8.) Write a conjecture using the information provided. If two numbers are odd, then their sum is even. The two numbers are 3 and 19.

Q: 4. x and y are two positive integers. (x,y) = 5, Icm (x,y) = 200 and 15, find x and y. gcd x - y =

A: Given that     gcd(x,y) = 5 ;   lcm(x,y) = 200   and  x-y = 15 Formula :     xy =…

Q: prove theorem: if a square is inscribed into a right triangle in such a way that one side of the…

A:

Q: if we add two positive irrational numbers, then their sum remains irrational.

A: Given statement is false

Q: 10. Solve the factorial. Use a calculator if necessary. O 6 30 24 15 120

A:

Q: A. Let a be an irrational number and r a nonzero rational number. Prove that if s is a real number,…

A: (A) Let's prove part (A) by contradiction.Assume that both and are rational numbers, where is…

Q: pard and named some pc red 30 rays in all and the

A: here teacher drew a number line on the board and named n points it. then we have (n-1) points didn't…

Q: 3.) On the number line below, point P represents -6 and point Q represents 6. Which statement is NOT…

A: Representation of real line

Q: The diagram below shows ten circles joined by six lines with three circles each. Place all the…

A: Requirements: 1. Numbers should be 1 to 10. 2. Each line has 3 circles. 3. Every line should have…

Q: p> 2 and p is a prime number. Find the values of p if a number such that n = 4p is a perfect number.

A: The definition of perfect number is given as follows :

Q: Three irrational numbers are given below. Select the option that correctly plots the approximate…

A:

Q: Use a direct proof. Let "a", "b", and "c" be integers, where "a" is not equal to 0. “if a|b and b|c,…

A:

Q: two consecutive odd numbers are both primes, they are called twin primes. One example of a pair of…

A: A) 19 and 21 : 21 = 7*3 so it's not prime. B) 39 and 41 : 39=13*3 so it's not prime. C) 49 and 51 :…

Q: Notice that two intersecting lines determine 4 pairs of supplementary angles and 3 concurrent lines…

A:

Q: Solve this question, use pencil and paper to solve it, show your work as well.  1.  How many pairs…

A: How many pairs of two distinct integers chosen from the set  have a sum that is even ?

Q: Consider sum 1+5+9+13+...+81 what is a6

A:

Q: 3. Show that if m and n are integers and nº + 5 is odd then n is even using a) a proof by…

A: (a) proof by contraposition  Let, n be odd. Then, n³ is also odd (infact any integral power of odd n…

Q: Prove: For all integers n, if n is odd then n is odd.

A: Given below the detailed solution

Q: write a paragraph proof using any appropriate technique. Use complete sentences and identify which…

A: According to the given information, it is required to prove that for all real numbers a and b if a…

Q: (4) (a) Prove that the sum of an even natural number and an odd nat- ural number is always odd. (b)…

A:

Q: The natural numbers are N= {1,2,3,..}. The prime numbers are P = {2,3,5,7...}. True or false? {2}sP…

A: The given problem is to determine whether the statement is True or False. To check whether the {2}…

Q: Prove that if 7 divides n with remainder 1, 7 divides n² + 2n + 7 with remainder 3.

A: Given, if 7 divides n with remainder 1. We have to prove that 7 divides n2+2n+7 with remainder 3.

Q: 8. Express each of the following with integer addition or subtraction. Then, evaluate the equation.…

A: see below the answer and calculation

Q: Find the smallest five consecutive composite integers.

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

Q: 3. Consider the numbers A and B below. A = 235 × 512 × 7²1 B = 223 x 37 x 732 (a) Consider the…

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: 1. Give 5 examples of perfect number using Euclid's formula. Show your solution. 2. Give 3 examples…

A:

Q: 3) Two points are plotted on the number line below. 十+ -10 -9 -8 -7-6 -5-4 -3-2-1 十十+ 1 3 10 Which…

A:

Q: (1) For all real numbers a and b, if a is a rational number and b is an irrational number, then a −…

A:

Q: A. At some time you may have been shown a “mathematical trick” like the following. You ask a person…

A: A) Let  x be the number chosen. Then, add 5 : x+5 multiply by 4 : x+54=4x+20 Subtract 6  :…

Q: 10. Even and odd Fibonacci Numbers a.) Which of the Fibonacci numbers are even? What pattern do you…

A: (a) Find the terms of the Fibonacci series. xn=xn−1+xn−2 such that…

Q: Prove the inequality x² + x² + ... + x² n IV 2 2+...+ ²₂ ) ² n

A: Explanation of the answer is as follows

Q: Fill in the blank so that the resulting statement is true. n If a #0, the degree of ax" is n If a 0,…

A: Given query is to find the degree of : axn

Q: Using the information provided, which of the following is a conjecture could be proposed from the…

A: Using the information provided, which of the following is a conjecture could be proposed from the…

Q: 1 キ

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.