BD and AC are chords that intersect at point Y. A circle is shown. Chords B C and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY? 2 units 3 units 4 units 6 units

4 units

Step-by-step explanation:

we know that

The Intersecting Chord Theorem states that:  When two chords intersect each other inside a circle, then the products of their segments are equal.

do

In this problem

substitute the given values

solve for x

therefore

The length of segment AY is 4 units

AY = 4 units

Step-by-step explanation:

The image is attached below.

We have to find the value of AY (or x).

We need the intersecting chord theorem to solve this easily.

The intersecting chord theorem tells us that the product of line segment of each chord are equal.

From the figure, we can state:

BY * YD = AY * YC

Thus, we can write:

Hence,

AY = 4 units

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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