John finds that the sum of two numbers is 24 and their difference is one sixth of the sum. Find the smallest number between the two numbers.

Given:

The sum of two numbers is 24 and their difference is one sixth of the sum.

To find:

The smaller number between the two numbers.

Solution:

Let x and y be the two numbers where x>y.

The sum of two numbers is 24.

          ...(i)

Their difference is one sixth of the sum.

             ...(ii)

Adding (i) and (ii), we get

Putting in (i), we get

The two numbers are 14 and 10.

Therefore, the smaller number between the two numbers is 10.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.