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Answer :
The equation given is [tex]\( g = 13 - 0.3h \)[/tex], where [tex]\( g \)[/tex] represents the gallons of gas left and [tex]\( h \)[/tex] represents time in hours. We need to determine what the number 13 represents in this context.
To understand this equation, let's break it down:
1. Variables and Coefficients:
- [tex]\( g \)[/tex] is the amount of gas left in the tank.
- [tex]\( h \)[/tex] is the amount of time in hours.
- [tex]\( 0.3 \)[/tex] is the rate at which the gas is consumed per hour.
2. Equation Concept:
- The equation shows that as time increases, the amount of gas decreases due to the subtraction of [tex]\( 0.3h \)[/tex].
3. Analyzing the Equation:
- At [tex]\( h = 0 \)[/tex] (the beginning of the trip), substitute this value into the equation:
[tex]\[
g = 13 - 0.3 \times 0 = 13
\][/tex]
- This tells us that at the start of the trip, when no time has elapsed, the amount of gas in the tank is 13 gallons.
From this, we can conclude that the number 13 represents the initial amount of gallons of gas in the tank at the start of the trip, or at time [tex]\( h = 0 \)[/tex].
Therefore, the correct interpretation of the number 13 is:
- The number of gallons of gas at time [tex]\( h = 0 \)[/tex].
To understand this equation, let's break it down:
1. Variables and Coefficients:
- [tex]\( g \)[/tex] is the amount of gas left in the tank.
- [tex]\( h \)[/tex] is the amount of time in hours.
- [tex]\( 0.3 \)[/tex] is the rate at which the gas is consumed per hour.
2. Equation Concept:
- The equation shows that as time increases, the amount of gas decreases due to the subtraction of [tex]\( 0.3h \)[/tex].
3. Analyzing the Equation:
- At [tex]\( h = 0 \)[/tex] (the beginning of the trip), substitute this value into the equation:
[tex]\[
g = 13 - 0.3 \times 0 = 13
\][/tex]
- This tells us that at the start of the trip, when no time has elapsed, the amount of gas in the tank is 13 gallons.
From this, we can conclude that the number 13 represents the initial amount of gallons of gas in the tank at the start of the trip, or at time [tex]\( h = 0 \)[/tex].
Therefore, the correct interpretation of the number 13 is:
- The number of gallons of gas at time [tex]\( h = 0 \)[/tex].
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