1. Suppose you and your friends form a band. You want to record a demo. Studio A rents for $100 plus $50 per hour. Studio B rents for $50 plus $75 per hour.
a. Write an equation to represent the cost of each studio.
Studio A:
Studio B:
b. Solve the system by graphing. Solution:
c. Explain what the solution of the system means in terms of renting a studio.

Step-by-step explanation:

y is the cost after x hours

A: y = 50x + 100

B: y = 75x + 50

Solution: (2,200)

If the demo takes less than 2 hours to record, then Studio B charges less.

If the demo takes more than 2 hours to record, then Studio A charges less.

If the demo takes exactly 2 hours to record, the studios charge the same.

Question

A rectangular pyramid has a height of 5 units and a volume of 60 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

a) A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

b) A rectangular prism in which BA = 12 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

c) A rectangular prism in which BA = 36 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.

d) A rectangular prism in which BA = 12 and h = 5 has a volume of 60 units³; therefore, Shannon is incorrect.

a) A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.

Step-by-step explanation:

The formula for the volume of a Rectangular Pyramid = 1/3 × Base Area × Height

In the question,

Base Area = ?

Height = 5 units

Volume = 60 units³

So,

60= 1/3 × BA × 5

Cross Multiply

180 = 5BA

BA = 180/5

BA = 36 units²

Also, the Volume of a Rectangular Prism =

Base Area × Height

From the above question

Base Area = 36 units²

Height = 5 units

Volume of the Rectangular prism = 36 units² × 5 units

= 180 units³

Therefore , the statement that explains whether Shannon is correct is option a,

" A rectangular prism in which BA = 36 and h = 5 has a volume of 180 units³; therefore, Shannon is correct.