Remmber
(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)
conver to improper
4 and 1/5=20/5+1/5=21/5
2 and 1/3=6/3+1/3=7/3
(21/5)/(7/3)=(21/5)(3/7)=63/35=9/5=1 and 4/5
(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.
Answer: D. 41 cm
There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,
a^2+b^2 = (b+1)^2
a^2 + b^2 = b^2 + 2b +1
a^2=2b+1
So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.
b = (a^2 - 1)/2
a=3, b=(3^2-1)/2=4, c=b+1=5
a=5, b=(5^2-1)/2 =12, c = 13
a=7, b=24, c=25
a=9, b=40, c=41
a=11, b=60, c=61
a=13, b=84, c=85
It's good to be able to recognize Pythagorean Triples when we see them.
Otherwise we'd have to work the calculator:
√(9² + 40²) = √1681 = 41
1.) 8,281 people/km²
2.)
3.) 1226.88 grams
4.) 999.74 grams
5.) 6
I am not sure about number 2.
5n+10-8=2n
5n+2=2n
-3n=2
n=-2/3
