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Sagot :
To determine which statement correctly describes the temperature, we need to analyze the given equation:
[tex]\[ y = -2x + 43 \][/tex]
In this equation:
- [tex]\( y \)[/tex] is the temperature in degrees Fahrenheit ([tex]\( F \)[/tex]).
- [tex]\( x \)[/tex] is the number of hours since the measurements started.
Starting with the key points of the equation:
1. Initial Temperature:
- When the temperature was first measured, [tex]\( x = 0 \)[/tex].
- Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -2(0) + 43 \][/tex]
[tex]\[ y = 43 \][/tex]
- Therefore, the initial temperature when the measurements started was [tex]\( 43^\circ F \)[/tex].
2. Rate of Temperature Change:
- The coefficient of [tex]\( x \)[/tex] in the equation, which is [tex]\(-2\)[/tex], represents the rate of temperature change.
- A negative coefficient indicates that the temperature is decreasing.
- Specifically, the temperature is dropping by [tex]\( 2^\circ F \)[/tex] per hour.
Now, let's examine each of the given statements:
A. It was [tex]\(-2^\circ F\)[/tex] after four hours, and it is rising by 43 degrees per hour:
- Incorrect. The initial temperature is [tex]\( 43^\circ F \)[/tex] and it is dropping, not rising.
B. It was [tex]\( 43^\circ F \)[/tex] after four hours, and it is dropping by 2 degrees per hour:
- Incorrect. The temperature was [tex]\( 43^\circ F \)[/tex] initially (at time [tex]\( x = 0 \)[/tex]), not after four hours.
C. It was [tex]\( 43^\circ F \)[/tex] when the temperature was first measured, and it is dropping by 2 degrees per hour:
- Correct. This statement accurately reflects that the initial temperature was [tex]\( 43^\circ F \)[/tex] at the start of the measurements and that it is decreasing by [tex]\( 2^\circ F \)[/tex] each hour.
D. It was [tex]\(-2^\circ F\)[/tex] when the temperature was first measured, and it is rising by 43 degrees per hour:
- Incorrect. The initial temperature was [tex]\( 43^\circ F \)[/tex] and the temperature is dropping, not rising.
Therefore, the correct statement is (C): "It was [tex]\( 43^\circ F \)[/tex] when the temperature was first measured, and it is dropping by 2 degrees per hour."
[tex]\[ y = -2x + 43 \][/tex]
In this equation:
- [tex]\( y \)[/tex] is the temperature in degrees Fahrenheit ([tex]\( F \)[/tex]).
- [tex]\( x \)[/tex] is the number of hours since the measurements started.
Starting with the key points of the equation:
1. Initial Temperature:
- When the temperature was first measured, [tex]\( x = 0 \)[/tex].
- Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = -2(0) + 43 \][/tex]
[tex]\[ y = 43 \][/tex]
- Therefore, the initial temperature when the measurements started was [tex]\( 43^\circ F \)[/tex].
2. Rate of Temperature Change:
- The coefficient of [tex]\( x \)[/tex] in the equation, which is [tex]\(-2\)[/tex], represents the rate of temperature change.
- A negative coefficient indicates that the temperature is decreasing.
- Specifically, the temperature is dropping by [tex]\( 2^\circ F \)[/tex] per hour.
Now, let's examine each of the given statements:
A. It was [tex]\(-2^\circ F\)[/tex] after four hours, and it is rising by 43 degrees per hour:
- Incorrect. The initial temperature is [tex]\( 43^\circ F \)[/tex] and it is dropping, not rising.
B. It was [tex]\( 43^\circ F \)[/tex] after four hours, and it is dropping by 2 degrees per hour:
- Incorrect. The temperature was [tex]\( 43^\circ F \)[/tex] initially (at time [tex]\( x = 0 \)[/tex]), not after four hours.
C. It was [tex]\( 43^\circ F \)[/tex] when the temperature was first measured, and it is dropping by 2 degrees per hour:
- Correct. This statement accurately reflects that the initial temperature was [tex]\( 43^\circ F \)[/tex] at the start of the measurements and that it is decreasing by [tex]\( 2^\circ F \)[/tex] each hour.
D. It was [tex]\(-2^\circ F\)[/tex] when the temperature was first measured, and it is rising by 43 degrees per hour:
- Incorrect. The initial temperature was [tex]\( 43^\circ F \)[/tex] and the temperature is dropping, not rising.
Therefore, the correct statement is (C): "It was [tex]\( 43^\circ F \)[/tex] when the temperature was first measured, and it is dropping by 2 degrees per hour."
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