The sum of two numbers is 51, and their difference is 9. what is the value of the smaller number?

Hi there!

We will create a system of equations to find the numbers you are looking for.

Let's say that the x is one number, and the y is the other number, system looks like this:

x + y = 51

x - y = 9

since the y has different sign in both equations, we will add these two equations together and solve it by x, like this:

2x = 60

x = 60/2

x = 30 => x + y = 51

               y = 51 - x

               y = 51 - 30

               y = 21

The value of the smaller number is 21.

Hope this helps!

  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.

number one is the correct answer

step-by-step explanation: dogs and cats are mentioned, no other animals