If two positive integers p and q are written as p = a^2b^3 and q = a^3b, where a and b are integers, then show that lcm(p, q) * hcf ( p, q) = pq

The LCM is the lowest expression that both p and q divide into.

LCM (p,q) = a^3b^3

The HCF is the highest common factor of p and q:-

HCF (p,q) = a^2b

HCF(p,q) * LCM (p,q)  = a^3b^3 * a^2b = a^5b^4  and

pq = a^2b^3 * a^3b =  a^5b^4

Therefore HCF(p,q) * LCM(p,q) = pq

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation:

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)