Let f(x)=2x^2−1. the quadratic function g(x) is f(x) translated left 2 units. enter the equation of g(x) in the box.

Step-by-step explanation:

The place to start is ...

After that, the next step is to make use of the relationships you know between the items of information given and those asked for.

__

The first box you're asked to fill is the value of the third angle of the triangle. You know A is 30° because that's the way it is marked. You know C is 90° because it has the right-angle symbol there, and a right angle measures 90°. You know the sum of the three angles in any triangle is 180°, so you have ...

  30° +90° +∠B = 180°

Subtracting 120° from both sides of this equation gives us ...

  ∠B = 60°

__

Comment on this answer

It should also be pretty obvious that ∠B is the complement of ∠A in a right triangle. That is ...

  30° +∠B = 90° . . . . . subtracting 90° from both sides of the above equation

The second box you're asked to fill in is the length of the side opposite the given angle. You know this is a right triangle, so you know the definitions of the trig ratios apply. The mnemonic SOH CAH TOA reminds you of the sine relation:

  Sin = Opposite/Hypotenuse

In this triangle, that means ...

  sin(30°) = a/8

Multiplying by 8, we get ...

  a = 8·sin(30°) = 8·1/2

  a = 4

The same mnemonic makes reference to the adjacent side, which is side b of the triangle. That is the measure asked for in the third box.

  Cos = Adjacent/Hypotenuse

  cos(30°) = b/8

Multiplying by 8, we get ...

  b = 8·cos(30°) = 8·0.866025 ≈ 6.92820

  b ≈ 6.93