For nonzero integers, a, b, prove the following properties of divisibility and gcds. (you may use the fact that gcd(a, b) is an integer linear combination of a and b. you may not appeal to uniqueness of prime factorization because the properties below are needed to prove unique factorization.) (a) every common divisor of a and b divides gcd(a, b). (b) if a | bc and gcd(a, b) = 1, then a | c.

You are responsible for designing a new city. you are inspired by pierre charles l'enfant, who laid out the streets of our nation's capital. numbered streets run north and south, and lettered streets run east and west. avenues are named after states, and they intersect the streets on a diagonal. the streets are parallel and the intersections form similar triangles. 18th st. is 454 meters long and the intersection of 18th and k st. is 207 meters from connecticut ave. if 19th st. and k st. is 385 meters from connecticut ave., what is the length of 19th st.?

At the newest animated movie, for every 9 children, there are 4 adults. there are a total of 39 children and adults at the movie.

Solve each quadratic equation by factoring and using the zero product property. [tex]x^2+6x+8=0[/tex]