A. Express in factorial form: a) 7x6х5x4x3х2x1 с) 4x3x2x1

Q: Construct a two-column proof to prove the following by using factoring: Given: a³ - 11a²-9a = -99…

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Q: What is the coefficeint of a²b³cª in the expansion of (a + 2b + 3c)® ?

A: In the given question we have to find the coefficient of  a2b3c4 in expansion of a+2b+3c9

Q: Find x if meIBA- 2x + 14, MLCBA - 5x + 8, and MCBI - 27. O-6 O11

A: We have given m∠IBA=2x+14, m∠CBA=5x+8 and m∠CBI=27° From the given figure, we can find that…

Q: 1-The sides of a triangle are represented by the expressions 2x2 +4, 5x2-6x and 8x+3. Determine the…

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: 4. Show that if k is a triangular number, then 8k + 1 is a perfect square.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Theorem mDF : 52' D 162

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Q: 4. a) Find (123, 456) and find integers x and y such that 123x + 456y = (123,456).

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Q: 4. Describe all zero-divisors and units of Z6 O ZOQ

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Q: Prove that multiplication is associative in Q.

A: Prove that multiplication is associative in Q. Let r, s, t be in Q. Then  r=ad, s=be, t=cf; such…

Q: Insert either , or = in the area between two expressions to make a true statement. 7. |-3| 11 11

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Q: Show that if m is an integer then 3 divides m3−m.

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Q: (b) Let z = 24695 + 99288 i. Enter a square root of z, in maple syntax, in the box below.

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Q: Show that 4(44!) + 49 is divisib by 47

A: Given: To show that 4(44!)+49 is divisible by 47. To explain the given statement as follows,

Q: what is the element a34

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Q: , ABCD-EFGH. Find AB. *

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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 greatest common divisor of a, b, and c and write it in the form ax + by + cz for integers…

A: Given that, a = 14  ;  b = 28  ;  c = 35 Then the greatest common divisor of a, b and c is the GCD…

Q: a box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in.…

A: Volume of a box =  Length × Width × Height

Q: Given that a + bv3 = V151+ 28V3, where a and b are positive integers, calculate the value of a and…

A: To find- Value of a and b.

Q: 9. Use fix) = 3-4 and gix)-5-2' to evaluate the expressions in simplitied form: * (g )

A: We have the given functions as f(x)=3x-4g(x)=5-2x3   We have to find (a) f∘g(x) (b) g∘f(x)

Q: tind the resolvent kernel and Solut of yox) = + by Alternative procedure

A: We have to solve the given integral equation by finding the appropriate kernel function.

Q: Find all integer solutions to 105x+343y=35 Using Magic Box | Elementary Number Theory

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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: »(플), 43. Evaluate the cube root of z when z = 32cis 3

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

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Q: 7. Circle all the expre-

A: INTRODUCTION: To make it less hard or difficult; to make it simpler or easier To condense an…

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: Expand the expression: (4r – 3)' = %3D Submit Question

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Q: All perfect squares are divisible by 2. A.) True B.) False, counterexample of 16 C.) False,…

A: Numbers that are divisible by 2 are {0,2,4,6,8 ,10 } Perfect sq 1X1=1 2X2=4 3X3=9  4X4=16 5X5=15…

Q: Find all sollutions in integers of 34x+8y=6

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Q: Develop a simple expression for the entries of A", where n is a positive integer and 1 A = -IN -IN

A: To get a simple expression for the entries of An, where n is a positive integer. A=112012

Q: Let R = Z10 O Z100- (a) How many units does R have? (b) How many zero divisors does R have?

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Q: The positive integers that are divisors of 68 are

A: We will use multiple method to find all the divisor of the given number .

Q: Number Theory

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Q: JsinsetI

A: We are authorized to solve only 1 question, please repost remaining  Domain and range of function

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

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Q: (c) Prove that n? + 1 is not divisible by 3 for every integer п.

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Q: How many zero divisors are in Z,, where n = 32547?

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Q: b) Expand by using Binomial Theorem (2x + 3)*.

A: Apply binomial theorem:  a+bn=∑i=0nnian-ibi

Q: are Qunctionwrite walltn in the form Waf(z) 242

A: Here, given that: u(x,y)=x2-y2+x, v(x,y)=2xy-yw=u+iv

Q: Find a polynomich of Jegree 4 with Zeros x = 1₁ x=2, and x=i.

A: Given polynomial has zeros x=1, x=2 and x=i. Therefore (x-1) ,(x-2) and (x-i) is factor of…

Q: Find the product of - 10 - 6i and its conjugate. Question Help: DPost to forum

A: Given -10-6i

Q: 10) Let pla)= axtx?_4X. Simpify plad -pQ-)

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Q: In each part, find the greatest common divisor (a, b) and integers m and n such that (a,b) =am+ bn.…

A: Given:                  a= 0 and b=-3;   To determine:                         The integers m and n…

Q: the acdjainbaf square of As of 2.

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Q: 15. If mZABD = (6x + 26)" and MLACD = (13x – 9)' , find mAD.

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Q: (2) 13 Place all answers in the following blank, separated by commas:

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in.…

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Q: 5) Given that MZDEF =87° , find MZDEG and M2GEF %3D

A: NOTE: Refresh your page if you can't see any equations. . here we have