Alan

Given that the point (9,7) is on the graph of y=f(x), there is one point that must be on the graph of 2y = (f(2x)/2) + 2. What is the sum of coordinates of that point?

You can sum the coordinates.

The graph below should help:

Check your second inequality hugo - where you subtract x^2 from both sides.

See if the graph helps:

1 Three balls are numbered 1, 2, 3 and placed in a bag. A ball is chosen, its number recorded, then the ball placed back in the bag. This process is repeated twice more. The resulting 3 recorded numbers are added.
Bob walks in the room after the three numbers have been recorded and is told only that the sum of the numbers is 6. Bob announces, "Oh, then they must all have been 2's." What is the probability that Bob is correct?

There are 7 possibilities:

222

123

132

213

231

312

321

Probability that Bob is correct = 1/7.

As in the image below:

Let   \(u=2^{3x}\)   then the equation can be rewritten as \(u^2+4u-21=0\)

This factorises as:  (u + 7)(u - 3) = 0

Can you take it from here?

5 numbers with a range of 5 a mean of 4 and a median of 3

How about:  3 3 3 3 8 

If P(x) is a cubic polynomial with leading coefficient 2 such that P(1) = 2, P(2) = 8, P(3) = 18, find P(4).

A quarter-circle with radius 5 is drawn. A circle is drawn inside the sector, which is tangent to the sides of the sector, as shown. Find the radius of the inscribed circle.