The current temperature in degrees Celsius, where x equals the number of hours after noon, is 2x+10

Question

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

2°C
2 degrees C

−10°C
negative 10 degrees C

10°C
10 degrees C

−2°C

GPT-4o mini · Answer

To find the initial value of the temperature in degrees Celsius, we need to evaluate the equation $ 2x + 10 $ when $ x = 0 $ (which represents noon, the start time).

Substituting $ x = 0 $ into the equation:

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

Thus, the initial value of the temperature at noon (when $ x = 0 $) is $ 10°C $.

The correct response is:

10°C

BTS ARMY · Answer

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 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 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 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 −250
ft./sec., and the initial value is 3,000 ft.

GPT-4o mini · Answer

In this scenario, the falcon is descending from an initial height of 3,000 feet at a rate of 250 feet per second.

Rate of Change: Since the falcon is descending, the rate of change in elevation is negative. Therefore, the rate of change is $-250$ ft/sec.
Initial Value: The initial elevation of the falcon when it starts its descent is 3,000 feet.

Therefore, the correct statement is:

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

BTS ARMY · Answer

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 35 represents the one-time membership fee.
The initial value of 35 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 50 represents the one-time membership fee.

GPT-4o mini · Answer

The function $ f(x) = 35x + 50 $ represents the total cost of the gym membership after $ x $ months. In this function: - The term $ 50 $ represents the one-time membership fee. This is the initial value, which is the total cost when $ x = 0 $ (before any monthly fees are incurred). - The term $ 35x $ represents the monthly fee of $ 35 $ dollars for each month $ x $. Therefore, the correct interpretation of the initial value is: **The initial value of 50 represents the one-time membership fee.**

BTS ARMY · Answer

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 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 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 75 represents the monthly cost of your phone.
The initial value of 75 represents the monthly cost of your phone.

The initial value of 1,200 represents the monthly cost of your phon

GPT-4o mini · Answer

The function $ f(x) = -75x + 1200 $ represents the value of your cell phone $ x $ months after purchase. In this function: - The term $ 1200 $ is the initial value, which is the value of the cell phone at the time you purchase it (when $ x = 0 $). - The term $ -75x $ indicates that the value of the cell phone decreases by $75 for each month that passes, representing depreciation. 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.**

BTS ARMY · Answer

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

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

GPT-4o mini · Answer

The function $ C(x) = 2.83x + 1350 $ represents the cost of producing $ x $ beach umbrellas. In this function: - The term $ 1350 $ is the initial value, which represents the **fixed cost** that the factory must pay regardless of how many umbrellas are produced (when $ x = 0 $). - The term $ 2.83x $ represents the **variable cost** per umbrella produced, where $ 2.83 $ is the cost for each individual umbrella. Therefore, the correct interpretation of the initial value is: **The initial value of 1,350 represents the fixed cost.**

BTS ARMY · Answer

why do balloons stick to the wall when you rub them on your head or sweater?

GPT-4o mini · Answer

Balloons stick to the wall after being rubbed on your head or a sweater due to a phenomenon known as static electricity. Here's how it works:

Friction: When you rub a balloon against your hair or a sweater, electrons (which are negatively charged) are transferred from your hair or sweater to the surface of the balloon. This process is called the triboelectric effect.
Charge Imbalance: As a result of this electron transfer, the balloon becomes negatively charged, while your hair or the sweater becomes positively charged because it has lost some electrons.
Attraction: The negatively charged balloon has an imbalance of electric charge compared to the neutral wall (which has an equal number of positive and negative charges). When you bring the negatively charged balloon close to the wall, the negative charges on the surface of the balloon repel the negative charges in the wall. This causes the positive charges in the wall to be attracted to the balloon.
Sticking to the Wall: As a result of this attraction, the balloon gets pulled toward the wall and can stick to it temporarily due to the electrostatic force.

This sticking effect lasts until the charge on the balloon dissipates (which can happen over time or through contact with other surfaces), reducing its ability to stick to the wall.