Tell whether the two rates form a proportion.
5. 55 miles in 1 hour; 450 miles in 8 hours
6. $3.00 for 32 ounces of strawberries; $1.75 for
24 ounces of strawberries
7. 45 baskets in 85 shots; 54 baskets in 102 shots
8. 18 push-ups in 60 seconds; 27 push-ups in
90 seconds
9. one type of cereal has 2 grams of protein per 1-cup
serving. another cereal has 1 gram of protein per
half-cup serving. do these rates form a proportion?
10. a 50-fluid-ounce bottle of laundry detergent washes
32 loads of laundry. a 100-fluid-ounce bottle washes
60 loads of laundry. do these rates form a proportion?

  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.

d

step-by-step explanation:

∈3,600

step-by-step explanation:

answer: i feel you honey.

step-by-step explanation: