2)(¯ 4).

A:

Q: W found that 2,3,5,7 and 11 are not factors of 211. Can we conclude that 211 is prime? Why or why…

A: To check whether 211 is prime number on not.

Q: 10. If the product of N consecutive posi- tive integers is divided by N, the remainder is always (A)…

A:

Q: 3. Are the following statements true or false? Justify your conclusions. (a) For each integer a, if…

A:

Q: What is the multiplicity of the factor 5 for the number 5°1001º11?

A: Given number is 551001011 . we have to find the multiplicity of the factor 5

Q: Determine all prime numbers a, b and c for which the expression a² + b² + c² – 1 is a perfect…

A: We have to determine all the prime numbers a, b and c for which the expression a2+b2+c2−1 is a…

Q: In the diagram below, ABCD is a rectangle with side lengths AB = 3 and BC = 11, and AECF is a…

A: Properties of rectangle Opposite sides are parallel and equal. Each interior angle has measure of…

Q: If the product of two integers is 2'3*5?7!" and their great- est common divisor is 2°345, what is…

A:

Q: 4. Prove by contradiction: VmeZ, 7m+4 is not divisible by 7

A: Contrary suppose that,   m is an integer such that 7 m+4 is divisible by 7. By using the definition…

Q: Find the order of 2 2; in C

A: Order is 8

Q: Find the number of divisors of n= 2020. %3D (а) 24 (b) 6 (c) 12 (d) None Answer B C. Submit

A:

Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: What is the number of nonnegative integer solutions of the equation x1 + x2 + x3 + x4 + x5 = 15,…

A:

Q: 1. Simplify the expresslon below. @3x ®. x12 ©3x12. . . n... O x64

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Prove by induction that the expression for the number of diagonals in a polygon of n sides is…

A: Solution: Let Dn=nn-32 We will prove by induction that for all n∈ℕ, the total number of diagonals in…

Q: How many integer solutions to x1 + x2 + x3 + x4 = 32 are there for which x1≥6, x2 ≥5, x3 ≥3 and x4…

A:

Q: of its prime factors. 2. 24

A:

Q: Prove that 4 divides 6 7" - 2.3" for all integers n 20.

A: We need to prove that 4 divides 6.7n-2.3n for all integers n≥0.

Q: Prove that if a and b are both odd integers, then 8 (2a2+36²).

A:

Q: What is the coefficient of p5q5 in the expansion of (p+q)10?

A:

Q: 2. What is the prime factorization of 15x y? O 3.5 2y O 3.5 x y Y O 15 - x * y Y 3-5 22 y y

A:

Q: If m is a positive integer, does 6 divide (2m)(m+2)(3m+3)? True False

A: Here, the given number is: (2m)(m+2)(3m+3)=2(m(m+2))3(m+1)=6m(m+1)(m+2) because multiplication is…

Q: Number Theory

A:

Q: 2) 10! + 1 is not divisible by 11 a) True b) False

A: By using Wilson's Theorem, (p-1)! ≡-1 (mod p) or (p-1)! + 1 ≡0 (mod p)

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers

A:

Q: Determine all prime numbers a, b and c for which the expression a² + b° + c° - 1 is a perfect…

A: We have to find the prime numbers a, b and c such that the expression a2+b2+c2-1 is a perfect…

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers n.

A:

Q: Let m and n be positive integers. Show that mZ+nZ= (m, n)Z.

A: Given: Let m, n be two positive integers. To prove: mℤ+nℤ=m,nℤ. Proof: Let I=mℤ,J=mℤ Since…

Q: The number of divisors of a natural number n is 15 then the number of solutions (n,m) of n-m? = 4(m…

A: Here, the given equation is n-m2=4. Here, n∈N and m∈I. Given that, n must have 15 factors. If m=0,…

Q: Find all positive integers n for which n1º +1 is divisible by 10.

A:

Q: If  n×k divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is…

A:

Q: Can you think of the smallest number N such that ot can be expressed as a product of the two factors…

A: We have to find out the number N that can be expressed as a product of the two factors which are…

Q: 14. If mZABC = 115°, find MZADB. (4x + 6)° E A (6x – 11)°

A:

Q: 1. Use Direct Proof to prove that the product of two consecutive integers is divisible by 2.

A: We have to prove that product of two consecutive integers is divisible by 2.

Q: is ' (3n– 1)? n=1

A:

Q: Suppose that A is a 7 x 15 m How can Proposition 6.2.5 h.

A: Given, an m×n matrix A, the row space of A is the column of AT:            Row(A)=Col(AT).

Q: Abby notices that for the first twenty perfect squares, each square is either a multiple of 5, one…

A: If n is a natural number, then n2 can be written as 5k- 1,5k, or 5k +1, where k is a whole number.…

Q: 3. Prove that if n is a triangular number, then so are 9n + 1, 25n + 3, and 49n+ 6. Hint: Recall…

A:

Q: 3. Prove that if n is a triangular number, then so are 9n +1, 25n + 3, and 49n + 6. Hint: Recall…

A:

Q: . What is the answer in (1) in the coefficients table?

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.