Exam 4: Lines parabolas and Systems

Determine an equation of the vertical line that passes through the point (3,-6).

The demand function for a manufacturer's product is p = f(q)= 600 - 2q,where p is the price (in dollars)per unit when q units are demanded (per week).Find the level of production that maximizes the manufacturer's total revenue and determine this revenue.

The shape of the main cable on a suspension bridge can be described by the function where y is the height of the cable (in feet)above the roadbed and x is the horizontal distance (in feet)from the center of the bridge.A cross support passes by the cable,and its position can be described by the function Where does the cross-support intersect the cable? Use a graphing calculator to answer the question by finding the point(s)of intersection of the two equations.

Find a general linear equation of the line that passes through the points (-2,5)and (5,2).

Two species of deer,A and B,living in a wildlife refuge are given extra food in the winter.Each week they receive 3.5 tons of food pellets and 7 tons of hay.Each deer of species A requires 4 pounds of the pellets and 8 pounds of hay.Each deer of species B requires 2 pounds of the pellets and 4 pounds of hay.How many of each species of deer will the food support so that all of the food is consumed each week? Use a graphing calculator to graph both of your equations at the same time.What do you notice about the graphs?

Find the range of the function y = f(x)= - + 3x + 2.

Solve the following system algebraically:

Graph the general linear form of the Fahrenheit-Celsius conversion equation whose slope-intercept form is

A coffee wholesaler blends together three types of coffee that sell for $1.95,$2.10,and $2.25 per pound so as to obtain 100 pounds of coffee worth $2.13 per pound.If the wholesaler uses the same amount of the two higher-priced coffees,how much of each type must be used in the blend?

Which of the following statements are true? I.Slope is not defined for a vertical line. II.A line that falls from left to right has a negative slope. III.A line with slope Is more nearly horizontal than a line with slope )

A delicatessen owner starts her business with debts of $100,000.After operating for 5 years she has average profits of $40,000 per year.Use a graphing calculator to graph the resulting equation and determine when the business will have accumulated $300,000 in profit.

Solve the following system of equations algebraically.(If the system does not have a solution,then say so or if it has more than one unique solution,then please describe the solutions.)

Suppose f is a linear function such that f(-2)= 5 and f(5)= 2.Find f(x).

The diagram below shows lines with slopes 0,1,-1,3,and -3.What is the slope of (a)line and (b)line ?

The daily profit for an electronics store from the sale of small televisions is given by P(x)= + 40x + 825,where x is the number of small televisions sold.Find the function's vertex and intercepts,and graph the function.

Determine whether the following lines are parallel,perpendicular or neither. 12x + 4y = 16 24x + 8y = 36

A line passes through the points (1,1)and (9,8).The point on it that has a y-coordinate of -6 is

The value of an antique figurine is expected to appreciate each year after it is purchased for $550.If x is the number of years that have passed,the current value of the figurine can be estimated by the function Graph the function by finding and plotting two points.

A chemist has two solutions that contain different concentrations of hydrochloric acid.One is a 20% concentration and the other is a 12% concentration.How many cubic centimeters of each should he mix to obtain 100 cc with a concentration of 15.2%?

An x-value of a solution of the system is