The school playground is in the shape of a pentagon. There is a drinking fountain at each of the 5 corners of the playground. Th

we understand that

A fast method for estimating the total of two numbers involves rounding each number and adding the rounded results.

case a) We round to the nearest hundred

so

Round up equals

Round up equals

Calculate the estimated sum

case b) We round to the nearest ten

so

Round up equals

Round down equals

Calculate the estimated sum

Solution:

Let x be the distance in miles from the house to the theater.

Total time taken for the trip

Then average speed

Terrence walks at a speed of 2 miles per hour to the theater and returns home at 40 miles per hour.

Thus, Average Speed mi/hr

Both average speeds must be equivalent. Hence, we can express this as:

Consequently, the distance from home is 13.125 miles.

Answer:

• 2(x + 2) + 2 = 2(x + 3) + 1
• 2x + 3(x + 5) = 5(x – 3)
• 5(x + 4) – x = 4(x + 5) – 1

Step-by-step explanation:

To identify solutions, subtract the right side from both sides and simplify.

1. For 2(x + 2) + 2 = 2(x + 3) + 1

   Subtract right side: 2(x + 2) + 2 - (2(x + 3) + 1) = 0

   Simplify: 2x + 4 + 2 - 2x - 6 - 1 = 0

   Which results in -1 = 0, meaning no solutions.

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2. For 2x + 3(x + 5) = 5(x – 3)

   Subtract right side: 2x + 3(x + 5) - 5(x – 3) = 0

   Simplify: 2x + 3x + 15 - 5x + 15 = 0

   This leads to 30 = 0, no solutions again.

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3. Equation 4(x + 3) = x + 12

   Subtract right side: 4(x + 3) - (x + 12) = 0

   Simplify: 4x + 12 - x - 12 = 0

   Equals 3x = 0, so one solution: x = 0.

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4. Equation 4 – (2x + 5) = (–4x – 2)

   Subtract right side: 4 – (2x + 5) - (–4x – 2) = 0

   Simplify: 4 - 2x - 5 + 4x + 2 = 0

   Gives 2x + 1 = 0, meaning one solution: x = -1/2.

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5. Equation 5(x + 4) – x = 4(x + 5) – 1

   Subtract right side: 5(x + 4) – x - (4(x + 5) – 1) = 0

   Simplify: 5x + 20 - x - 4x - 20 + 1 = 0

   Results in 1 = 0, no solution here.