Given that x + y = 13 and xy = 24, find the distance from the point (x, y) to the origin.

Distance from the point (x, y) to the origin is approximately 11 units.

Step-by-step explanation: Given equations x+y=13 and xy =24.

Solving first equation for y, we get

y = 13-x.

Substituting y=13-x in second equation, we get

x(13-x)= 24.

13x -x^2=24.

-x^2+13x =24.

-x^2+13x -24=0.

Dividing each term by -1, we get

x^2-13x+24=0.

Applying quadratic formula

Plugging x=10.77 in first equation

y= 13-10.77 = 2.23

and plugging x=2.23 in first equation, we get

y = 13-2.23 = 10.77.

Therefore, (x,y) are (10.77, 2.23) and (2.23, 10.77).

Now, we need to find the distance of (x,y) from origin (0,0).

Applying distance formula :

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0