If BD = 7x – 10, BC = 4x – 29, and CD = 5x – 9, find each value.

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:

C. The mean daily salary is not above $350 per day

Step-by-step explanation:

The calculation is displayed below:

Y = a + bX

where,

Y = earnings of a randomly chosen agent

a = $150

b = $50

X = number of loans closed

Now

E(x) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)

= 3.94

Consequently,

E(y) = $150 + ($50 × 3.94)

= $347

therefore, option C is incorrect

The true value is 25.7 ml.
The calculated error is 15.6%.
Thus, the error amount equals 0.156 times 25.7, which calculates to 4.0092 ml.

The percentage error indicates that the student's measurement could either exceed or fall short of the true value by this error amount.

This leads to two potential readings:
one possibility is: 25.7 + 4.0092 = 29.7092 ml
the other possibility is: 25.7 - 4.0092 = 21.6908 ml

Answer:

Step-by-step explanation: The error made by the student was dividing the wins by the losses.

The student should have divided the wins by the total number of games played.

Initially, the student ought to have summed 20 and 10 to conclude there were 30 games in total.

Answer:

Here is the solution to the entire assessment: https://school.ckseattle.org/documents/2019/2/8_2_The_Pythagorean_Theorem_and_Its_Converse.pdf

Step-by-step explanation: