Katelynrocksoneidn
Answered

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This question has four parts.
32 Colton is heating a pot of water. He records the temperature of the water in
the pot every minute. This equation models Colton's data, where x represents
the number of minutes the water has been heated, and y represents the
temperature of the water in degrees Fahrenheit.
y = 7.5x + 40
What is the temperature in degrees Fahrenheit of colton's pot of water after 16 minutes. Hi Ayer boils at a temperature of 212 after 16 minutes of heating how much additional time to the nearest minute will be needed for the water to boil.

Sagot :

Answer:

Step-by-step explanation:

PART A

7.5 represents the ounces of water heating up inside the pot.

PART B

40 in the equation will represent the starting point. It can be described as where the temperature started.

PART C

The temperature, of Colton's pot of water after 16 minutes will be 120°  7.5(16) = 120  7.5 being the ounces of water and 16 being minutes.

PART D

After 16 minutes of heating, about 13.3 as additional time will be added for the water to start boiling at 212°.

The temperature in degrees Fahrenheit of colton's pot of water after 16 minutes is 160° F. The additional time to the nearest minute will be needed for the water to boil is 7 minutes approximately.

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

For this case, it is specified that:

  • y = 7.5x + 40 ( where x = number of minutes the number of minutes the water has been heated, and y represents the temperature of the water in degrees Fahrenheit.)

So, if the water is boiling for x = 16 minutes, then the temperature would be:

[tex]y = 7.5 \times 16 +40 = 160^\circ \: \rm F[/tex]

Also, we need to make the temperature reach to 212 degree Fahrenheit after 16 minute of boiling.

Let it takes T time (in minutes more) to reach 212 degree Fahrenheit, then: y = 212, x = 16 + T

Putting these values in the equation, we get:

[tex]y = 7.5x + 40\\212=7.5\times(16+T) + 40\\212 = 120 + 7.5T + 40\\7.5T = 212-160\\\\T = \dfrac{212-160}{7.5} = \dfrac{52}{7.5} \approx 6.93 \: \rm minutes \approx 7 \: \rm minutes[/tex]

Thus, the temperature in degrees Fahrenheit of colton's pot of water after 16 minutes is 160° F. The additional time to the nearest minute will be needed for the water to boil is 7 minutes approximately.

Learn more about evaluating a function at a value here:

https://brainly.com/question/2753269

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