What is the approximate area of the shaded sector in the circle shown below

C. 297

Step-by-step explanation:

The area of the whole circle is

A = πr²,    here r is given as 18, so

A = π(18²)

 A = 324π cm²

The shaded region has an arc length of 105°.  Divide this arc length by 360° to determine how much of a circle this makes up...

105°/360°   now reduce the fraction...

This reduces to   7/24

So the shaded region make us 7/24 of a circle.  The area of this shaded region will 7/24 of the area of the full circle, so we have

A(shaded region) = (7/24)(324π)

             A(shaded region) = 296.8805 cm²  or about 297 cm²

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