Find, If possible, A + B, A- B, 2A, 2A - B, and B +A. (If not possible, enter IMPOSSIBLE In any single [1 2] [-6 -2

Q: Determine whether it is possible to express 1 as a liner combination of 1 = m· 44 + n· 91 ,. for…

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Q: Show that for any integer n, n² – 2 is not divisible by 3.

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

Q: What is the coefficient of x' in (3-x)10

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Q: Does 2|0? O Yes, because 0 = 0· 0. O Yes, because 2 = 0 · 0. O Yes, because 0 = 2 · 0. O No, because…

A: We have to check

Q: Show that for any integer n , n2 – 2 is not divisible by 3.

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Q: Find integers ? and ? such that 3220? + 6006? = gcd(3220,6006).

A: Remark: The greatest common divisor (gcd) of two integers is the greatest integer that divides both…

Q: Find all integers x + 3 such that x – 3 is divisible by x – 3. |

A: To find all integers such that x^3-3 is divisible by x-3

Q: so-Z of what is 21

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Q: Prove that if for some integers a, b, c we have that a + b3 + c* is divisible by 9, then at least…

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Q: 2. What is the quotient of and?

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Q: Use the following diagram, with OABCD. (3x+5)° (4х-7)°

A: A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral with each pair of…

Q: Find all possible values of P in x^2+10x+P=(x-A)(x-B) if P, A and B are all whole numbers

A: To find all possible values of P in x2+10x+P=(x-A)(x-B) if P,A and B are all whole numbers.

Q: Find x and a21 if 5x - 3, X+2, and 3x - 11 form an arithmetic scquence

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Q: Find all four-digit numbers abba with the property aa . 10b= abba if a is not equal to b.

A: We know if abcd is a four - digit number then, abcd = 1000a+100b+10c+d

Q: How to find the last two ditgits of 2^2021 ?

A: Solve the given problem.

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

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Q: Show that ∗ : R × R → R given by         (a, b) → a + 4b2 is a binary operation.

A: Given for all real number a and b

Q: Is the statement, "If a number is divisible by 2 and 3, then the number is divisible by 6" true or…

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Q: True or False: There are integers x, y such that 15 = 215x + 497y. O True O False

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Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: The digits 1, 2, 3, 4, 5, A and B are all different and nonzero. Each of the two six-digit integers…

A: So for this problem I'm attaching hand written solution.

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

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Q: 5. Given a real number x and a positive integer k, how many multiplications are used to find kx by…

A: Given,A real number x and positive integer kTo find: Total number of multiplications used with the…

Q: If x is odd, then (x^2+3)(x^2+7) is divisible by 32

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Q: SHOW THAT 3^2N - 1 IS DIVISIBLE BY 8 FOR ALL POSITIVE INTEGERS.

A: We prove this by induction.

Q: Find an integer that leaves a remainder of 2 whan divided by either 3 or 5, but that is divisible by…

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Q: Find the term of (a – 2b)3 that has b in it. |

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Q: Let a be an integer such that the remainder of dividing a by 17 is 15. What is the remainder of…

A: We will find out the required value.

Q: 4. Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can…

A: We have to find the sum of all divisor of 5020 and then the amicable pair of the number.

Q: Let the binary operation *

A: Given,          a*b=a+2b where a and b are real numbers

Q: How a single interpretation is possible for μ1 – μ2?

A: The parameter of interest is the difference in population means, μ1 - μ2. Where, μ1 and μ2 are the…

Q: 2- w = - w

A: We have given a complex number property;

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

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Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: Show that a6-1 is divisible by 168 whenever (a, 42)=1.

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

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Q: R.2. Show that among 29 distinct integers, there must be a set of 5 integers all of which have the…

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Q: 14. Perform the indicated operations. (3x² - 9) + (3x² + 4x + 9) - ( - 6x² + 4)

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Q: In a round-robin chess tournament, each player is paired with every other player once. The formula 2…

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Q: Find all x such that 7x+3 is divisible by 9.

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Q: EV2K –1 . Write out, simplify, and leave exact: k=2

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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: Compute  7!/3!(7-3)!

A: Obtain the value of 7!/3!(7-3)!:

Q: The Greatest Common Divisor of two prime numbers a and b

A: Prime numbers are those numbers which have only two factors one factor is 1 and other factor is the…

Q: 7-メナ メ= t ४%= +" Find az -1/3

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Q: For natural numbers k,m,n, and p, let k be the greatest common divisor of m and n, and let p<k. The…

A: Theorem: The greatest common divisor of m and n is the least positive value of an+bm where a and b…

Q: For all numbers x , x4 >x true or false

A: Given, All number x We have to find Whether    x4 &gt;x        is true or false