1. the points A (3,5) and B (6,2) are reflected over the y-axis. find the area of the figure formed by joining the points.

2. Liza wants tostart a small business of making souvenir items for sale. the fixed cost is 1200.00. the cost of making each souvenir is 30.00, and she sells each for 45.00. a.) how many souvenir items must be made in order to break even? b) what is the loss if only 400 items are made and sold? c) what is the profit if 1000 items are made and sold?

1.

The area of a parallel trapezoid is half of the product of the height and the sum of the lengths of the parallel sides.

The height is difference between the projections of A and B on the y-axis. (Ie: 5-2)

The length of each side is the difference between the x-axis projections of the point and its reflection across the y-axis. (Ie: 3-(-3) and 6-(-6))

2.

Profit of n items made and sold is:
P(n) = (45.00-30.00)n - 1200.00

a. Find n when P(n)=0

b. Find: -P(400)
(Loss is negative profit)

c. Find: P(1000)

1. To find the area of a figure formed by joining points, we need to determine the shape of the figure after reflecting the points over the y-axis.

When a point is reflected over the y-axis, its x-coordinate becomes its opposite value while the y-coordinate remains the same.

For example, point A (3,5) when reflected over the y-axis becomes (-3,5), and point B (6,2) when reflected becomes (-6,2).

Now, we can join the reflected points (-3,5) and (-6,2) to form a shape. In this case, it forms a triangle.

To find the area of a triangle, we can use the formula:
Area = (1/2) * base * height

The base of the triangle is the distance between the x-coordinates (-3 and -6) which is |-3 - (-6)| = 3 units.
The height of the triangle is the difference between the y-coordinates (5 and 2) which is |5 - 2| = 3 units.

So, the area of the triangle formed by the reflected points A and B is:
Area = (1/2) * 3 * 3 = 4.5 square units.

Therefore, the area of the figure formed by joining the reflected points A and B is 4.5 square units.

2.
a) To break even, the total cost of making the souvenir items needs to equal the total revenue earned from selling them.

Let's assume the number of items Liza needs to make is 'x'.

The total cost can be calculated as:
Total Cost = Fixed Cost + (Cost per item * Number of items)
Total Cost = 1200 + (30 * x)

The total revenue can be calculated as:
Total Revenue = Selling Price per item * Number of items
Total Revenue = 45 * x

To break even, Total Cost should be equal to Total Revenue, so:
1200 + (30 * x) = 45 * x

Now, solve this equation to find the value of 'x'.

b) To find the loss if only 400 items are made and sold, we need to calculate the total cost and total revenue.

Total Cost = 1200 + (30 * 400)
Total Revenue = 45 * 400

Then, subtract the total revenue from the total cost to find the loss.

c) Similarly, to find the profit if 1000 items are made and sold, calculate the total cost and total revenue as follows:

Total Cost = 1200 + (30 * 1000)
Total Revenue = 45 * 1000

Then, subtract the total cost from the total revenue to find the profit.