If the hypotenuse of a 45°-45°-90° triangle is 13, what is the length of one of the legs?

  B.  (13√2)/2

Step-by-step explanation:

Let L represent the length of one leg of the triangle. We note that the triangle is isosceles, so both legs are the same length. Then the Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs:

  13² = L² + L²

  13² = 2L²

  13 = (√2)L

  L = 13/√2 = (13√2)/2 . . . length of one leg

To "rationalize the denominator", we multiply the fraction 13/√2 by (√2)/(√2). The result is (13√2)/2.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions