Xander says that it is not possible to draw a quadrilateral that is not a parallelogram and not a trapezoid. Devin says it is po

Response:

We define a line L.

In a two-dimensional space, a line can be expressed as follows:

y = a*x + b

where 'a' denotes the slope and 'b' represents the y-intercept.

To determine the slope for a line passing through points (x1, y1) and (x2, y2), the formula is:

a = (y2 - y1)/(x2 - x1).

Using one of these points will help to find the value of 'b'.

Once we have the line's equation:

y = a*x + b

we can substitute in a specific point (x, y)

to verify if the equation holds true. If it does, that point lies on the line L.

*Refer to the image attached below

Answer:

346.4 ft

Step-by-step Explanation:

The distance between the boats, CD = BD - BC

Using trigonometry, find the length of BD in triangle ∆ABD and also calculate the length of BC in triangle ABC.

Length of BD in triangle ABD:

Opposite side to <30° = 300 ft

Adjacent side = BD

Divide both sides by tan(30)

(rounded to nearest tenth)

Length of BC in triangle ABC:

Opposite side to <60° = 300 ft

Adjacent side = BC

Divide both sides by tan(60)

(rounded to nearest tenth)

The distance, CD, between the boats is calculated as BD - BC

= 519.6 - 173.2 = 346.4 ft

Let’s evaluate the provided pairs one by one.

A. ∠MKR and ∠OAR

In the diagram, it’s visible that the angle bisector of the right-angled vertices creates angles MKR and OAR.

Thus, they are congruent measuring 45°

B. ∠ONT and ∠MTN

From the diagram, MTN forms a right angle, while ONT is created by bisecting this right angle.

Hence, these angles are not congruent with ∠MTN at 90° and ∠ONT at 45°

C. ∠IRS and ∠MRO

In the diagram, MRO is a right-angle, while IRS results from the bisection of the right angle.

Accordingly, these angles are not congruent with ∠MRO equal to 90° and ∠IRS at 45°

D. ∠URC and ∠TRO

In the diagram, it’s shown that the angle bisector of the right-angled vertices forms angles URC and TRO.

Thus, they are congruent, both measuring 45°

Therefore, the pairs of congruent angles are

A. ∠MKR and ∠OAR and D. ∠URC and ∠TRO

Response:

a

    f'(t) is negative

b

 The unit is degC/min

c

At 35 minutes since the coffee was placed on the counter, the temperature is 68, and it will drop by approximately 0.75 in the next 30 seconds.

Detailed explanation:

According to the question, we are informed that

   The temperature of a cup of coffee on a counter is represented by the equation

where t indicates the time in minutes since the coffee was set on the counter.

In general, f(t)' denotes the derivative of f(t), indicating the change in temperature over time for the coffee

As the coffee rests on the counter, its temperature tends to decrease after a few minutes; thus, f(t)' is negative.

The temperature is measured in degrees Celsius while time is expressed in minutes.

Therefore, the change in temperature with respect to time, f(35)', will be given in degrees Celsius per minute (i.e., degC/min).

The question states that

which means the rate of temperature change after 35 minutes is 1.5.

And

indicating that the coffee's temperature after 35 minutes is 67 degrees Celsius.

Subsequently, after another t= 30 seconds = the rate at which the coffee's temperature changes is

=>        

=>            

Thus

At 35 minutes since the coffee was placed on the counter, its temperature is 68 and will drop by roughly 0.75 in the next 30 seconds.