What is the area of the composite figure? (6π + 4) cm2 (6π + 16) cm2 (12π + 4) cm2 (12π + 16) cm2

16 + 6pi

Step-by-step explanation:

We have a square and 3 semicircles

The area of the square is

A = s^2 and the side length is 4

A = 4^2 = 16

The radius of the semi circle is 2

The area of a semicircle is

1/2 pi r^2

1/2 pi (2)^2 = 2pi

We have 3 of them

3 *2pi = 6pi

Add the areas together

16 + 6pi

(6π + 16) cm²

Step-by-step explanation:

The composite shape can be cut into 4 shapes.

3 equal semi-circles and 1 square.

The square has a side length of 2 + 2 = 4cm.

The radius of the semi-circle is 2 cm.

The area of the square is:

4 × 4 = 16 cm²

The area of the semi-circle is:

2²π × 1/2

= (2π) cm²

There are 3 equal semi-circles, so multiply the area by 3.

2π × 3 = (6π) cm²

Add the areas of the 4 shapes.

16 cm² + (6π) cm²

= (6π + 16) cm²

The total area of the composite shape is (6π + 16) cm².

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3