Find two consecutive positive integers such that the square of the smaller integer is nineteen more than five times the larger integer.

8 and 9

Step-by-step explanation:

let 'n' = smaller positive integer

let 'n+1' = larger

n² = 5(n+1)+19

n² = 5n + 5 + 19

n² = 5n + 24

n² - 5n - 24 = 0

(n-8)(n+3) = 0

n = 8  [this is the smaller positive integer]

n+1 = 9  [this is the larger positive integer]

n = -3  [this value can be discounted because it is not positive]

a orange at the grocery store idk what other product that could be

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.