The whole town of calamba together with San Pedro biñan and sta Rosa were originally a part of town

the whole town of Calamba together with San Pedro biñan and sta Rosa were originally a part of town Tabuco present-day Cabuyao

Step-by-step explanation:

The cities of  Pedro biñan and sta Rosa, as well as Calamba, were all a part of town Tabuco a large expanse of land, also known as Cabuyao. It was after the colonization of the territory by the Spanish colonists that these cities were separated from Tabuco.

The name Cabuyao stems from the Kabuyaw tree, that is Citrus hystrix. When the barangay of Malabanan which includes all the three cities mentioned above became the estate of the religious leaders, they were then separated from Tabuco or Cabuyao.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

go on the tube you might find some information there