Find the equation that can represent the situation if the sum of two numbers is 56. We also know that the greater number is 4 more than the smaller number.(5 points) a
x - (x + 4) = 56

b
x (x - 4) = 56

c
x (x + 4) = 56

d
x + (x + 4) = 56

D

Step-by-step explanation:

So first you would set your two numbers as variables. Let y be the greater number and x be the smaller number. This means that our equation for y will be x + 4. Now all we need to do is add x and y. INSTEAD of using y, we will SUBSTITUDE with the equation for y, x + 4. Now our equation looks like

x + (x + 4) = 56

  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.