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Harlamova29_29 [7]

3 years ago

13

Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 8 feet,

15 feet, and 20 feet long. Will he be able to make a right triangle with his fence? Why or why not.

1 answer:

BlackZzzverrR [31]3 years ago

6 0

Answer:

Step-by-step explanation:

The three pieces of fencing he has to use are 8 feet, 15 feet, and 20 feet long. For him to be able to make a right triangle with his fence, the length of the sides must form a Pythagoras triple. To determine if the lengths make a Pythagoras triple, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent².

Therefore

20² = 8² + 15²

400 = 64 + 225 = 289

Since they are not equal, it means that they do not form Pythagoras theorem, thus,.

He will not be able to make a right triangle with his fence.

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Given a leading coefficient of 8, polynomial roots of 1 & 2, and the known point on the graph (4,5). Write an equation that

m_a_m_a [10]

Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

$y=a(x-c_1)(x-c_2)...(x-c_n)$

Where, a is a constant and $c_1,c_2,...,c_n$ are the roots of the polynomial.

Polynomial roots are 1 and 2. So, $(x-1)$ and $(x-2)$ are the factors of the polynomial.

Let the third root of the polynomial by c, then $(x-c)$ is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

$y=8(x-1)(x-2)(x-c)$

The graph passes through the point (4,5). Putting $x=4,y=5$ , we get

$5=8(4-1)(4-2)(4-c)$

$5=8(3)(2)(4-c)$

$5=48(4-c)$

Divide both sides by 48.

$\dfrac{5}{48}=4-c$

$c=4-\dfrac{5}{48}$

$c=\dfrac{192-5}{48}$

$c=\dfrac{187}{48}$

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<h2>Step-by-step explanation:</h2>

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