The product of two consecutive odd integers is 22 less than the square of the greater integer. Find the integers.

Q: The product of two numbers is 4 and the sum of their squares is 8.Find the numbers.

A: Assumption of the numbers and their solution helps to find the required numbers. Addition of the…

Q: The sum of two nonnegative numbers is 20. Find the numbers if the product of one number and the…

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Q: The sum of four consecutive integers is 14 less than 5 times the smallest integer. Find the four…

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Q: the sum of two numbers is 7 and the difference of their squares is 21. Find the numbers.

A: Let the first number be ‘x’ and second number be ‘y’.

Q: The average of two numbers is 5x. If one of the numbers is 2x + 3 find the other number.

A: We can find the answers as below

Q: The sum of the squares of two positive numbers is 65 and the difference of the squares of the…

A: We have to find numbers.

Q: The sum of two consecutive even integers is 26. What is the product of the two integers?

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Q: The product of two numbers is 10 and the difference of their squares is 21. FInd the numbers.

A: Let x be the first number and y be the second number.The product of two numbers is 10.Then,

Q: The sum of two numbers is 4 and the difference of their squares is 64. Find the numbers.

A: Let the two numbers be x and y.Then, we have

Q: The product of 2 consecutive integers is 10 less than 5 times their sum. Find both integers.

A: Let two consecutive numbers are x and x+1

Q: The sum of the squares of two consecutive even integers is 1252. Find the integers.

A: Given: The sum of the squares of two consecutive even integers is 1252. To find the integers.…

Q: The sum of the squares of two consecutive positive odd integers is 74. What is the value of the…

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Q: The product of some negative number and 5 less than twice that number is 375. Find the number.

A: Firstly we make the equation according to the question and then we solve it for unknown value by…

Q: The length of a rectangle is 4 inches greater than twice the width. If the diagonal is 2 inches more…

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Q: The sum of three consecutive even integers is 258. Find the three integers.

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Q: The square of the tens digit of a two-digit number is 7 less than the sum of the digits. If the…

A: Assume unit digit of number is x and tens digit is y, then use the condition given in the question

Q: The product of a number and 8 is smaller than 7 less than a number

A: Let the number be x. Product of number and 8= 8x

Q: The sum of a positive number and twice its square is 11.88.Find the number.

A: Let the unknown number is 'x'.

Q: Four times the square of a number decreased by 6 is equal to seven times the number increased by 9.…

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Q: The dimensions of a rectangle with a perimeter of 82 cm if the length is 3 cm less than three times…

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Q: The sum of a positive number and twice its square is 11.88. What is the number.

A: Given, let us take a positive number be

Q: The sum of the squares of two consecutive natural numbers is 313 . Find the numbers

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Q: The difference of two positive numbers is 2 and the difference of their squares is 44. Find the…

A: Let x and y are those two positive numbers and x>y.So, x-y=2 and x^2-y^2=44

Q: Find the length of the shorter leg of a right triangle if the longer leg is 15 feet more than the…

A: Here use the Pythagoras theorem  given as  H2  = B2 + P2 to solve the problem.

Q: A 21-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece…

A: Given that a rope is cut into 2 pieces. Here seven less than three times the length of the longer…

Q: The area of a rectangle is 81 square inches. Given that the length is 9 inches more than twice the…

A: We have to find dimensions of the rectangle. Given the length is 9 inches more than twice the width.

Q: The length of a rectangular carpet is 4 feet greater than twice its width. If the area is 48 square…

A: Let l be the length and w be the width of the rectangular carpet. Now given that the length of a…

Q: The sum of three consecutive integers is 12 more than twice the largest integer. Set up and equation…

A: Let the 3 consecutive numbers be a, a+1,a+2 Their sum is a+a+1+a+2 Here 12 more than twice the…

Q: If the difference between the squares of two consecutive integers is 15, findthe larger integer.

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Q: The difference of the square of a number and 24 is equal to 5 times that number. Finc the negative…

A: let us consider the number is x then according to given condition the difference of x2 and 25 will…

Q: The difference of the square of a number and 12 is equal to 4 times that number. Find the positive…

A: Suppose that number is x . Form the equation of one variable according to given in the question.

Q: Thrice the sum of two numbers is 30 and the sum of their squares is 52. Find the product of the…

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Q: The sum of the squares of two negative numbers is 145 and the difference of the squares of the…

A: Given,The sum of the squares of two negative numbers is 145 and the difference of the squares of the…

Q: The length of a rectangle is three more than its width. If the perimeter is 46 feet, what are the…

A: Let the width of the rectangle be x. Thus, the length is (x+3). The perimeter of the rectangle is 46…

Q: The sum of the squares of two consecutive even numbers is 340 ,Find the numbers

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Q: The sum of the square of a number and 12 times the number is −27. Whatis the smaller possible value…

A: Let the number is = x So, The sum of the square of a number and 12 times the number is −27 is…

Q: If the square of the number is added to 3 times the number, the number is 108. Find the number.

A: We have to find the number if square of the number is added to 3 times the number then number is…

Q: The average of two numbers is 2x. If one of the numbers is x + 3 , find the other number.

A: We know if average of two numbers = a, then total of these two numbers = 2a.

Q: The sum of two nonnegative numbers is 20. Find the numbers if one number plus the square root of the…

A: according to given problem x+y=20x+y=b

Q: The sum of the number and its square is twelve times the next higher number. Find the number.

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Q: The sum of the square of a positive number and the square of 4 more than the number is 58. What is…

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Q: The sum of the squares of two negative numbers is 97 and the difference of their squares is 65. Find…

A: Let the two numbers be x and y (both negative) respectively.Then we have

Q: The square of a negative number is 18 more than 3 times the negative number. Find the number.

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Q: The sum of the square of a positive number and the square of 3 more than the number is 149. What is…

A: We have to find the positive number.

Q: find two consecutive even integers if the sum of their squares is 164

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Q: The product of two consecutive integers is 19 more than their sum. Find the integers

A: Let x be an integer and x+1 be its consecutive integer.It is given that their product is 19 more…

Q: The square of a number equals nine times that number. Find the number.

A: Assume number be x

Q: The sum of a number and its square is 56. Find the number.

A: