The current temperature in degrees Celsius, where x equals the number of hours after noon, is 2x+10 . Interpreting this equation, what is the initial value? (1 point) Responses −10°C negative 10 degrees C 2°C 2 degrees C 10°C 10 degrees C −2°C negative 2 degrees C

Answer 1

To find the initial value from the equation \( T(x) = 2x + 10 \), we need to evaluate \( T(x) \) when \( x = 0 \). This represents the temperature at noon (0 hours after noon).

Substituting \( x = 0 \) into the equation:

\[ T(0) = 2(0) + 10 = 10 \]

So, the initial value (the temperature at noon) is \( 10 , \text{°C} \).

The correct response is:

10°C

Answer 2

From a height of 3,000 feet, a falcon descends at a rate of 250 ft./sec. What is the rate of change in the falcon’s elevation, and what is the initial value? (1 point) Responses The rate of change is 250 ft./sec., and the initial value is 3,000 ft. The rate of change is 250 ft./sec., and the initial value is 3,000 ft. The rate of change is 3,000 ft./sec., and the initial value is −250 ft. The rate of change is 3,000 ft./sec., and the initial value is negative 250 ft. The rate of change is 3,000 ft./sec., and the initial value is 250 ft. The rate of change is 3,000 ft./sec., and the initial value is 250 ft. The rate of change is −250 ft./sec., and the initial value is 3,000 ft. The rate of change is negative 250 ft./sec., and the initial value is 3,000 ft.

Answer 3

To determine the rate of change in the falcon's elevation and the initial value, we analyze the information given:

1. Initial Value: The falcon starts at a height of 3,000 feet. This is the initial elevation.

2. Rate of Change: The falcon is descending at a rate of 250 feet per second. When discussing elevation, a descent indicates that the elevation is decreasing, which means the rate of change should be negative. Therefore, the rate of change in the falcon's elevation is \(-250 , \text{ft/sec}\).

Based on this analysis, the correct response is:

The rate of change is -250 ft./sec., and the initial value is 3,000 ft.

Answer 4

Hector would like to join a gym that has a one-time membership fee plus a monthly fee. He can use the function f(x)=35x+50 to model the cost of gym membership after x months. Identify and interpret the initial value of the function.(1 point) Responses The initial value of 50 represents the monthly fee. The initial value of 50 represents the monthly fee. The initial value of 50 represents the one-time membership fee. The initial value of 50 represents the one-time membership fee. The initial value of 35 represents the monthly fee. The initial value of 35 represents the monthly fee. The initial value of 35 represents the one-time membership fee.

Answer 5

The function \( f(x) = 35x + 50 \) represents the total cost of the gym membership after \( x \) months, where:

• \( 35x \) represents the total cost of the monthly fees (at a rate of $35 per month).
• \( 50 \) is the one-time membership fee, which is charged at the start.

To identify and interpret the initial value, we need to evaluate \( f(0) \):

\[ f(0) = 35(0) + 50 = 50 \]

This means the initial cost of joining the gym (before any months have passed) is $50.

Therefore, the initial value of 50 represents the one-time membership fee.

The correct response is:

The initial value of 50 represents the one-time membership fee.

Answer 6

The function f(x)=−75x+1,200 represents the value of your cell phone x months after you purchase it. Identify and interpret the initial value of the function.(1 point) Responses The initial value of 1,200 represents the value of your cell phone at the time you purchase it. The initial value of 1,200 represents the value of your cell phone at the time you purchase it. The initial value of 1,200 represents the monthly cost of your phone. The initial value of 1,200 represents the monthly cost of your phone. The initial value of 75 represents the value of your cell phone at the time you purchase it. The initial value of 75 represents the value of your cell phone at the time you purchase it. The initial value of 75 represents the monthly cost of your phone.

Answer 7

The function \( f(x) = -75x + 1,200 \) models the value of your cell phone \( x \) months after you purchase it. In this function:

• The term \( 1,200 \) represents the initial value of the cell phone at the time of purchase.
• The term \( -75x \) indicates that the phone's value decreases by $75 for each month that passes.

To find the initial value, we evaluate \( f(0) \):

\[ f(0) = -75(0) + 1,200 = 1,200 \]

This calculation shows that the initial value of the cell phone at the time of purchase is $1,200.

Therefore, the correct interpretation of the initial value is:

The initial value of 1,200 represents the value of your cell phone at the time you purchase it.

Answer 8

A factory produces beach umbrellas. They have a fixed cost they must pay no matter how many umbrellas they produce, and a variable cost they must pay for each umbrella they produce. The cost of producing x umbrellas is modeled by the function C(x)=2.83x+1,350 . Identify and interpret the initial value.(1 point) Responses The initial value of 1,350 represents the fixed cost. The initial value of 1,350 represents the fixed cost. The initial value of 1,350 represents the variable cost. The initial value of 1,350 represents the variable cost. The initial value of 2.83 represents the fixed cost. The initial value of 2.83 represents the fixed cost. The initial value of 2.83 represents the variable cost. The initial value of 2.83 represents the variable cost.

Answer 9

The function \( C(x) = 2.83x + 1,350 \) models the total cost of producing \( x \) beach umbrellas, where:

• The term \( 2.83x \) represents the variable cost, which is the cost incurred for producing each umbrella ($2.83 per umbrella).
• The term \( 1,350 \) represents the fixed cost, which is the cost incurred regardless of the number of umbrellas produced.

To find the initial value, we evaluate \( C(0) \):

\[ C(0) = 2.83(0) + 1,350 = 1,350 \]

This shows that the initial value, or the cost incurred when no umbrellas are produced, is $1,350, which reflects the fixed cost.

Therefore, the correct interpretation of the initial value is:

The initial value of 1,350 represents the fixed cost.

Answer 10

In which case would the kinetic energy of particles be increasing? (1 point) Responses Metal is cooled at 1,300°C. Metal is cooled at 1,300°C. Metal is at room temperature, 37°C. Metal is at room temperature, 37°C. Metal is melted at 1,300°C. Metal is melted at 1,300°C. Metal is heated from room temperature to 200°C.

Answer 11

Kinetic energy of particles is associated with their motion. When a substance is heated, the kinetic energy of its particles increases because heating causes the particles to move faster.

Given the options:

1. Metal is cooled at 1,300°C. (This would decrease kinetic energy.)
2. Metal is at room temperature, 37°C. (This is a stable state where the kinetic energy is constant.)
3. Metal is melted at 1,300°C. (Melting involves a phase change where energy goes into breaking bonds rather than increasing kinetic energy during that process.)
4. Metal is heated from room temperature to 200°C. (This would increase the kinetic energy of the particles.)

The correct response is:

Metal is heated from room temperature to 200°C.