Aboater travels 27 miles per hour on the water on a still day. during one particularly windy day, he finds that he travels 42 miles with the wind behind him in the same amount of time that he travels 21 miles into the wind. find the rate of the wind.

The rate of wind is 9 miles per hour.

Step-by-step explanation:

We are given the following information:

A boater travels 27 miles per hour on the water on a still day.

The w be the rate of wind.

27 + w = speed with the wind    

27 - w = speed against the wind

Time taken by him to travel with the wind =

Time taken by him to travel against the wind =

Since, the time is equal,

Thus, the rate of wind is 9 miles per hour.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.