In parallelogram abcd point k belongs to diagonal
bd
and divides
bd
so that bk: dk=1: 4. if ray
ak
meets
bc
at point e, what is the ratio of be: ec?

Step-by-step explanation:

Consider triangles BKE and DKA. In this triangles:

as vertical angles; as alternate interior angles (lines BC and AD are parallel and BC is a transversal); as alternate interior angles (lines BC and AD are parallel and BE is a transversal).

Thus triangles BKE and DKA are similar by AA theorem. Similar triangles have proportional sides lengths:

Thus,

Since AD=BC and BC=BE+CE, we have that 4BE=BE+EC, EC=3BE. Hence, the ratio BE to EC is

Hello!

The equation in the image above has been written in slope-intercept form. Slope-intercept form uses the following formula:

y = mx + b

M represents the slope while B represents the y-intercept. In the problem above, we are given that X represents the number of identical deposits while Y represents the amount of money in Mario’s account. We can also conclude, based on the formula above, that the y-intercept of the given equation is 50.

Let’s begin at a time when Mario had not yet made any of his monthly deposits (x). In this case, we would let X equal 0:

y = 75x + 50
y = 75(0) + 50

Now simplify the right side of the equation:

y = 0 + 50
y = 50

Before Mario made any deposits (x = 0), his bank account held only 50 dollars. Therefore, Mario must have gotten these 50 dollars for his birthday (before the monthly deposits began). We have now come to the conclusion that the y-intercept represents the following:

He was given $50 for his birthday.

I hope this helps!