Grace is comparing cell phone plans. A prepaid phone plan costs $0.20 per minute and has no monthly fee. A contracted phone plan

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:

Php 973.00

Detailed explanation:

Aling Luz purchased 3/8 yards of linen priced at Php 72.00 per yard. She paid Php 1000.00 to the cashier. What will be her change?

Amount of yards acquired = 3/8

Cost per yard = Php 72.00

Total cost of the purchased yards = Amount of yards acquired × Cost per yard

= 3/8 × Php 72.00

= Php 27.00

She provided Php 1000.00 to the cashier.

What amount will she receive back?

= Amount given - total cost

= Php 1000.00 - Php 27.00

= Php 973.00

The answer is found by dividing the total pages by the total time in minutes.

Calculating 7.5 divided by 9 equals approximately 0.8333, so Monica reads around 0.83 pages each minute on average.

To find the unit rate, we simply divide 4 by 2.

4 ÷ 2 = 2

This means the artist can complete 2 paintings every hour, establishing the unit rate as 2 paintings per hour.

Hope this assists

-AaronWiseIsBae