Let f= {(-5,1).( - 4,0).(0,6)} Find f(0) f(0)=

Mathematics

1 answer:

sweet [91]3 years ago

5 0

Given:

It is given that the coordinates of the function are $f=\{(-5,1),(-4,0),(0,6)\}$

We need to determine the value of f(0)

Value of f(0):

The value of f(0) is the value of the function when the input is 0.

We need to determine the value of f(0) when the input is x = 0

Thus, from the coordinates of the function $f=\{(-5,1),(-4,0),(0,6)\}$ , it is obvious that the input value of the function is x = 0 , then the value of the function f(0) = 6.

Thus, when the input value x = 0, the output is f(0) = 6.

Therefore, the value of f(0) = 6.

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4. To determine if a triangle is a right triangle, given that you know the length of its sides, you have to check if its lengths follow the Pythagorean theorem.

This theorem states that the square of the hypothenuse (c) is equal to the sum of the squares of the legs of the triangle (a and b), following the expression:

$a^2+b^2=c^2$

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We have to check that a²+ b² is equal to c².

The square of the hypothenuse is:

$\begin{gathered} c^2=10^2 \\ c^2=100 \end{gathered}$

The sum of the squares of the legs of the triangle is:

$\begin{gathered} a^2+b^2=8^2+6^2 \\ a^2+b^2=64+36 \\ a^2+b^2=100 \end{gathered}$

As you can see, the sum of the squares of the legs of the triangle is 100, which is the same as the square of the hypothenuse. The triangle follows the Pythagorean theorem and can be considered a right triangle.