The figure below consists of a triangle, a rectangle, and a trapezoid. What is the area of the figure in square units?
A. 39
B. 37
C. 49
D. 42

Area of the figure = 39 square units

Step-by-step explanation:

Find the diagram attached

Area of the triangle = 1/2 * base * height

Base of triangle = 4

Height = 1 + 5  = 6

Area of the triangle = 1/2 *4 * 6

Area of the triangle = 12units²

Area of rectangle = Length * Width

Length = 4

Width = 5

Area of rectangle = 4 * 5

Area of rectangle = 20units²

Area of trapezoid = 1/2(a+b)*h

a and b are the parallel sides

h is the height

a = 2

b = 5

h = 6-4 = 2

Area of trapezoid = 1/2(2+5)*2

Area of trapezoid = 1/2*7*2

Area of trapezoid = 7units²

Area of the figure  = Area of the triangle +Area of the rectangle + Area of the trapezoid

Area of the figure = 12 + 20 + 7

Area of the figure = 39 square units

(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

8

step-by-step explanation: