Micha constructs a rectangular prism with a volume of 360 cubic units. The height os the prism is 10 unita. Micah claims that th

square. The opposite angles are equal, the diagonals intersect at midpoint, opposite sides remain parallel, and the diagonals bisect the angles.

Answer:

Part 1) The equation is

Part 2) When x=40 m, the area of the schoolyard is A=2,800 m^2

Part 3) The valid domain consists of all real numbers exceeding zero and below 75 meters

Step-by-step explanation:

Part 1) Formulate an expression for A(x)

Let

x -----> the length of the rectangular school yard

y ---> the width of the rectangular school yard

It is known that

The perimeter for the fencing (taking the school wall as one side) is

thus

-----> this is equation A

The area of the rectangular school yard is

----> this is equation B

Substituting equation A into equation B yields

Change to function notation

Part 2) What is the area when x=40?

With x equal to 40 m

substitute the value into the expression from Part 1 to determine A

   

Part 3) What would be a suitable domain for A(x) in this scenario?

We understand that

A signifies the area of the rectangular school yard

x characterizes the length of the rectangular school yard

It follows that

This forms a vertical parabola opening downwards

The vertex indicates a maximum point

The x-coordinate of the vertex corresponds to the length that maximizes the area

The y-coordinate of the vertex denotes the maximum area

The vertex corresponds to (37.5, 2812.5)

Refer to the accompanying figure

Consequently,

The peak area achieved is 2,812.5 m^2

The x-intercepts are located at x=0 m and x=75 m

The domain for A is the range -----> (0, 75)

All real numbers greater than zero and less than 75 meters

Response:

240- 360

Step-by-step breakdown:

First, determine how many minutes are in an hour, which is 60. Multiply that by 2 to find the total for 2 hours, resulting in 120 minutes. Next, you calculate the total for 2 hours by multiplying 2 by 120, yielding 240. Then, multiply 3 by 120 for a total of 360.

I'm unsure if this answer is accurate, but that's my approach.:)

The formula for determining the number of ways to select two pairs of sneakers from three pairs labeled A, B, and C is represented by 3C2 (3 combinations of 2), which calculates as 3! / (2!(3 - 2)!) = 3! / (2! x 1!) = (3 x 2) / (2 x 1) = 3. Therefore, the sample space is S = {AB, AC, BC}.

Answer:

D

Step-by-step explanation:

You should insert the provided x and y coordinates into the equations to determine which one satisfies both points.

D is valid for both:

5 = 5/4(4)

0 = 5/4(0)