Question

pregunta 12
noah is going on a trip and hes using the celsius scale. he is curious about converting celsius temperatures to fahrenheit. noah determines 68°f is equivalent to 20°c and 86°f is equivalent to 30°c. which function models the relationship between fahrenheit and celsius?
○ f = 9/5 c - 512/5
○ f = 9/5 c - 32
○ f = 5/9 c - 512/9
○ f = 9/5 c + 32

Explanation:

Step1: Identificar la ecuación de conversión

La fórmula estándar para convertir Celsius a Fahrenheit es \( F = \frac{9}{5}C + 32 \). También podemos verificar con los datos dados: cuando \( C = 20 \), \( F = \frac{9}{5}(20)+32 = 36 + 32 = 68 \), que coincide. Cuando \( C = 30 \), \( F = \frac{9}{5}(30)+32 = 54 + 32 = 86 \), que también coincide.

Step2: Comparar con las opciones

• Opción 1: \( F=\frac{9}{5}C - \frac{512}{5} \). Al probar \( C = 20 \), \( F=\frac{9}{5}(20)-\frac{512}{5}=36 - 102.4=-66.4

eq68 \).

• Opción 2: \( F=\frac{9}{5}C - 32 \). Al probar \( C = 20 \), \( F=\frac{9}{5}(20)-32 = 36 - 32 = 4

eq68 \).

• Opción 3: \( F=\frac{5}{9}C - \frac{512}{9} \). Al probar \( C = 20 \), \( F=\frac{5}{9}(20)-\frac{512}{9}=\frac{100 - 512}{9}=\frac{-412}{9}\approx - 45.78

eq68 \).

• Opción 4: \( F=\frac{9}{5}C + 32 \). Coincide con la verificación anterior.

Answer:

D. \( F = \frac{9}{5}C + 32 \) (assuming the last option is D, if the options are labeled as A, B, C, D with the last one being \( F = 9/5 C + 32 \), then the answer is the option with \( F = 9/5 C + 32 \), for example, if it's option D: D. \( F = 9/5 C + 32 \))