(i) Prove that for all ne N, n²+2 is not divisible by 4 (ii) "Given x € R, the value of |3x-28 is greater than or equal to the value of (x-9)." State, giving a reason, if the above statement is always true, sometimes true or never true.

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: My question is The product of two integers will have the same sign as the quotient of the two…

A: The given statement is true always ,becauseLet take two numbers x and yCase I x and y both are…

Q: If all variables in the expression 5/x10y – 4x/xy represent nonnegative real numbers, then which of…

A: Given,          The expression is 5x10y9-4xxy9 .

Q: Use the definitions  to show that the following statements are true. For example, to show that 5 |…

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Q: 1 which of the following is equivalent to 2x-4 O B. -4x²+6x + 5 0 4x²-6x-5 >0 E. 4-2x

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Q: what is the counter example for all numbers x,      x + x    >  x

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Q: x2-2x-15 x2-9 x-3 :x+-3.0,3 Which of the following expressions is equivalent to the one above?

A: Simplify the given expression.

Q: x²-2x-15 マ+3x-4 +5x+4 5-x What is the quotient in simplified form? State any restrictions on the…

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Q: Example 1. Evaluate the following: b) A" + (4B)"; c) (A + 2B)" 0 3 4 [-3 2 4 A =-1 and B =-1 8. -5 a…

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Q: Which of the following is NOT correct ? 3x (6+9)=3x6+3x9 is distributive 3x (6+9)= (6+9) x 3 is…

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Q: 5. Rewrite using absolute value notation. 1 2 4 b) 4-3 3 4 4-3-2-1 1 2 3 0 1 2 3

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Q: 2. |a + ib|= √a² + b² O True O false

A: This question is based on modulus of complex number.

Q: 2) + 2 <0 IX + 31 4,

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Q: 1. Can you reduce this expression?  (x2 + 3x)/ (2x - 1) 2. Aren't there math symbols available on…

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Q: P show that (α) |=1 = 12/

A: A detailed solution is given below.

Q: *(2 + 16) (a + 8)(x + 4) 16 where z # a + 8 Submit Question

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Q: b.) 3x-2y < 12

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Q: 14. The expression -3x- 5x+2 can be rewritten as which of the following expressions? x +2x A -3x-3…

A: Explanation of the solution is given below.....

Q: True or false: If a is any integer, then (5a + 2,7a + 3) =1. Justify your answer.

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Q: ) Recall that r > 0 for every positive real number r. Prove that if a and b are positive real…

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Q: 5. Which of the following is the value of 7-x+3 when x= -20? (1) 7 (2) 9 (3) 10 (4) 16

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Q: Prove by contrapositive that if 7x+9 is even , then x is odd

A: Prove by contrapositive that if 7x+9 is even then'x' is odd = proof by contrapositive suppise 'x' is…

Q: B. Find a number that provides a counterexample to show that a given statement is false x, x³…

A: For all number x, (x+1)(x-1) over (x-1) is equals to x+1

Q: (а) — 122 (b) - 10 (c) 0 (d) 14 18 (e) /25 (f) /31 (g) 81 From the list above, determine the…

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Q: 8) Find the derivative of each function: 2. a)g(x) = 3x +5x

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Q: Part 1: Let M solution to M = 2 0 5 5 -15 -5 48 -5 12 and let b= = 15 60 [24] 6 3 .There is a very…

A: Part 1- we can write the given matrix into equation form

Q: 1.) Simplify the expression if b = 9 [38 – (b- 3)2] + 3b

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Q: Which expression is equivalent to X +7 x2 + 4x – 21 restricted so that the expressions are defined?…

A: We will simplify the problem.