Answer:
- dimensions: 12 ft by 5 ft
- area: 60 ft²
Step-by-step explanation:
Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...
x² + (x+7)² = 13²
2x² +14x + 49 = 169 . . . . eliminate parentheses
x² +7x -60 = 0 . . . . . subtract 169 and divide by 2
(x +12)(x -5) = 0 . . . . factor the equation
x = -12 or +5 . . . . . . . only the positive value of x is useful here.
The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².
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<em>Comment on finding the area</em>
The quadratic equation above can be rearranged and factored as ...
x(x +7) = 60
Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.
composite function J[P(W)=J(1/3w+4) represent paintings Jeremy completes in a year .
this equation means number of paintings= weeks(rate)
The function P takes a number of weeks as an argument and returns the number of paintings.
The function J takes some argument (unspecified) and returns a number of weeks per year.
The composite function that will give the number of paintings per year will be P(weeks per year) = P(J(y)).
P(J(y)) = 1/3·J(y) +4 .
Looking at the units of the input and output of each of the functions is called "units analysis."
<h3>What is Unit analysis?</h3>
Unit analysis means using the rules of multiplying and reducing fractions to solve problems involving different units.
To learn more about unit analysis from the given link
brainly.com/question/14742503
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Answer:
y=-1/2x+80
Step-by-step explanation:
