What can you conclude about the numbers m and n if X " = 7 and r is an even number and m and n are integers?

Q: show that SZ+5 is irrational number

A: If a number cannot be written in ab form, where a and b are integers is known as an irrational…

Q: "If a and b are positive integers, a divides b and b divides a, then a = b."

A: To Prove: '' If a and b are positive integers, a divides b and b divides a, then a = b''.

Q: Is the statement true or false? If an odd number is less than 15, then it is prime. False Give a…

A: We have to check

Q: the fourth power of an integer is x, and x is between 100 and 600. What is x?

A: It is given that the fourth power of an integer is x.That is, x = n^4, where n is a positive…

Q: 8. If * is defined as a*b = 3a+b where a and b are real numbers, what is 4*3?

A: Given operation is a*b = 3a+b

Q: Suppose that nine times a number is added to 63 and the result is positive. What are the possible…

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Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

Q: b. Write the set of natural numbers less than 23 needed) orete answ ers aS

A:

Q: Suppose that two times a number is added to 8 and the result is positive. What are the possible…

A: Lets assume number =n as per given information    2n+8>0

Q: If x is an odd integer then 5x – 7 is an even integer.

A: 5 and x are odd integers. Multiplication of two odd integers is always odd. Hence, 5x is an odd…

Q: 2) The product of an even number and any other number is even.

A:

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: If n E N and n < 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Here n  N and n&lt; 2000. So, n= 1,2,3,........,1999.

Q: How many mombers between 50 and 200 can be expressed as 4k-1, where k is an integer?

A:

Q: 11.) The sum of four consecutive even integers is 68. Find the four consecutive even integers. What…

A: We know that an even integer is always divisible by 2. Let the first even integer in the consecutive…

Q: If n is an even integer then 7- n3 ) is an odd integer. ) is an even integer. is sometimes even and…

A:

Q: Show that 2 + V5 is imational number

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Q: is an even integer then n square is .A Negative

A: Suppose n=m is an even integer.Since n=m , then n2=m2

Q: How many integer solutions are there to x1+ x2 + x3 = 0  with Xi >= -5 ?

A: We need to find the integer solutions to x1+x2+x3=0 such that each of the three numbers is greater…

Q: A true or false test consist of 10 questions. If all the questions are answered, in how many…

A: Given that all questions are true or false type. So each question has 2 choices.  There are total 10…

Q: When 32 is divided by an integer, the remainder is 4. When 51 is divided by the same integer, the…

A: We can use concept of HCF to solve the problem

Q: If 48 ÷ x is a positive integer and x is an integer, what are the possible values of x?

A: We have to find interger

Q: 2 then show that |2A-4|A If A- 4 2

A: We have to verify that 2A=4A where A=1242 and A is used to denote the  determinant of the matrix A.…

Q: A realtor uses a lock box to store the keys to a house that is for sale . The access code for the…

A:

Q: Show that for n ≥ 3, ô(n) is even.

A: We have from the definition of Euler ϕ function: ϕ(1)=1 and ϕ(2)=1 Now Let n ≥ 3

Q: 2(5) – 3(1 – 6) Is even integer?

A: If an integer is divisible by 2, then it is called an even integer. For example, 2,4,6 etc. are even…

Q: Show that 2 + V5 is irrational number

A: To prove that 2+53 is irrational number. (It is evident that 2 is irrational, but here providing its…

Q: is an integer greater than 1 Quantity a= the tens digit of N Quantity b= 0 which is greater or…

A:

Q: How many integer solutions to x1+ x2+ x3+ x4 = 36 are there for which æ1 > 5, x2 > 3, x3 > 5 and æ4…

A: We have to find the number of solutions to x1+x2+x3+x4=36 for which x1≥5, x2≥3, x3≥5 &amp; x4≥6.

Q: k is a prime number that has a ones digit of 7 and 0 <k < 100, how many values of k are possible?

A:

Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: Based on your answers for √16 . √4 and √(16 . 4) what can you conclude?

A: Logical: 16=4.4=44=2.2=2So 16.4=4.2=8

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

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Q: 2 6. The sum of the first n odd natural numbers is equal to n.

A:

Q: Is 1 raised to the power of 2 + 2 raised to the power of 2 equal to 3 raised to the power of 2?

A:

Q: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits…

A: What is the number of integers with (a) at most n (decimal) digits; (b) exactly n digits (don’t…

Q: If n E N and n< 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Given that, If n∈ℕ and n&lt;2000 then calculate how many numbers n have the property that the sum of…

Q: A realtor uses a lock box to store the keys to a house that is for sale. The access code for the…

A:

Q: A realtor uses a lock box to store the keys to a house that is for sale. The access code for the…

A:

Q: If n is an even integer then 7-n3 is sometimes even and sometimes odd. O is an odd integer is an…

A: We have to state whether the 7-n3 is an even integer, odd integer, or sometimes even and sometimes…

Q: (1) ,- (1 -2)"/3" (2) ,- nR/(2in+n) Z, -(-1)"-k +, where k is any integer.

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: True or false, for any integer x, x^2, - x will always result in an even number

A:

Q: How many solutions are there to the equation x1 + x2 +3 + x4 + x5 = 39, where each x; is an integer…

A: Solution

Q: A realtor uses a lock box to store the keys to a house that is for sale. The access code for the…

A:

Q: show that given two numbers m and n, if m is even and n is even, then the product is even

A: Solve by using product rule

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

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Q: i) If you have twenty ones and fifteen zeroes how many ways can we arrange these digits such that no…

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

Q: 4. The area of a parallelogram is 198 square units. If the base and the height of the parallelogram…

A: