To determine how many hours earlier Sanya first checked her thermometer, given that the temperature dropped [tex]\( 1.4 \)[/tex] degrees per hour and it dropped a total of [tex]\( 21 \)[/tex] degrees by 6 a.m., we need to find an expression to calculate the number of hours it took for the temperature to drop those [tex]\( 21 \)[/tex] degrees.
First, identify the variables involved:
- The steady rate of temperature drop is [tex]\( 1.4 \)[/tex] degrees per hour.
- The total temperature drop is [tex]\( 21 \)[/tex] degrees.
To find the number of hours [tex]\( h \)[/tex] that had passed for the temperature to drop [tex]\( 21 \)[/tex] degrees at a rate of [tex]\( 1.4 \)[/tex] degrees per hour, use the equation:
[tex]\[ \text{Total temperature drop} = \text{Rate of temperature drop} \times \text{Number of hours} \][/tex]
This can be written as:
[tex]\[ 21 = 1.4 \times h \][/tex]
Next, solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{21}{1.4} \][/tex]
Therefore, the correct expression to find how many hours earlier she had checked the thermometer is:
[tex]\[ 21 \div 1.4 \][/tex]
None of the options provided directly match this expression. However, the division expression translates to [tex]\( 21 + (-1.4h) \)[/tex] if you are considering an hourly sequence of temperature reduction by 1.4 degrees until the total becomes 21 degrees.
Given the options listed:
- [tex]\( -21 + -1.4 \)[/tex]
- [tex]\( -1.4 + -21 \)[/tex]
- [tex]\( -21 + 1.4 \)[/tex]
- [tex]\( 21 + -1.4 \)[/tex]
The most plausible option aligned with the correct approach [tex]\( 21 \div 1.4 \)[/tex] is
[tex]\[ 21 + -1.4 \][/tex]
Therefore, the correct option is:
[tex]\[ 21 + -1.4 \][/tex]
