Arectangular pyramid fits exactly on top of a rectangular prism. the prism has length 15 cm, width 5 cm, and height 7 cm, and the pyramid has height 13 cm. find the volume of the composite space figure.

a) 1500 cm3
b) 500 cm3
c) 2275 cm3
d) 850 cm3

Volume of composite figure =  850 cubic cm.

Step-by-step explanation:

Given : A rectangular pyramid fits exactly on top of a rectangular prism. The prism has length 15 cm, width 5 cm, and height 7 cm, and the pyramid has height 13 cm.

To find  : Find the volume of the composite space figure.

Solution : We have given that

Prism length 15 cm

Width =  5 cm.

Height = 7 cm.

pyramid height = 13 cm

Width = 5 cm

Length = 15 cm.

Volume of composite space = volume of prism + volume of pyramid .

Volume of composite space = (l* b * h )+( .

Plugging the values of length , width , height

Volume of composite figure = ( 15* 5 *7 ) +( tex]\frac{1}{3} 15 * 5 * 13)[/tex] .

Volume of composite figure = (525 ) +( 325)

Volume of composite figure =  850 cubic cm.

Therefore, Volume of composite figure =  850 cubic cm.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!

it would open into a square depending on the type of envelope i’m not sure about the second part