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Reduce the equation 30.7t−14.7=11.3t+32.930.7𝑡−14.7=11.3𝑡+32.9  to the form  mt+b=0𝑚𝑡+𝑏=0  and solve it.   Write down the answer as a decimal. Round off to two decimal places.

Question

Reduce the equation 30.7t−14.7=11.3t+32.930.7𝑡−14.7=11.3𝑡+32.9  to the form  mt+b=0𝑚𝑡+𝑏=0  and solve it.   Write down the answer as a decimal. Round off to two decimal places.

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Solution

First, let's simplify the equation by subtracting 11.3t from both sides:

30.7t - 11.3t = 11.3t + 32.9 - 11.3t

This simplifies to:

19.4t - 14.7 = 32.9

Next, let's get the equation into the form mt + b = 0 by subtracting 32.9 from both sides:

19.4t - 14.7 - 32.9 = 0

This simplifies to:

19.4t - 47.6 = 0

Now, let's solve for t by adding 47.6 to both sides and then dividing by 19.4:

(19.4t - 47.6 + 47.6) / 19.4 = 47.6 / 19.4

This simplifies to:

t = 47.6 / 19.4

Using a calculator, we find that t = 2.45 when rounded to two decimal places.

This problem has been solved

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