Respuesta :
The key word is "between." Example: a number x is between 5 and 17. Translation: 5 < x < 17.
You want the Celsius temperature to be between -40 and 125.
[tex]-40\ \textless \ \frac{5}{9}(F-32)\ \textless \ 125[/tex]
The second answer choice is correct.
The first answer choice is in the wrong order; it would mean that -40 > 125. Nope!
The third answer choice is "one-sided"; it says the Celsius temperature is larger than -40 but fails to mention the upper limit of 125.
The fourth answer choice is "one-sided," too. It says the Celsius temperature is less than 125 but doesn't mention the lower limit of -40.
I hope this helps a lot!
You want the Celsius temperature to be between -40 and 125.
[tex]-40\ \textless \ \frac{5}{9}(F-32)\ \textless \ 125[/tex]
The second answer choice is correct.
The first answer choice is in the wrong order; it would mean that -40 > 125. Nope!
The third answer choice is "one-sided"; it says the Celsius temperature is larger than -40 but fails to mention the upper limit of 125.
The fourth answer choice is "one-sided," too. It says the Celsius temperature is less than 125 but doesn't mention the lower limit of -40.
I hope this helps a lot!
Answer:
Option 2 - [tex]-40<\frac{5}{9}(F -32)<125; -40<F<257[/tex]
Step-by-step explanation:
Given : The label on the car's antifreeze container claims to protect the car between −40°C and 125°C. To convert Celsius temperature to Fahrenheit temperature, the formula is [tex]C = \frac{5}{9}(F -32)[/tex]
To find : Write and solve the inequality to determine the Fahrenheit temperature range at which this antifreeze protects the car?
Solution :
To convert Celsius temperature to Fahrenheit temperature,
the formula is [tex]C = \frac{5}{9}(F -32)[/tex]
So, Rearrange to make the formula to find Fahrenheit
Cross multiply in the formula,
[tex]\frac{9}{5}C=(F -32)[/tex]
[tex]\frac{9}{5}C+32=F[/tex]
The formula to determine the Fahrenheit temperature is
[tex]F=\frac{9}{5}C+32[/tex]
The label on the car's antifreeze container claims to protect the car between -40°C and 125°C.
i.e. [tex]-40<\frac{5}{9}(F -32)<125[/tex]
Substitute C= -40°C,
[tex]F=\frac{9}{5}\times (-40)+32[/tex]
[tex]F=9\times (-8)+32[/tex]
[tex]F=-72+32[/tex]
[tex]F=-40[/tex]
Substitute C= 125°C,
[tex]F=\frac{9}{5}\times (125)+32[/tex]
[tex]F=9\times 25+32[/tex]
[tex]F=225+32[/tex]
[tex]F=257[/tex]
So, [tex]-40<\frac{9}{5}C+32<257[/tex]
or [tex]-40<F<257[/tex]
Therefore, Option 2 is correct.
