Get the b all alone on one side of the inequality. To do this, we can divide both sides by 5.
5b / 5 ≤ -15 / 5
b ≤ -3
So, that means b has to be less than or equal to -3.
In interval notation it would look like [-3, -∞)
In a set builder notation: {x | x ∈ R, x ≤ -3}
Which is read as the set of all x, such that, x is a member of the real numbers and x is less than or equal to -3.
4x^2-5x=-1
4x^2-5x+1=0
4x+2.24x=1
6.24x=1
x= 0.16025641025641025641025641025641
We are given with the variable cost which is:
q = -20s + 400
The selling price is 's'. So, the profit can be represented by:
P = qs - q(12)
Subsituting:
P = (-20s + 400)s - 12 (-20s + 400)
P = -20s^2 + 640s - 4800
To optimize this, we must differentiate the equation and equate it to zero, so:\
dP/ds = -40s + 640 = 0
Solving for s,
s = 16
So, the selling price should be $16 to optimize the yearly profit.
All functions have an inverse expression.
- The cost function is:
. - The inverse function is:

From the question, we have the following observations:
- Base fare = 50000 pesos for first 100
- Additional guest = 100 pesos
So, the cost function would be:

Where: x represents the number of guests, and C(x) represents the cost function
Expand

Evaluate like terms

To calculate the inverse function, we have:

Replace C(x) with y

Swap x and y

Subtract 40000 from both sides

Divide both sides by 100

Rewrite as:

Split


Hence, the inverse function is: 
Read more about functions and inverse at:
brainly.com/question/10300045