Exam 4: Lines parabolas and Systems

An automobile factory produces two models.The first model requires 1 hour to paint and hour to polish.The second requires 1 hour for each process.During each hour that the assembly line is operating,there are 100 hours available for painting and 80 hours for polishing.How many of the first model can be produced each hour if all the hours available are to be used?

Suppose the cost to produce 100 units of a product is $5000,and the cost to produce 125 units is $6000.If cost c is linearly related to output q,find an equation relating c and q.

An investor has $12,000 to purchase stock in two companies.If the first stock sells for $45 per share,and the second stock sells for $62 per share,find an equation that shows the possible ways to purchase the stock.

In a test of a diet for pigs,the average live weight w (in kilograms)of a pig was a linear function of the number d of days after the start of the diet,where 0 ≤ d ≤ 50.The weight of a pig at the beginning of a diet was 25 kg and thereafter the pig gained 5 kg every nine days.(a)Express w as a function of d.(b)Find the weight of a pig 36 days after the beginning of the diet.

The equation of a certain line is 3(x - 4)- (y + 1)= 4.Find: (a)the slope-intercept form and (b)a general linear form.

Solve the system:

In testing an experimental diet for beef cows,it was determined that the (average)live weight w (in kilograms)of a cow was statistically a linear function of the number of days d after the diet was started,where 0 ≤ d ≤ 300.The weight of a cow starting the diet was 125 kg and 100 days later it was 245 kg.Determine w as a linear function of d and find the average weight of a cow when d = 200.

Suppose f is a linear function with slope 2 and f(1)= 3.Find f(2).

In testing an experimental diet for horses,it was determined that the (average)live weight w (in kilograms)of a horse was statistically a linear function of the number of days d after the diet was started where 0 ≤ d ≤ 300.The weight of a horse starting the diet was 170 kg and 120 days later it was 362 kg.Determine w as a linear function of d and find the average weight of a horse when d = 250.

Determine whether the following lines are parallel,perpendicular or neither. 12x + 4y = 16 15x + 5y = 23

Solve the following system for x,y,and z.(Answers are given in that order)

Solve the following system algebraically:

The slope of the line x = 2 is

Find the equation of the line with y-intercept 4 and slope - .

Two species of fish,A and B,are raised in one pond at a fish farm where they are fed two vitamin supplements.Each day they receive 100 grams of the first supplement and 200 grams of the second supplement.Each fish of species A requires 15 mg of the first supplement and 30 mg of the second supplement.Each fish of species B requires 20 mg of the first supplement and 40 mg of the second supplement.How many of each species of fish will the pond support so that all of the supplements are consumed each day? Use a graphing calculator to graph both of your equations at the same time.What do you notice about the graphs?

For the straight line 2x + y - 3 = 0 find: (a)the slope; (b)the y-intercept; and (c)sketch the graph.

A prediction made by early psychology relating the magnitude of a stimulus x to the magnitude of a response y is expressed by the equation y = k ,where k is a constant of the experiment.In an experiment on odor intensity,k = 5.Use a graphing calculator to graph the equation.

A prediction made by early psychology relating the magnitude of a stimulus x to the magnitude of a response y is expressed by the equation y = k ,where k is a constant of the experiment.In an experiment on brightness of light,k = 1.Find the function's vertex and graph the equation.

The area of rain forest in a South American country has decreased by 500 acres per year for the last 10 years.It had 12,000 acres 10 years ago.Use a graphing calculator to graph the resulting equation and determine when all of the rain forest in this country will be destroyed.

Determine whether the following lines are parallel,perpendicular or neither. 3x - 2y = -1 2x + 3y = -20