-7x-3x+2=-8x-8 | combine like terms
-10x+2=-8x-8 | add 8x
-2x+2=-8 | subtract 2
-2x=-10 | divide by -2
x=5
Answer:
V = 108 ft³
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Geometry</u>
Volume of a Rectangular Prism Formula: V = lwh
- <em>l</em> is length
- <em>w</em> is width
- <em>h</em> is height
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
<em>l</em> = 4 ft
<em>w</em> = 3 ft
<em>h</em> = 9 ft
<u>Step 2: Find Volume</u>
- Substitute in variables [Volume of a Rectangular Prism Formula]: V = (4 ft)(3 ft)(9 ft)
- Evaluate [Order of Operations]: V = 108 ft³
Substitute 2x+1 where y is in the equation:
9x-2(2x+1)=8
Then distribute the -2(2x+1)
9x-4x+2=8
Then combine like terms (the x)
5x+2=8
Then do -2 on both side of the equation sign
5x+2=8
- 2 -2
Then you'd get
5x=6
Then divide 5 on both sides
X= 1.2
Answer:
a) The demand function is

b) The nightly revenue is

c) The profit function is

d) The entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.
Step-by-step explanation:
a) Lets find the slope s of the demand:

Since the demand takes the value 79 in 7, then

b) The nightly revenue can be found by multiplying q by p

c) The profit function is obtained from substracting the const function C(p) from the revenue function R(p)

d) Lets find out the zeros and positive interval of P. Since P is a quadratic function with negative main coefficient, then it should have a maximum at the vertex, and between the roots (if any), the function should be positive. Therefore, we just need to find the zeros of P

Therefore, the entrance fees that allow Swing Haven to break even are between 10.03 and 23.41 dollars per guest.