Find the measure of the arc or central angle indicated. Assume that the lines which’s appear to be diameters are actual diameters.

m∠HKF = 87°

Solution:

Given data:

m(ar JF) = 135° and m(ar GH) = 42°

GJ is the diameter of the circle.

Angle in a diameter is 180°.

⇒ m(ar JF) + m(ar FG) = 180°

⇒ 135° + m(ar FG) = 180°

Subtract 135° from both sides of the equation.

⇒ m(ar FG) = 45°

⇒ m(ar FGH) = m(ar FG) + m(ar GH)

⇒ m(ar FGH)= 45° + 42°

⇒ m(ar FGH) = 87°

The measure of the central angle is congruent to the measure of the intercepted arc.

⇒ m∠HKF = m(ar FGH)

⇒ m∠HKF = 87°

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation: