4. problem iv.7. let un be the nth fibonacci number (for the definition see definition 5.4.2) prove that if n 2 2 the euclidean algorithm takes precisely n -1 steps to prove that gcd(un+1,un) 1, here we mean that the euclidean algorithm, as written in class or in the book, takes n - 1 steps to complete

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!

susie has 7 apples

7

step-by-step explanation:

most likely linear (proportionate)

step-by-step explanation:

as time increases heart rate increases