If a is a real number and n ≥ 2 is an integer, then which of the following expressions is equivalent to n√a , provided that it exists?(a) a-n (b) an (c) 1/an (d) a1/n

Q: In the proof of square of an odd number is odd, if you take a=2k+1 is an odd number, where k is an…

A: Let a be an arbitrary odd number. By definition, an odd number is an integer thatcan be written in…

Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

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Q: Show that √2 + √3 is irrational.

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Q: B. Find the value of k that makes x2 + (k + 5)x + (5k + 1) a perfect square.

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Q: 10. Consider the binary operation # on Q, the set of rational numbers, defined by h#k = 2h – 3k.…

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Q: One of the roos of the cquation x+3x-6=0 1s

A: The given equation equation is x2+3x-6=0

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: 8 53 - 4 9 3X tex -X'-7X -x'+7=0 a. How many non-real roots does the equation above have? Justify…

A: Given: 3x8+6x5-x3-7x4-x9+7 = 0 To find: (a) Number of non- real roots of the given equation. (b)…

Q: The cube root of any negative real number is negative.a. Given any negative real number s, the cube…

A: It is given that the cube root of any negative real number is negative.

Q: Prove: For any positive integer n, x™1 - yl = (x- y) xy' (You may use the laws | of exponent in your…

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Q: use proof by contradiction to show that the number is irrational. 4/11

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Q: what is the coefficient of x^4 in (2x+1)^5

A: 2x+15 Comparing with a+bn, we get a=2x,  b=1  &  n=5

Q: In the diagram, ABDE is a rectangle, ABCD is equilateral, and AD is parallel to BC. Also, AE = 2x…

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Q: at a, b and c be real numbers such that a #0 and ac+bc+c 4ac.

A: Given data is : a , b and c are real number such that a≠0 and ac+bc+c2<0 Show that b2>4ac

Q: 1. Identify whether the number is rational or irrational. 1. V3 une mia 2. V144 ib 3. 0 25 4. 100 er…

A: Rational numbers: The numbers which can be expressed in the form of pq, where p and q are integers…

Q: What is the number of nonnegative integer solution of the equations xi + x2 + x3 + x4 + x5 = 27…

A: Given x1+x2+x3+x4+x5=27 where x1≥0, x2≥1, x3≥2, x4≥0

Q: given A={x I x2 - 1 = 0 }, B = {x I x2 + x - 2 = 0}, and C = {x I x3-x2=0} A,B,C rational number…

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Q: Use a calculator to find a rational number r such that |r − π2| < 10−4.

A: Consider the given information. |r − π2| < 10−4 The absolute the function is defined as.…

Q: (b)If x is so small that its fourth and higher powers may be neglected show that (1 + x) + V(1- x) =…

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Q: Show that there is no rational number r satisfying 2r = 3.

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Q: If f(x)= 10x -37x+11, then there are two real numbers a<b such that fla)=f(b)=4, and there is a real…

A: Please see the answer below

Q: When P(x) is divided by (x-1), the remainder is 3. When P(x) is divided by (x+1), the remainder is…

A: When P(x) is divided by (x-1) then the remainder is 3. ⇒ P(1) = 3 When P(x) is divided by (x+1) then…

Q: If k is a positive integer, find the (n!)k + 6 Σ ((k + 6)n)! n = 0 R =

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Q: 12 Given that, for all values of x, 4x-8x2-12x + 11 (2x + k)Q(x) + where Q(x) is a quadratic…

A: Quadratic expressions

Q: Given that z = V3+i. (a) Find z10 and express your answer in the form a + ib, where a and b are real…

A: Given that  z=3+i Let z=reiθ=rcosθ+isinθ, then rcosθ=3, rsinθ=1 ⇒r=3+1=2 and θ=tan-113=π6. So,…

Q: If lim 12 00 k-1 (-1)*k 3x +4x +5 lim T-00 ar + 6x +7 34 then what is the value of the real number a…

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Q: 4. Show that the real number VV2 – 2 is algebraic. (Here 2 is a real number that satisfies (2)3 =…

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Q: If Q is a rational number, which statement cannot be true? O is a decimal number that terminates at…

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

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Q: :By equating the coefficients of various powers of x from the following expression (x + 1x3+3 x + 15…

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Q: D. We extend from Q20 to Q by another application of the method of ordered pairs, exactly as we did…

A: To explain: Rational numbers in terms of pair of coordinates using addition operation.

Q: 0. If k is a real number, then the real part of 2+i(ki – 3) is А. 2- k. В. -k. С. -1. D. k-3.

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Q: 2 0 Given that 3x² + p(1 – 2x) =-3. show that, for x to be real, p-3p – 9 2 0

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Q: nslate this statement into its symbolic form: "For every rational number here exists a real number y…

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Q: (а) 2 | п?. (b) 3| п3 — п. — п. (с) 4 | n4 — п.

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Q: The small positive integer n for which (1+i)?n=(1-i)ên is 4 12 2 8

A: Given:- (1+i)2n =(1-i)2n To find:- Smallest value of n for which give expression true

Q: If f(x) = 3x2 + βx + 4 and f(−1) = 12, what is the value of β? 2)     Show that If 2 is a root of…

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Q: Which of these, when simplified, represents an irrational number? (0.83) because the product of two…

A: As we know,                       An irrational number is a type of real number which cannot be…

Q: given f(x)= 3cx+2, for x&lt; 2                    -cx-8, for x&gt;2      find c so that f(x) is…

A: We have to find value of c so function is continous at x=2 ,where f(x) is given by:

Q: 1. Tell which property or axiom of the real numbers justifies each of the following mathematical…

A: 1)a) Given:              2x+y=2x+2y   Since here they are distributed through parentheses, it is a…

Q: Number Theory

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Q: a. Suppose that r E Q and r E Qª. Prove or disprove: The number (r – x)-1 e Qª. b. Prove or…

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

Q: , ABDE is a rectangle, △BCD is equilateral, and AD is parallel to BC. Also, AE = 2x for some real…

A: In the diagram, ABDE is a rectangle, △BCD is equilateral, and AD is parallel to BC. Also, AE = 2x…

Q: How many nonnegative integer solutions of x₁ + x2 + x3 + 4 = 12 are there in which no r; exceeds 4?…

A: The given problem is to find that number of nonnegative integer solutions for the given equation…

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: と 2. X.. Q3 「ニ」 Prove thete

A: We have to proof the given statement

Q: Show that the real number V2- 2 is algebraic.

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Q: Use complex analysis to prove the formula 2n n 7 7n V 3 n=0

A: It is given that

Q: The cube root of any negative real number is negative a.) Given any negative real number s , the…

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

Q: 9. What is the largest integer value of k for which the equation x2 - 6x + k = 0 gives a real number…

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Statements and Logic

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