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see explanation

Step-by-step explanation:

The equation of a circle centred at the origin is

x² + y² = r² ( where r is the radius )

x² + y² = 49 ← is in this form with

r² = 49 ( take square root of both sides )

r = = 7

Thus A = (7, 0 ) and B = (0, 7 )

To find M use the midpoint formula

M = ( , ) = (3.5, 3.5 )

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (3.5, 3.5 )

m = = = 1

y = x ← equation of line passing through O and M

Below in bold.

Step-by-step explanation:

(a)

At point A,  y = 0 so the coordinates of A are found as follows:

x^2+ 0^2 = 49

x^2 = 49

x = 7   so A is (7, 0).

In a similar way,  by putting x = 0 in the equation, we can show that

B = (0, 7).

(b)

M is the midpoint of the line AB so its coordinates are:

(7+ 0)/2, (0 + 7) /2 = (3.5, 3.5).

So the slope of OM  which also passes through the origin (0,0) is:

(3.5 - 0) /(3.5 - 0) = 1.

y - y1 = m (x - x1)

y - 3.5 = 1(x - 3.5)

y = x - 3.5 + 3.5

y = x is the required equation.

b

step-by-step explanation:

the word superfluous means unnecessary

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!