Linear/Quadratic Equations
2x+5. Solve for X.
x=-2.5
Find the Vertex of the Absolute Value equation
|x-5| + 8
Vertex: (5, 8)
p = D(q)= 32-2.50q. Find the price, p, when demand is 0.
Flip's Toy Factory records a marginal cost of $14 per bear and a fixed cost of $700. Write out the cost function, c(x).
C(x)= 14x + 700
x2-25. Solve for X
x=-5,5
use (2,1) and (3,-1) to find your slope and graph.
sqrt(x+18)=x-2
x=7, x=-2
(extra credit: are there any false answers here?)
p=D(q)= 28-1.25q. q is the quantity demanded in hundreds. find p when the quantity demanded, q, is 4.
D(4)= $23.
Find the average cost of 400 books, if it costs $60 per book plus a flat rate of $360.
average cost = c(x)/x = $60.90
using points (1, 15) and (2, 18), find your y=mx+b equation and solve for x.
x=4
Vertex: (0,-25) X Intercepts: (-5, 0) and (5, 0) Sketch the Graph.
Find the Vertex of the Quadratic Equation 5x2-3x+5
hint: (-b/2a, f(-b/2a))
(0.3, 4.55)
Find (q), quantity demanded, when p= 17, and p=12 using p=D(q)=16-2.25q.
q for $17 = -0.44.
q for $12 = 1.77.
The cost of renting tuxes for the Choral Society's formal is $20 down, plus $86 per tux. Express the cost C as a function of x, the number of tuxedos rented.
a) What is the cost of renting 5 tuxes?
b) What is the cost of the 5th tux?
C(x)= 86x + 20
a) C(5)=450
b) The cost of the 5th tux is $86.
3x2+11x+6=0, Solve using the AC method. Leave your answer as a fraction if you get one.
(3x+2)(x+3)
x=-3,-2/3
f (x) =
-2x - 1 if x is less than or equal to 2.
-x + 4 if x is greater than 2.
find
f(-3), f(2), f(4)
f(-3) = 5, f(2)=-5, f(4)=0
find quantity demanded, q, when p is $0 for p=S(q)=1.50q.
The quantity would be zero as well.
A soft-drink manufacturer can produce 1000 cases of soda in a week at a total cost of $6000, and 1500 cases of soda at a total cost of $8500. Find the manufacturer’s weekly fixed costs and marginal cost per case of soda. (hint: ordered pairs + the equation to find slope)
c(x) = 5x+ 1000
2x2-5x+3 using the quadratic formula, find x.
x=3/2, x=1
f (x) =
-2x - 1 if x is less than or equal to 2.
-x + 4 if x is greater than 2.
sketch the graph.
Using the Difference Quotient,(f(x-h)-f(x))/h , find the answer for x^2-4
2x+h
Given a demand function, p=D(q)=16-2.25q, and a supply function, p=S(q)=1.50(q), find the equilibrium quantity and price.
q= 4.27, p= 6.4
Your college newspaper, The Collegiate Investigator, has fixed production costs of $70 per edition, and marginal printing and distribution costs of 40¢/copy. The Collegiate Investigator sells for 50¢/copy.
a)Write down the associated cost, revenue, and profit functions. (200 points)
b) What profit (or loss) results from the sale of 500 copies of The Collegiate Investigator? (300 points)
c) How many copies should be sold in order to break even? (extra 100 points)
a) C(x)=0.40x + 70, R(x)= 0.50x, P(x)=0.10x-70
b) P(500)= -20
c) x=700