Z^5=-7776i

Answer:

Refer to the explanation below

Step-by-step explanation:

The graph can represent a relay race scenario.

Jamie describes a situation that corresponds to the piecewise function illustrated in the graph.

On the graph, the x-axis denotes time in minutes, while the y-axis shows distance in miles.

The initial segment of the graph is a line that extends from the origin to the point (12, 1), with the second segment going from (12, 1) to (20, 2).

1. A runner starts the race and maintains a consistent speed for 1 minute.

• This statement is erroneous as it identifies the incorrect axis.

It should state: a runner initiates the race and runs consistently for 12 minutes, covering 1 mile.

The equation for this segment:

• y = mx + b
• b = 0 since it originates from the starting point.
• m = 1/12
• y = 1/12x
• x = [0, 12], y = [0, 1]

2. Then, his partner takes over and runs faster at a steady pace for another 1 minute.

• Once again, as mentioned earlier, this misrepresents the axis.

It should say: his partner then continues and runs at a constant, quicker pace for an additional 8 minutes, finishing the final mile of the race.

The equation for this segment:

• b = 1, serving as the initial point
• m = (2-1)/(20-12) = 1/8
• y = 1/8x + 1
• x = (12, 20], y = (1, 2]

The diagram is not available, so I included a supplementary figure.

Response:

The segments ST and UT are equal in length.

Detailed explanation:

As seen in the additional figure

∵ ST and UT act as tangents to circle K at points S and U respectively

∵ SK and UK are the radii of circle K

- A tangent is perpendicular to the radius at the point where it touches the circle.

Thus, ST ⊥ KS at point S

Thus, m∠KST = 90°

Thus, UT ⊥ KU at point U

Thus, m∠KUT = 90°

Therefore, m∠KST = m∠KUT

In triangles KST and KUT

∵ KS = KU because they are both radii

∵ m∠KST = m∠KUT confirms the equality

∵ KT is common to both triangles

- Therefore, the triangles are congruent according to the HL criterion

∴ Δ KST ≅ KUT as per the HL criterion

- Thus, from the congruency result

∴ ST = UT

The segments ST and UT are equal in length.

I believe the answer is D.

Answer:

Davide is 10 years old.

L'età di Davide è 10.

Step-by-step explanation:

The average ages of Aldo, Bruno, Carlo, and Davide amount to 16 years.

Let’s denote:

x for Aldo's age.

y for Bruno's age.

z for Carlo's age.

w for Davide's age.

The average for all four is 16 years.

This gives us:

Excluding Davide, the average age of the other three is 18. Therefore:

Substituting into the original equation:

Hence, Davide’s age is indeed 10.

L'età di Davide è 10.

There are a total of 20,000 available numbers. To ascertain how many phone numbers are available, the number of digits in each number must be known. Here, I will assume each number has 7 digits. This leads to the format starting with either 373XXXX or 377XXXX, where each X can be any digit from 0 to 9. This results in 10 options for each X. Therefore, there are 10×10×10×10 = 10,000 distinct phone numbers starting with 373 and another 10,000 with 377, totaling 20,000 numbers.