Find the area of the following figure. Assume that all lines that appear to be parallel are parallel. Round to the nearest tenth if necessary.

466in³

Step-by-step explanation:

Cut the figure in to two rectangles and one triangle. Draw an imaginary line like I did in the photo. Then solve the area of each one. First to solve the area of a, or the largest rectangle, multiply 29 by 10. You will get 290. Next, solve the area of b, or the small rectangle. Multiply 7 by 16, and you will get 112. Then, solve the area of the triangle. To get the length of the base of the triangle, subtract 10 and 7 from 25. The base length is 8. Solve the area of the triangle by multiplying 8 by 16 and then dividing by two. The area is 64. Finally, add all the areas. 290+112+64= 466. The area of the figure is 466in³.

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!