Laura placed a bucket of water in her garden. Over the course of a week, she watched the water evaporate and recorded the volume

Solution:

We know, g(x) = f(x) + k --------(1)

It is given that f(x) = (x+2)

and g(x) = (x+5)

Substituting f(x) and g(x) into equation (1):

→ (x+5) = (x+2) + k

→ = k

→ k =

Thus, the value of k is 1.

Manuel has opted to construct a fence to define a play area for his dogs, which will be a rectangular shape. Since only three sides require fencing because his house acts as one side of the rectangle, we conclude that the optimal area configuration will consist of two shorter sides each measuring 20 feet and a longer side measuring 40 feet.

Let’s tackle the problem. We know the formula for <span>the height of the ball is as follows:

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Here, x represents </span><span>the horizontal distance in yards that the ball has traveled in the air. Given that distance is always a positive value, we conclude that x must be greater than or equal to 0. Thus:

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The horizontal plane indicates the function's zero point, and since the ball cannot have negative height values, must also remain positive. Ultimately, the graph reveals that the suitable domain is:

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