In the following diagram \overline{DE} \parallel \overline{FG}

Response:

The loop's length is roughly 49.58 km.

Step-by-step details:

Given:

Duration to cycle the loop = 2 hours and 30 minutes

It is known that;

60 minutes = 1 hour

30 minutes = 0.5 hour

therefore, 2 hours and 30 minutes =

∴ Time to cycle the loop = 2.5 hours

Let 's' denote the cycling speed.

Denote the total loop distance as 'd'

From our understanding;

Distance equals speed times time.

Representing this as an equation we have;

Given:

If her speed increased by 1 km/hr, the time taken around the loop would decrease by 7 minutes.

As a result, we can say;

Speed =

The time then will be shortened by 7 minutes.

7 minutes = 0.12 hours

Consequently, time = 2.5 - 0.12 = 2.38

Again, Distance is calculated as speed times time.

This can be expressed with equations;

The distances are equivalent in both scenarios, thus we will determine speed by equating the equations.

So, Speed = 19.83 km/hr

Loop length (d) =

Therefore, the loop length is approximately 49.58 km.

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: The following comparison is made.

Detailed explanation:

At the playground, a climbing structure is 6 feet high and stretches 4 feet horizontally.

The slope can be calculated as vertical height divided by horizontal length.

=  6/4 = 3/2 = 1.5

In contrast, a climbing structure in the gym stands 10 feet tall, extending 6 feet horizontally.

Therefore, slope, =  10/6 = 5/3 = 1.67 (approximately)

As such, <

Thus, the slope of the first climbing structure is less than that of the second.

Answer:

b = 5√3

b = -5√3

Step-by-step explanation:

We have

Keep in mind, the root of a function corresponds to the value of x at which the function's output is zero.

In this case

The roots of the equation are the b values for which f(b) equals zero.

Thus

For f(b)=0

Take the square root of both sides

Now simplify

 and

So we find that

b = 5√3

b = -5√3

Answer:

E. P(W | H)

Step-by-step explanation:

Meaning of each probability:

P(H): Likelihood of the game occurring at home

P(W): Likelihood of the game resulting in a win.

P(H and W): Likelihood that the game is both at home and a win.

P(H|W): Likelihood of a win occurring when at home.

P(W|H): Likelihood of winning at home games.

Which probabilities are necessary to determine the fraction of home games that were victories?

This is the probability of winning a home game. Hence, the answer is:

E. P(W | H)