Beth does not charge a registration fee for her dog-walking service, but she charges $5 per mile that each dog is walked. Tonya's dog-walking service charges a registration fee of $20, plus $3 per mile that each dog is walked. Write and solve an equation to find the number of miles m for which Tonya and Beth would charge the same amount.

The question is about clock hands. The acute angle measure of the hands of a clock at the time 2:20 is 80 degrees.

Clock hands are essential components of analog clocks and watches, indicating the time by their positions. Typically, a clock has three hands: the hour hand, the minute hand, and the second hand. The hour hand is shorter and denotes the hours, while the longer minute hand points to the minutes. The second hand, the thinnest and longest, measures seconds. Clock hands move in a clockwise direction, and their synchronized motion helps people tell time at a glance, making them fundamental features of timekeeping devices for centuries.

To find the acute angle measure of the hands of a clock at the time 2:20, we need to determine the angle covered by the hour hand. In going from 12 to 3, the hour hand covers 1/4 of the 12 hours needed to make a complete revolution. Therefore, the angle between the hour hand at 12 and at 3 is 90 degrees. Since it is 20 minutes past 2, the minute hand will be 1/3 of the way between 2 and 3. This means the minute hand will be at an angle of 1/3 x 30 degrees = 10 degrees. The acute angle between the hour and minute hands can be found by subtracting the smaller angle from the larger angle. So, the acute angle measure of the hands of the clock at the time 2:20 is 90 degrees - 10 degrees = 80 degrees.

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Answer:

50 degrees

Step-by-step explanation:

To find the acute angle measure between the hour and minute hands of a clock at 2:20, you can use the following method:

   First, calculate the minute hand's position:

       The minute hand moves 360 degrees in 60 minutes, so in 20 minutes, it covers (20/60) * 360 = 120 degrees.

   Next, calculate the hour hand's position:

       The hour hand moves 360 degrees in 12 hours, so in 2 hours and 20 minutes, it covers (2 + 20/60) * (360/12) = (2 + 1/3) * 30 = (7/3) * 30 = 70 degrees.

   Now, find the acute angle between the hour and minute hands:

       Subtract the hour hand position from the minute hand position:

       120 degrees (minute hand) - 70 degrees (hour hand) = 50 degrees.

So, the acute angle measure between the hands of the clock at 2:20 is 50 degrees.

Final answer:

The correct function that describes the height of the ball on a replay that runs at half speed is h(t) = -16(t/2)^2 + 3. This is because the time in the original function enters as a square, so it must be halved before being squared.

Explanation:

In this problem, a slow motion replay means the time factor is slowed down by a half. The original function is h(t) = -16t2 + 3. However, the time factor isn't just halved, it's halved before being squared, because time enters the function as a square. So in the replay function, every instance of t in the original function is replaced with 0.5t or t/2. Hence, the correct option that describes the height of the ball in the replay is h(t) = -16(t/2)2 + 3.

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The possible values of for are and .

The expression is equivalent to the expression, which represents a second orderpolynomial, that is, a polynomial of the form:

(1)

Where are coefficients.

The possible values of x represents all possible roots of x, which are found analytically by the quadratic formula:

(2)

If we know that , and , then all possible values of are, respectively:

,

The possible values of for are and .

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Answer:

f(x) = 2(x + 3)(x - 6)

Step-by-step explanation: