A company decides to give I'd numbers to its employees that consist of one letter by three digits how many different is numbers are there

25,974 possible ID combinations

Step-by-step explanation:

Since the ID card will consist of one letter and three digits to find the total number of possibilities we simply multiply the number of letter options that exist by the total amount of numbers each letter can be followed by. There are a total of 26 letters in the English Alphabet. Since each letter is followed by only 3 digits, then the largest number that can exist after the letter is 999. Therefore, we simply multiply 26 by 999 to find the total number of possible outcomes.

26 * 999 = 25,974 possible ID combinations

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240