Prove the following by contrapositive: If x is an odd integer, then x^2 + 3x + 5 is odd.

Q: Prove by cases that 25x² + 35x is an even integer whenever 5x-7 is an integer. Note here that the…

A: Apply the condition for 5x-7 to be an integer case by case.

Q: 1. Prove that 7(x – 1) 2.

A: Let, f(x)= ex-7x+7 ,for x≥2. Differentiating both sides with respect to x, f'(x)= ex-7≥0 . This…

Q: Suppose that Y and Z are points on the number line. If YZ = 11 and Y lies at , where could Z be…

A: Given query is to find the location of Z

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

A: For the solution follow the next step.

Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m) + (-n) = - (m + n)

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Q: Solve for x: 7x = 3 mod 11

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Q: Prove the following by contrapositive: If x is an even integer, then x² is even.

A: Let x is not even, it has to prove that x is not an integer or x2 is not even. Let x is not even…

Q: Prove by contrapositive: if x is odd then x²+3x+5 is odd

A: Concept: Contrapositive method: A conditional statement's contrapositive is built through negating…

Q: 14. Demonstrate that 21 has no primitive root.

A: An integer n≥2 has a primitive root if and only if the the number n is one of the following; 2,4,…

Q: Outline a proof of the theorem by contradiction

A: On considering the theorem If A and B are comingled matrices then the product AB is commingled…

Q: 11. CheCK TUr exLi aneU SulutioIs. 35 1+== x2

A: Given rational equation is  1+(2/x)=(35/x^2)

Q: Find the smallest distinct postive numbers that provide a counterexample to show the statement is…

A: Let the odd numbers be 1 and 3 and the even number be 2, According to the question, The sum of any…

Q: Suppose that Y and Z are points on the number line If YZ = 16 and Y lies at 4, where could Z be…

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m ) + ( - n ) = - ( m + n)

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Q: find a number that provides a counterexample to show that the given statement is false. 1. For all…

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Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: Find a number that provides a counterexample to show that a given statement is false, For all number…

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Q: If 2x³ - 4x² + x + 1 = 0 so x = 4x² - 2x³ - 1 then |x5-x4] < €, X4 = 1.36603, x5 = 1.366024, is the…

A: As per the question we are given an equation and the approx root after 4th and 5th iteration of the…

Q: Prove by CONTRAPOSITIVE if x is an odd integer, then x²+3x+5 is odd

A: Explanation of the answer is as follows

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

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Q: Prove that 3:8 is equivalent to 12:32

A: According to the question, we have to prove that the ratio 3:8 is equivalent to 12:32. A ratio is a…

Q: 1. Show that the distance between two numbers in the real number line, given by d(x,y)=|x-yl,…

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

Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Use a proof by contrapositive to prove that, if (x + 12)/x is an integer, then x < 13.

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Q: Suppose that J and K are points on the number line. If JK= 10 and K lies at 3, where could J be…

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (- m ) + ( - n) = - ( m + n)

A: To prove: -m+-n=-m+n Where m and n are real numbers.

Q: Prove 3√3  is irrational

A: See the attachment.

Q: If 2x³-4x²+x+1=0 so x = 4x² - 2x³ - 1 then x5-x4|< €, X4 = 1.36603, x5 = 1.366024, is the error…

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Q: Prove by contraposition that if x^5 + 7x^3 + 5x >= x^4 + x^2 +8, then x >= 0

A: Proof using contraposition: If we want to prove "if A, then B", then using contrapositive statement…

Q: 3. How many zeros at the end does the number 2022! have? (n! is a product of all positive integers…

A: Given,Number = 2022!To find: Number of zeros at the end (trailing zeros) of the given number  As per…

Q: 2. Possible whenn A- Zero b. Negutive integer C- Negative Yational d- Positive integer

A: We know that Laplace transform of

Q: 27. Show that if x and y are positive real numbers that have the same first n digits in their…

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Q: : a number is even  if

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Q: So what's the final value of x1 x2 x3 and x4? indivually

A: Answer :  No value  the system of equations does not converge to any value. so there doesn't exist…

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: If the sum of two counting numbers is an even number, then the product of the two counting numbers…

A: ANSWER:- 1) From the given statement, If the sum of two counting numbers is an even counting number,…

Q: 3. Show that (5+ 13)e + (5- i3)-" is a real number if is also a real number.

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Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

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Q: There is no integer that has a reciprocal that is an integer.

A: As per the instructions, we will be answering only the first question. For (32), Notice that the…

Q: Suppose that J and K are points on the number line. If JK = 18 and lies at - 3 , where could K be…

A: NOTE: Refresh your page if you can't see any equations. . the distance between J and K is 18 and the…

Q: Let x be a real number. Prove by contrapositive that if æ + 7x = 90, then x < 4.

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Q: Prove that a natural number (an-1an-2a1ao)10 is divisible by 9 if and only if the sum of the digits…

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Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

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Q: Show that 5 – V7 is an algebraic number.

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Q: Compute the exact answer mentally by finding compatible numbers or substitutions: 4x 273 x 25 4x273…

A: The steps are as follows

Q: Determine whether the statement is true or false. Justify your answer with a proof counterexample,…

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Q: Let x be a real number. Prove by contrapositive that if x' + 7x = 90, then x < 4.

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Q: Suppose x is a real number and x is not equal to zero. Prove that if ((x^1/3)+5)/((x^2)+6)=1/x, then…

A: Given that, x is a nonzero real number, and 8 is not a root of given equation.

Q: Find a number that provides a counterexample to show that the given statement is false.

A: We have to find counter example for each of the given statement.

Q: Suppose x is a real number and x + 0. Prove that if then x 7 8. 2 16

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