If a, b e R, prove the following. (a) If a +b = 0, then b= -a, (b) —(-а) — а,

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A: Given: An isosceles triangle with a base of length b and height of h has a rectangle inscribed. The…

Q: An operation * is defined on the set of real numbers by a * b = a + b – ½ ab. What is (3 * 2) * 2? *

A: The rational number and irrational number are together called real numbers. An operation is a rule…

Q: -. For any integer m and any real number x, if x is not an integer, then [x]+[m - x] = m-1.

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Q: State all real-number values of x which will make this statement true:    x  + 4 > 5 – (1 – x)

A: The given inequality is  x + 4 > 5 – (1 – x)

Q: ∀ (x,y) ∈ ℝ^2 (x and y are real numbers), then | |x| - |y| | ≤ |x - y|

A: Case 1: Suppose x≥0 and y≥0. By definition of modules function, we have x-y=x-y≤x-y. Case 2: Suppose…

Q: What two nonnegative real numbers with a sum of 50 have the largest possible product? The numbers…

A: We are asked to find the largest possible product of the two non negative number whose sum is 50

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Q: Prove that if a, b e R, then (a) -(a+b) = (-a) + (-b), (b) (-a)·(-b) = a · b,

A: (a) Proof of the fact -(a+b)=(-a)+(-b): Since -1 is additive inverse of 1, hence  −1+1=0   (zero in…

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: These statements about real numbers x are equivalent: (i) (ii) x is rational x/2 is rational (iii)…

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Q: Multiplication on the number pairs is defined as follows: (a, b) · (c, d) = (ad + bc, ac + bd).& in…

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

Q: Find two positive real numbers such that they sum to 105 and the product of the first times the…

A: Let the first number is x and the second number is y. Given sum of two numbers is 105 That is…

Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given 3(x+4)=3(x)+3(4)…(1) We need to state the property of the real number that justifies the above…

Q: Using an algebraic proof, prove that x is an even number, then x2 + x is an even number.

A: Here we have to prove that, If x is an even number, then p(x)=x2+x is an even number.

Q: From the set {-2, 6+3i,  8i, 3.25, ¼ , √(-36), √5, 12,  -1/3, 9} i) List the set of…

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Q: 2.) Describe the following sets using the two methods of writing set. a) The set of integer greater…

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Q: Real numbers are either rational or irrational Select one: O True O False

A: 1) True Real numbers is union of rational and irrational numbers. They form a disjoint set. So every…

Q: What is the most appropriate translation of the given mathematical symbols below? * να R, α > 0,…

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

Q: 6 181 元 - 15 0.8

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Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given a equality, 3(98)+3(2)=3(98+2) We need to state the property of the equality.

Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given:  if 2 = x + 3, then x + 3 = 2 is true because of the symmetric property of equality.

Q: Set of real numbers and the set of irrational number. is it  a. equivalent b. equal c. both d.…

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Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given that : The statement , [(17)(4)](25) = (17)[(4)(25)]

Q: الموضوع 1. -2 so A-4I- A -41? = -4. -3 -2 3- -4 A-4年 。 3. to not of th above

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Q: The of any negative real number is positive. negative square а. Given any real number а, the square…

A: Part (a) - Blank space = a is positivePart (b) - Blank space = negative real number then a2 is…

Q: by x * y = 1 + x + y on the set of real numbers. Show that * is commutative but not associative

A: Given: x*y =1+x+y To show: * is commutative and associative.

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: I am having trouble figuring out question b. Could you please give me an idea how to solve it?

A: Given that

Q: Va - 1 3va - V5 Rationalize the denominator of Assume that all variables represent positive real…

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Q: R.3. Let [a, b] be an interval on the real number line (with a < b). Prove that a,b]-[0,1].

A: We have to find a continuous bijective from a,b to 0,1 to show that a,b~0,1

Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given statement: 7+3+-8=7+3+-8

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Q: • 21 real imaginary 2)

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Q: Moving to the next question prevents changes to this answer. 11 Vbe the set of all ordered pairs of…

A: Use definition of zero element and calculate

Q: 2) (a) Find all integer solutions to the equation 161x + 71y =1. (b) Find all integer solutions to…

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Q: Explain the Pythagorean Theorem, its proofs and applications. Between 200-500 words

A: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the…

Q: 13. Find the real numbers missing from the following equation (that is, rewrite the equation with…

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Q: b) Rewrite the statements in the form of “∃ _______ X, _______.” i. Some exercises have answers. ii.…

A: Given statements are ; i. Some exercises have answer. ii. Some real numbers are rational.

Q: An algebraic number is any real root of an equation ao + a₁x + +anx"=0, where the coefficients a;…

A: We use properties of Countable union of countable sets and set of polynomials.

Q: Two problems in Mathematics came out in the latest ATBUISU about Algebra and Analytic Geometry. How…

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Q: There is a real number whose product with every number leaves the number unchanged. a.Some __has the…

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Q: 11! -0.2³ . 0.2* . 0.6* 4 · 0.2 - 0.6° 3!4!4! = 0.019

A: Given: PX=11!3!4!4!×0.23×0.24×0.64

Q: Prove that –(|a| + |b|) ≤ a + b ≤ |a|+ |b| for any real numbers a and b. (Hint: Use cases when…

A: We have to prove the condition

Q: Example 4: For each pair of real numbers, place one of the symbols in the blank. a) 2 b) -5 1 c)

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Need assistance with these. 1. a) From the set {-5, 3+4i, 0.25, 6, 1⁄2 , √(-49), √2, 3i, -1/5, 8,…

A: Solving the questions according to the question numbers: 1) Natural number = 6,8 Rational number =…

Q: The sum of an irrational number and an irrational number is irrational.

A: The sum of an irrational number and an irrational number is irrational. The above statement is…

Q: True or False? 5. Let x and y be integers. If 5x − 7 is even, then x is odd. 6. Let x and y be real…

A: To find which of the above is true or false :-

Q: For any real numbers a and b. it is true that labl-3 3 7 ab)+7 O(A) O (C) 0 O (D) ∞ (E) 3 lab-3 7…

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Q: A b- -1, a-1 n b- 1, a-0 b = 0, a- any real number b = 1, a- 1 b = any real number, a = 1 CCCCC

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Q: state the property of equality or the property of real numbers that justifies each of the…

A: Given, -1(x+2)=-(x+2)