m quiz review 1.5 & 1.7\n6. maria runs a lawn care service. she charges a flat rate of $60 for any job that…

m quiz review 1.5 & 1.7\n6. maria runs a lawn care service. she charges a flat rate of $60 for any job that takes 3 hours or less. for jobs that take longer than 3 hours, she charges an additional $18 per hour beyond the first 3 hours.\nwrite the equation that models maria’s pricing.\nequation: price = $60 + 18(______) (hours after 3)\nif a job takes 5 hours:\nstep 1: extra hours = ________\nstep 2: price = $60 + 18(__________)\nstep 3: price = ____________\n7. a local bowling alley charges a fee for renting a lane. the cost is $12 for up to one hour.\nafter one hour, the price increases to $18.\nafter three hours, the price increases again to $40.\nthe maximum time someone can rent a lane is 8 hours total. write an equation that represents this situation.\na. what is f(4)? answer: ________\nb. what is f(1)? answer: ________\nc. for which x values does f(x) = 40? answer: ________

m quiz review 1.5 & 1.7\n6. maria runs a lawn care service. she charges a flat rate of $60 for any job that takes 3 hours or less. for jobs that take longer than 3 hours, she charges an additional $18 per hour beyond the first 3 hours.\nwrite the equation that models maria’s pricing.\nequation: price = $60 + 18(______) (hours after 3)\nif a job takes 5 hours:\nstep 1: extra hours = ________\nstep 2: price = $60 + 18(__________)\nstep 3: price = ____________\n7. a local bowling alley charges a fee for renting a lane. the cost is $12 for up to one hour.\nafter one hour, the price increases to $18.\nafter three hours, the price increases again to $40.\nthe maximum time someone can rent a lane is 8 hours total. write an equation that represents this situation.\na. what is f(4)? answer: ________\nb. what is f(1)? answer: ________\nc. for which x values does f(x) = 40? answer: ________

Answer

Explicación:

Paso 1: Encontrar horas adicionales para Maria

Calculamos las horas adicionales para un trabajo de 5 horas. Restamos las primeras 3 horas. $5 - 3=2$

Paso 2: Calcular el precio para Maria

Sustituimos el número de horas adicionales en la fórmula de precio. $Precio = 60+18(2)$

Paso 3: Obtener el precio final para Maria

Calculamos el valor del precio. $Precio = 60 + 36=96$

Para el bowling alley:

Paso 4: Definir la función para el bowling alley

Tenemos un caso a caso. Para $0 < x\leq1$, $f(x)=12$; para $1 < x\leq3$, $f(x)=18$; para $3 < x\leq8$, $f(x)=40$.

Paso 5: Calcular $f(4)$

Como $3 < 4\leq8$, entonces $f(4)=40$

Paso 6: Calcular $f(1)$

Como $0 < 1\leq1$, entonces $f(1)=12$

Paso 7: Encontrar $x$ para $f(x) = 40$

Como $f(x)=40$ para $3 < x\leq8$, entonces $3 < x\leq8$

Respuesta:

Para Maria:

  • Ecuación: $Precio = 60+18(\text{horas después de 3})$
  • Paso 1: $2$
  • Paso 2: $2$
  • Paso 3: $96$

Para el bowling alley:

  • a. $40$
  • b. $12$
  • c. $3 < x\leq8$