The greatest common divisor of 9n + 10 and 10n +9 is Oa 10 or 19 оь. 19 O. None d. 1 or 19 Oe. 1

Q: 15) n(n*+5) is divisible by for each integer

A:

Q: 10 use n= n1c 16 +hlk-1 + h 16 +no pug of Rul e cf divisibility for 7 16,21

A: we have, n=nk10k+nk-110k-1+....+n1(10)1+n0 Let n=nk10k+nk-110k-1+....+n110+n0=7k for some integer k.…

Q: [The answers to the following two subquestions(a and b) are INTEGERS.Put ONLY the integer in the…

A: Given the expansion  a 2z3-3z9b y+z5+y-z5

Q: 7p The simplified product of 5m³n3 and p5 where m + 0, n # 0 and 10m4n p + 0, can be represented by…

A: We have to simplified the product.

Q: 2. 6n - 1 is divisible by 5 for n any positive integer

A:

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

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Q: 12 Find the term of (a – 3b)" that has b in it.

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Q: 21. Determine 61 +2j -4j + k

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Q: he notions of the greatest common divisor and the least common multiple extend naturally to more…

A: Solution Given

Q: The factorial of n is the product of all positive integers less than or equal to n. It is…

A: Note:Hey there! Thank you for the question! We have solved this problem using trial-and-error…

Q: Show that the the greatest common divisor gcd(16" – 4",17" – 2") is divisible by 3 for all n E N.

A: Consider the provided question,

Q: Discrete Math

A: According to the given information, Suppose that:

Q: the parentheses are gcd (5) Let a and b be relatively prime integers. Show that (a) (ab, a+b) = 1 or…

A:

Q: In Z6, show that 4 | 2; in Z8, show that 3 | 7; in Z15, show that 9 | 12.

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Q: Find the exact value of 1sin (14°) 2 + 1cos (4°)2 - 3.

A: Consider the given expression: sin14°2+cos14°2−3Use the trigonometric identity:sin2θ+cos2θ=1

Q: The greatest common divisor of a and a +5 is a. 5 Ob None O. 1 or a ed. l or 5 Oe. 1

A:

Q: 11+2 + 122n+1 is divisible by 133

A:

Q: Vn E N, nº – n is divisible by 6.

A:

Q: Suppose n is a natural number greater than 100. Alex and Jerry each compute the gcd(4n, 20n2 + 15)…

A: Given that n is a natural number greater than 100. Alex and Jerry computed the gcd4n,20n2+15 and got…

Q: Suppose that in a popular restaurant, 4 people can sit around a lazy susan table (a round table with…

A: Given" Total persons=6  Number of seats on round table=4

Q: 11. What do you obtain when you raise 27 to the 8/3 power ? * 1/3 of (27 to the 8th power)

A: Any number a can be written as , where b is any natural number. Also, 27 is a cube of 3, so 27 can…

Q: please explain in detail and clearly  i dont understand big o properly so i need extra clarifcation…

A: Please see the below picture for detailed solution.

Q: What is the coefficient of z12 in (6-12z)12 O a. P(12,6)* -612 O b. C(12,0)* -(1212) O . 1212 O d.…

A:

Q: How would you respond to Tawana, who claims that mn is the least common multiple of m and n in every…

A: Consider two natural numbers m, n.   Then, the multiples of m are m, 2m, 3m, 4m   and the multiples…

Q: Prove that 13n13 + 11n" is always divisible by 24.

A: Consider the given expression.

Q: Suppose m = apɑp-1*** a2ɑ1ao and n = bpbp-1*…* b½b¡bo are two numbers with the same digits so that n…

A: 7) a. Given that ai=bj. Without loss of generality assume that i>j. Now the value of the digit ai…

Q: [7 0] Consider A = 5 7 and find AA" and ATA and AA"A or explain why these products do not exist.

A:

Q: If 53*+8 - 253-, then the value of x is %3D Select one: 2. O a. 5. O b. c. Od. 3.

A:

Q: Prove that 13n13 +11n is always divisible by 24.

A: We prove this by induction on n.

Q: The greatest common divisor of two number 1, b(integer) are b O None of the mentioned 10 b+1 O

A: Answer is 1.

Q: what is the particular solution to the difterential equahion y's +e, subject to y l) = 4e %3D why…

A: Given differential equation is y'=-yx+ex we can write it as y'+yx=ex I.F. is I.F.=e∫1xdx=elogx=x…

Q: If z1 = -4 + j5, z2 = -3 - j2, and z3 = 3 - j2, what is the simplified form of 33 17 13 13 61 19 13…

A:

Q: 14. If m/ABC = 115°, find MLADB. (+ 6 (6r-11)

A: In this problem first, we need to find the x value from the given angle and then calculate the…

Q: (a) (10432); to Octal system (c) (13D9E)16 to Quinary system Find the integers m, n such that 18m +…

A:

Q: A recent study shows that 18% of adults in the US do not use the Internet. Suppose that 12 adults…

A: It is given that n =12 and p =0.18.

Q: polyhomial iS equivalent t0 2n + 5)²? O 4n? + 25 O -4n? + 25 O 4n? - 20m + 25 O -4n? - 20n + 25

A: Given,  A polynomial  -2n+52  We have to find the polynomial equivalent to -2n+52

Q: How can 26n 7m +4(10n - 6m) be rewritten? O 36n 1377 O 40n 9m O 662 317m O 357mn

A: To choose the correct option

Q: Having a following funclion af funcdion of au polf. IS +. 64 64 fly) = -ky 8. elsewhere o What is…

A: The probability density function gives the probability at each possible value of a continuous random…

Q: The greatest common divisor of a = 169! +1 and b= 170! +1 is Ob None Oc 34 Od 91 e 169

A:

Q: rn is not divisible by 3k +1 or n = 3k + 2.

A: Introduction: If a number a is divided by b, then there must exist an integer k such that, b=ak.

Q: 5. Find the value of AB. B AL 5 in 5 in X16 in

A: We have to find AB

Q: -)) In how many days does 7 masters paint the wall painted by 5 masters in 14 days

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Q: Obtain a + ib form of the ff: -i77 a. z = −6+9e

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: The number of generators of Z15 is 7 9.

A: ℤ15 is a finite group.we have to find the total number of generators in ℤ15

Q: Find the coefficient specified in each item. a) a4 in (6−1⁄2a)6

A:

Q: se mathematical induction to show    n ≥ 0, 7n - 1 is divisible by 6

A: Given: n≥0, 7n-1 To prove: 7n - 1 is divisible by 6

Q: Prime divisors of two numbers a and b are 2,3 and 5 and product of these numbers a and b is 5400.…

A: The prime factors of the two numbers are 2, 3, and 5 and the product of these two numbers is 5400.

Q: In a study of pain relievers, 50 people were given product A, and all but 11 experienced relief. In…

A:

Q: Abel says (6)- 6°. Is he correct? Explain.

A: Given statement  (6^3)^3=6^5 Is the given statement correct or wrong.

Q: 3. A divisibility test for divisibility by 13: а. Prove that 13|(10x + y) if and only if 13|(x +…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.