Nellie is analyzing a quadratic function f(x) and a linear function g(x). will they intersect? f(x) g(x) graph of the function f of x equals one half times x squared, plus 2 x g(x) 1 5 2 10 3 15 (6 points) yes, at positive x-coordinates yes, at negative x-coordinates yes, at negative and positive x-coordinates no, they will not intersect

Hi! :)

If we substitute 13 to f(x) and get a value for x, then the two equations will intersect.

So,

f(x) = x^2 + 6x +10
13 = x^2 + 6x+ 10
x^2 + 6x - 3 = 0

Solving the quadratic equations:

The roots of the equation is
x = 0.4641 and x = -6.4541

Therefore, the line will intersect with the quadratic function.

9514 1404 393

  10

Step-by-step explanation:

The Pythagorean theorem tells you the relationships of sides in a right triangle is ...

  a² + b² = c² . . . . . . where 'a' and 'b' are the legs, and 'c' is the hypotenuse

  6² +8² = c²

  36 +64 = c² = 100

  c = √100 = 10

The length of the hypotenuse is 10.

Additional comment

The ratio of the leg lengths is 8/6 = 4/3. The only right triangle with legs in the ratio 4/3 has the relationship ...

  hypotenuse : long leg : short leg = 5 : 4 : 3

If you multiply these numbers by 2, you see they correspond to the side lengths in this triangle. Your familiarity with a 3-4-5 right triangle can let you write down the answer immediately.