Please help me, I don't know how to do this...

Mathematics

1 answer:

Lunna [17]2 years ago

8 0

Answer:

A. 5

Step-by-step explanation:

The triangle will be a right triangle when the side lengths satisfy the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.

(x +1)^2 +x^2 = (√61)^2

x^2 +2x +1 +x^2 = 61 . . . eliminate parentheses

2x^2 +2x = 60 . . . . . . .subtract 1, collect terms

x^2 +x -30 = 0 . . . . . divide by 2, subtract 30

(x +6)(x -5) = 0 . . . . factor the quadratic

x = -6 or +5

The solution is x = 5.

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Side lengths cannot be negative. Solution values are values of x that make the factors zero. x+6=0 when x=-6, for example.

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Provide a recursive definition of the function f(n) = (n+1)!.

fiasKO [112]

Answer:

See definition below

Step-by-step explanation:

Since we have to give a recursive definition, we must give a initial value f(0). Additionally, the value of f(n) must depend on the value of f(n-1) for all n≥1.

The required value of f(0) is (0+1)!=1!=1.

Now, the factorial itself is a recursive function, because (n+1)!=(n+1)n!. In terms of f, this means that f(n)=(n+1)f(n-1) for all n≥1.

Then, our definition is: f:N→N is defined by