During low tide in Wrightsville, North Carolina, the beachfront in some places is about 350 feet from the ocean to the homes. High tide can chance the width of a beach at a rate or -17 feet an hour. It takes 6 hours for the ocean to move from low to high tide.

a. What is the change in the width of the beachfront from low to high tide?
b. What is the distance from the ocean to the homes at high tide?

Answers

Answer 1

The change in the width of the beachfront from low to high tide is 102 feet, and the distance from the ocean to the homes at high tide is 248 feet.

a. To find the change in width from low to high tide, we multiply the rate of change (-17 feet/hour) by the time it takes for the ocean to move from low to high tide (6 hours).

So, -17 feet/hour * 6 hours = -102 feet. Therefore, the width of the beachfront decreases by 102 feet from low to high tide.

b. At high tide, the distance from the ocean to the homes is the sum of the original distance (350 feet) and the change in width during the tide change (-102 feet), resulting in 350 feet + (-102 feet) = 248 feet.

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Step-by-step explanation:

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The value of x is 32.

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[tex]x=\frac{m-9}{3-d}[/tex]

Step-by-step explanation:

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[tex]m-9=9-9+3x-dx[/tex]

[tex]m-9=3x-dx[/tex]

Factor out x from right side:

[tex]m-9=x(3-d)[/tex]

Switch sides:

[tex]x(3-d)=m-9[/tex]

Divide both sides by [tex](3-d)[/tex]:

[tex]\frac{x(3-d)}{3-d}=\frac{m-9}{3-d}[/tex]

[tex]x=\frac{m-9}{3-d}[/tex]

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Answers

The answer: The equation is true. x = all real numbers.
_____________________________________________
Given:
_________________________________
-6 − 8(1 − x) = -14 + 8x ;
_________________________________
Note the "distributive property of multiplication" :
_______________________________________________a(b+c) = ab + ac ;
a(b−c) = ab − ac ;_______________________________________________As such:_______________________________________________ -8(1 − x) = (-8 * 1) − (-8*x) = (-8) − (-8x) = -8 + 8x

→ So, rewrite the original equation, substituting: "-8 + 8x" for: "−8(1 − x)" :

→ - 6 − 8 + 8x = -14 + 8x ;
Note: -6 − 8 = -14 ;

Rewrite as:
_____________________________

-14 + 8x = -14 + 8x ;
____________________________________

The answer: The equation is true. x = all real numbers.
_____________________________________________

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