Among all pairs of numbers (x,y) such that 3x+y=8 , find the pair for which the sum of squares, x2+y2 , is minimum. Write your answers as fractions reduced to lowest terms

Q: The product of the squares of a number and two more than a number is 225. Find all possible values…

A: Let the number be n According to the question, n2(n+2)2=225 ⇒n(n+2)=±225⇒n(n+2)=±15 Case 1 : When…

Q: The sum of two integers is 144. If their quotient is (7/5) , find the two integers.

A: Let the required numbers be x and y. It is given that the sum of the numbers is 144. x+y=144…

Q: The product of y and 7 is less than or equal to -28

A: Given: y×7≤-28

Q: Two integers differ by 4. If the sum of their squares is 170, determine the two integers.

A: The detailed solution is as follows below:

Q: Find three positive numbers whose sum is 12 and whose sum of squares is as small as possible

A:

Q: Find two numbers whose sum is 9 and their difference is 60.   Smaller- Large number-

A: We have given the - sum of two numbers = 9. difference of two numbers = 60. we have to find the…

Q: sum of two non-negative numbers x and y is 16. What is the smallest possible value of x2 + y2

A:

Q: The product of two consecutive odd integers is 255. Find the integers

A: In question, We'll find two consecutive odd integers whose product is 255. The solution is below,

Q: Write the sum of the two terms T24,5 + T24,6 in a single term.

A: This question from pascals triangle. Lets solve the question

Q: The product of two numbers is 7. Determine the second factor if one is 6/5.

A:

Q: ind the product of two numbers whose sum is 11 and difference is 3

A: Here from the given information, first, we have to find two numbers whose sum is 11 and the…

Q: The product of two consecutive positive odd integers is 399. The two integers are and Enter the…

A:

Q: the sum of a number and 12 times its reciporcal is 8. find the number(s).

A: Given:Sum of a number and 12 times its reciprocal is 8.

Statements and Logic

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