The inclusion/exclusion principle states that

That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).
Therefore,

will have the most elements when the sets

and

are disjoint, i.e.

, which would mean the most we can can in this case would be

(Note that

denotes the cardinality of the set

.)
Answer:

Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
we know that
The figure shows a kite
The kite has two pairs of consecutive and congruent sides and the diagonals are perpendicular
That means
TS=VS
TQ=VQ
TR=RV
we have


so

solve for x

<em>Find the value of RV</em>

substitute the value of x

Remember that
---> by segment addition postulate
we have

so

Answer:

Step-by-step explanation:
We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.
Recall that the equation of a circle is given by:

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
Since our center is at (3, -2), <em>h</em> = 3 and <em>k</em> = -2. <em>r</em> = 6. Substitute:

Simplify:

In conclusion, the equation of the circle will be:

We can notice from the figure that : Area of the home plate is equal to sum of the Area of the rectangle ( 8 in x 15 in) and Area of the triangle with height 6 in and base 15 in.
Area of the rectangle : Length x Width
⇒ Area of the rectangle = 15 x 8 = 120 in²
Area of the triangle : 1/2 x Base x Height
⇒ Area of the triangle = 1/2 x 15 x 6 = 45 in²
Area of the home plate = Area of rectangle + Area of triangle
⇒ Area of the home plate = 120 in² + 45 in² = 165 in²
<u>Answer</u> : D