Prove that the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a belongs to set of real numbers (R).

Q: There is a real number whose product with every real number equals zero. a. Some has the property…

A: Note: As per company guidelines we are supposed to solve 1 question. So, kindly repost other…

Q: Find all integer x satisfying the condition x = gcd(4x + 3, 2x). Justify your answer.

A: To find all integer x satisfying the condition  x=gcd4x+3,2x

Q: Prove: Let a > 0 and b > 0 then either a > 0 and b > 0 or a < 0 and b < 0. where a…

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Q: A(n) ______ ____________, denoted [a, b], consists of all real numbers x for which a ≤ x ≤ b.

A: It is known that any closed interval a, b can be represented as an inequality a≤x≤b.

Q: There exists an integer x so that (2x<3) ^ (5x<-1)

A: We have to give a justification for given proposition.

Q: To show that ( n + a ) b = θ ( n b ) ( n + a ) b = θ ( n b ) for any real constants a a and b b…

A: Here we use the binomial expansion:

Q: Prove that the product of a negative real number and a positive real number is negative.

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Q: onsider (G,*) where * is defined as a*b3Da is the set of all non-zero real numbers

A: Let  G=ℝ-0For a,b∈G⇒a*b=ab2a,b∈ℝ-0⇒ab2∈ℝ-0a*b∈G   The closure prosperity For…

Q: disprove

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Q: Let the domain of x be the set of real numbers. Then 3x, (x3 = x) is a false statement O a true…

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Q: Deduce expressions for the sum of the first 2n positive integers and the sum of the first n positive…

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Q: For some real numbers m and n, the list 3n2, m2, 2(n + 1)2 consists of three consecutive integers…

A: For some real numbers m and n, the list 3n2 ,  m2  , 2(n + 1)2  consists of three consecutive…

Q: What is the set of real values of c so that (A) [0, 1] (B) [0, 2] (C) [1, 2]

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Q: true or False For all number x, then |x| > 0.

A: For all number x then |x|&gt;0

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

A: Given: 6(-7) = -7(6) because of the commutative property of multiplication and if 2 = x+3 then x+3 =…

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 202n–3 19 cn 4 ac2 n-3 C - B

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Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

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Q: Show by contraposition that for any real number x if -5 <x<4 then x2+x- 20 <0

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Q: Give an example of a triple (a, b, c) of real numbers such that abc[a][b][c] = 2021, where [x]…

A: Give an example of a triple (a, b, c) of real numbers such thatabc[a][b][c] = 2021, where [x]…

Q: (1+ V5 (3 – V5) Without using a calculator, express in the form a+bV5, where a and b are integers.

A: The given expression is: 1+53-5-2 Express in the form a+b5, where a and b are integers. Rewrite the…

Q: Prove that for all real numbers a, b, c, d, the quantities a – b², b – c², c – ď² , d – a² cannot…

A: We will try to prove the given statement by contradiction.   Let us assume that all of a-b2, b-c2,…

Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

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Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: Let a,b be two real numbers and define a*b=ab+a+b. What is the identity element for this operation?…

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

A: According to the inverse property of multiplication: ab×ba=1 i.e. the product of a fraction with its…

Q: If a, b, c are non-zero real numbers, then bc ca ab ca ab bc vanishes, when ab bc ca ca 1.1 -+- 0…

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Q: Give an example of numbers a and b such that |a + b| &lt; |a|+|b|.

A: To give an example of numbers a and b such that

Q: Let a be a real number. For 1 A = 2 - fınd A² . a -2 – 2a 4 + 4a 2a? – 4 -2 | - None of the others…

A: First option is correct. See the attachment.

Q: What is the definition of z'? Show that if one value of z' is real, then all other values are real.…

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Q: Give an example of a triple (a, b, c) of real numbers such that abc[a][b][c] = 2021, where x|…

A: We need to give an example of a triple (a, b, c) of real numbers such that abcabc=2021. If a, b, and…

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

Q: Find the value of a such that 1 0. 3 2 2 a- 2

A: I have solved the determinant

Q: Prove that x (x-2) is always a negative real number if x 1-Ai for some real number A.

A: The given number is  x(x - 2) x = 1 - Ai

Q: a. Show that for any real number x, if x> 1 then | x4 |≤| 23x4 + 8x² + 4x |.

A:

Q: which

A: Explanation : a )  Let the three consecutive positive integers will be n, n+1 , n+2. If we sum all…

Q: If A is a set of real numbers that is not open, then A is closed.

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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: True or False Let a, b, and c be elements of real numbers. If a + b = b + a, then this property is…

A: Given that  Let a, b, and c be elements of real numbers. If a + b = b + a, then this property is…

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

A: Here, we need to fill in the blanks. Given: There is a real number whose product with every number…

Q: In P2, find all real numbers a such that x - ax +1-a? is in the span of x -2x+1, x-1,and3x -2x-1. Oa…

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Q: (a) Prove that 2x5 + 3y% > 5x²y³ for all positive real numbers z and y. (b) Generalise the result of…

A: Note the result : AM≥GM Generalized application :  Suppose a1,a2,a3,……,an are positive…

Q: Prove that the absolute value of the product of two integers is equal to the product of the absolute…

A: Prove that the absolute value of the product of two integers is equal to the product of theabsolute…

Q: (d) The set of all real numbers greater than 1 and less than 7.

A: A set builder notation is a set which consists of all the conditions a variable should satisfy.

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

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

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

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.