Sarah is setting up a garden plot in the shape of a right triangle. One leg off the triangle will be 7 feet longer than the other and the hypotenuse will be 1 foot longer than the longest leg. Find the length of each side of the garden plot. As a part of your work, include a sketch with the sides labeled. Show work algebraically.

The smallest leg of the triangular garden is 5 feet while the biggest leg is 12 feet.

The three-sided shape known as a triangle is sometimes used to allude to it.

The area of a triangle is defined as (1/2) base height, and the sum of all three angles within a triangle will be 180°.

As the given triangular garden has been drawn below,

By Pythagoras' theorem,

x² + (x + 7)² = (x + 8)²

x² + x² + 49 + 14x = x² + 64 + 16x

x² - 2x - 15 = 0

x² - 5x + 3x - 15 = 0

x(x - 5) + 3(x - 5) = 0

(x + 3)(x - 5) = 0

x = -3,5

Since length can never be negative thus x = 5.

The smallest leg = 5 feet

Biggest leg = 5 + 7 = 12 feet

Hence "The triangular garden's smallest leg is 5 feet long, while its longest leg is 12 feet".

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O No, the order of the questions is unknown.
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O No, the answers are not independent of one another.
O No, we do not know how many quizzes this teacher will give.
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A 95% confidence interval for the slope of the regression line relating the number of grams of carbohydrates and the number of kilocalories per 100-gram sample of various raw foods is given by (2.505,6.696). The confidence interval is based on a random sample of n raw foods. A check of the conditions for inference on the slope shows they are reasonably met. Which of the following is a correct interpretation of the interval?
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C. We are 95% confident that the slope of the regression line for the random sample of n raw foods is between 2.505 and 6.696.
D We are 95% confident that the predicted number of kilocalories per 100-g sample will be between 2.505 and 6.696.
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