Daniel claims that any two right triangles can be proven to be similar by the sas similarity theorem because both have right ang

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

Answer:

Step-by-step explanation:

According to the attached figure, Jaxon is positioned 10 blocks east and 5 blocks north.

Thus, Jaxon's x-coordinates are 10 units, while the y-coordinates are 5 units.

Therefore, the coordinates are given by (10,5)

Similarly, Isaac's coordinates are determined based on his distances towards the west and south.

Hence, the x-coordinates equal 8 units and the y-coordinates equal 15 units.

Thus, Isaac’s coordinates are depicted as (-8,-15).

Answer:

80.7 because you multiply

Answer:

Translate the circles so they align at a common center and subsequently enlarge circle Y using a scale factor of 3 ⇒ 3rd answer

Step-by-step explanation:

* Let's describe how to approach this problem

- To establish that all circles are similar, a translation and a dilation factor are necessary to align one circle with another

- We can reposition the circles to coincide at the center and then expand one of the circles by the defined scale factor, with the center of dilation being the common point for all circles.

* Let's resolve the issue

∵ Circle X displays a radius of 6 units

∵ Circle Y has a radius of 2 units

- Initially, we shift the circles so they coalesce at a central point

∴ We utilize translation to place the centers of both circles at the same location

- Determine the dilation factor based on the different radii of the circles

∵ The radius of circle X measures 6 units

∵ The radius of circle Y measures 2 units

∴ Therefore, the scale factor is calculated as 6/2 = 3

∴ Enlarge circle Y by a scale factor of 3

* The actions that affirm the circles are similar are as follows;

  Translate the circles so they share a common center point, and

  enlarge circle Y by a factor of 3.