5. y=6; de=7; fg=8
6. x=4.2; jl=14.2; mn=13
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.
the set of rational numbers.
the set of integers.
answer: 8.00 for a bag of popcorn, drink: 4: 00.
set up a system of equations, solve 6d+7b=80
2d+6b=56. solve for b and d.
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my assumption: you mean when you add the numbers, they equal 182.
let be the smallest number. then we are asked to solve the following equation:
rearranging the equation gives us:
7x + 21 = 182 => x + 3 = 26 => x = 23.
so the smallest number is 23 (since our assumption was that x is the smallest number.
you could very well have stated that x was the middle number as a lot of cancellations would occur. that is:
(x - 3) + (x - 2) + (x - 1) + x + (x + 1) + (x + 2) + (x - 3) = 182.
7x = 182 => x = 26 so the smallest would be 26 - 3 = 23.