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

The formula for a rectangular pyramid is equal to V=(l*w*h)/3 where "l" represent the length, the "w" represents the width and "h" represents the height.
We have givens such as:
l=15 cm
w=5 cm
h=7 cm
Solving for the volume, we have:
V=(15*5*13)/3
V=325

Solving for prism volume
V=l*w*h
V=15*5*7
V=175

For the composite volume:
CV=325+175
CV=500

The formula for a rectangular pyramid is equal to V=(l*w*h)/3 where "l" represent the length, the "w" represents the width and "h" represents the height.

We have givens such as:

l=15 cm

w=5 cm

h=7 cm

Solving for the volume, we have:

V=(15*5*13)/3

V=325

Solving for prism volume

V=l*w*h

V=15*5*7

V=525

For the composite volume:

CV=325+525

CV=850

Solution:

The two equation given which are in two variables are

1. y = x²-2 x -1 9

2. y + 4 x=5

Writing equation 2 as→y = 5 -4 x

Substituting the value of y in equation 1

⇒ 5 - 4 x = x² - 2 x - 19

⇒x² - 2 x + 4 x -19 -5=0

⇒ x² + 2 x -24=0

⇒x² + 6 x - 4 x - 24=0→→→[Breaking the middle term i.e term containing x]

⇒ x(x+6) -4(x+6)=0

⇒(x-4)(x+6)=0

⇒x-4=0 ∧ x+6=0

⇒x = 4     ∧    x= -6

Put x=4 in equation 2,

y + 4 ×4=5

y + 16=5

y = 5-16

y= -11

As one solution is (-6, 29), The other solution of the system of equation is (4, -11).