B R S are two points on a circle,
Centre O.
TS is a tangent to the circle.
Angle RST = x
Prove that ROS=2X
You must give reasons for each stage
of your working

Proved!

Step-by-step explanation:

Since TS is a tangent to the circle, ∠TSO = 90°.

Hence, ∠OSR = 90° - x.

Since OS and OR are radius, OS = OR.

So, ∠ORS = ∠OSR = 90° - x.

Thus, ∠ROS = 180° - ∠OSR - ∠ORS = 180° - 2 * (90° - x) = 180° - 180° + 2x = 2x.

So, it is proved.

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