Let's begin by breaking each number down into its prime factors: 4 = 2 x 2 5 = 5 6 = 2 x 3 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4, 5, and 6 by multiplying all common and unique prime factors of each number: common prime factors: 2 unique prime factors: 2,5,3 LCM = 2 x 2 x 5 x 3 = 60 Next, let's determine how many times 60 goes into 10,000 (excluding remainder): 10,000/60 = 166 and 2/3 Multiples of ALL 3 numbers (4,5,6) = 166 Next, let's determine the Lowest Common Multiple (LCM) of the numbers 4 and 5 by multiplying all common and unique prime factors of each number: common prime factors: none
unique prime factors: 2 x 2 x 5
LCM = 2 x 2 x 5 = 20 Next, let's determine how many times 20 goes into 10,000:
10,000/20 = 500
Multiples of BOTH numbers (4 and 5) = 500 Finally, let's subtract the multiples of ALL three numbers (4,5,6) from the multiples of BOTH numbers (4 and 5) to get our answer: Multiples of ONLY numbers 4 and 5 (excluding 6): 500 - 166 = <span>334</span>
Can you show the full question?
Answer:
13
Step-by-step explanation:
Let PS = x and RP = x-5
Using Pythagorean theorem on the two smaller rt triangles formed,
6^2 + x^2 = (ST)^2
6^2 + (x-5)^2 = (RT)^2
Now use Pythag on big triangle and sub in above values:
(2x-5)^2 = 6^2 + x^2 + 6^2 + (x-5)^2
Multiply out and simplify to
x^2 - 5x -36 = 0
Factor the quadratic: ((x-9)(x+4)=0 Therefore x=9 or x=-4. We may disregard the negative answer so x = 9. So PS is 9 and RP is 4.
Therefore entire hypotenuse is 4 + 9 or 13.
