Pre-Calculus

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1. One estimate for the ideal...

1. One estimate for the ideal body weight is shown below. Use this information to answer (a).

47 kg + 1.2 kg for each inch over 5 feet

(a) Find a linear model for an estimate of the idea weight of a woman using w for ideal weight (in kilograms) and h for height over 5 feet (in inches).

W=__ (type an equation using h as the variable)

2. At low altitudes the altitude of a parachutist and time in the air are linearly related. A jump at 3,900 feet lasts 150 seconds.

(a) Find the linear model relating altitude a (in feet) and time in the air t (in seconds).

(b) Find the rate of change of the parachutist in the air

(c) Find the speed of the parachutist at landing

3. The speed of sound through air is linearly related to the temperature of the air. If sound travels at 319 m/sec at 0 degrees Celsius and at 331 m/sec at 30 degrees Celsius, construct a linear model relating the speed of sound (s) and the air temperature (t). Interpret the slope of this model.

Construct a linear model relating the speed of sound (s) and the temperature (t)

S=___ (type an equation using the t as the variable)

4. Solve the system by the substitution method.

X+ 2y=-1

Y+-2x-14

Select the correct choice below and fill in any boxes present in your choice.

a. The solution is ___ (type an ordered pair)

b. There are infinitely many solutions

c. There is no solution

5. Solve by substitution method.

x-y+3

6x+4y=-22

What is the solution of the system? Select the correct choice below and fill in the answer box within your choice.

a. The unique solution to the system is ___ (Type an ordered pair)

b. There are an infinite number of solutions.

c. There is no solution

6. Solve the system by the addition method.

2x+15y=6

3x-15y=9

Select the correct choice below and fill in the answer box within your choice.

a) The unique solution to the system is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

7. Solve by using substitution or elimination by addition.

2x-4y=38

5x+3y=4

Select the correct choice below and fill in the answer box within your choice.

a) The unique solution to the system is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

8. Solve by using substitution or elimination by addition.

4x+7y= 5

-40x-70y=-49

Select the correct choice below and fill in the answer box within your choice.

a) The solution is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

9. Solve by using substitution or elimination by addition.

2x+7y=-4

4x+8y=-8

a) The solution is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

10. Solve by using substitution or elimination by addition.

4x-3y= 4

-8x+6y=-8

Select the correct choice below and fill in the answer box within your choice.

a) The unique solution to the system is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

11. At $0.47 per bushel, the daily supply for wheat is 475 bushels, and the daily demand is 576 bushels. When the price is raised to $0.86 per bushel, the daily supply increases to 605 bushels, and the daily demand decreases to 381 bushels. Assume that the price-supply and price demand equations are linear.

a. Find the price supply equation

P=___ (Type an expression using q as the variable. Round to three decimal places as needed.)

12. A company markets exercise DVDs that sell for $14.95, including shipping and handling. The monthly fixed costs (advertising rent, etc. ) are $14.620 and the variable costs (material, shipping etc) are $6.45 per DVD.

a. Find the cost equation ___and the revenue equation___

b. How many DVDs must be sold each month for the company to break even?

13. The United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $23.00 for shipping a 3-pound package and $79.25 for a 18-pound package. Find the base price and the surcharge for each additional pound.

The Base price is $___

14. The animals in an experiment are to be kept under a strict diet. Each animal should receive 35 grams of protein and 6 grams of fat. The laboratory technician is able to purchase two food mixes: Mix A has 30% protein and 8% fat; mix B has 50% protein and 5% fat. How many grams of each mix should be used to obtain the right diet for one animal?

One animal’s diet should consist of__ grams of Mix A

47 kg + 1.2 kg for each inch over 5 feet

(a) Find a linear model for an estimate of the idea weight of a woman using w for ideal weight (in kilograms) and h for height over 5 feet (in inches).

W=__ (type an equation using h as the variable)

2. At low altitudes the altitude of a parachutist and time in the air are linearly related. A jump at 3,900 feet lasts 150 seconds.

(a) Find the linear model relating altitude a (in feet) and time in the air t (in seconds).

(b) Find the rate of change of the parachutist in the air

(c) Find the speed of the parachutist at landing

3. The speed of sound through air is linearly related to the temperature of the air. If sound travels at 319 m/sec at 0 degrees Celsius and at 331 m/sec at 30 degrees Celsius, construct a linear model relating the speed of sound (s) and the air temperature (t). Interpret the slope of this model.

Construct a linear model relating the speed of sound (s) and the temperature (t)

S=___ (type an equation using the t as the variable)

4. Solve the system by the substitution method.

X+ 2y=-1

Y+-2x-14

Select the correct choice below and fill in any boxes present in your choice.

a. The solution is ___ (type an ordered pair)

b. There are infinitely many solutions

c. There is no solution

5. Solve by substitution method.

x-y+3

6x+4y=-22

What is the solution of the system? Select the correct choice below and fill in the answer box within your choice.

a. The unique solution to the system is ___ (Type an ordered pair)

b. There are an infinite number of solutions.

c. There is no solution

6. Solve the system by the addition method.

2x+15y=6

3x-15y=9

Select the correct choice below and fill in the answer box within your choice.

a) The unique solution to the system is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

7. Solve by using substitution or elimination by addition.

2x-4y=38

5x+3y=4

Select the correct choice below and fill in the answer box within your choice.

a) The unique solution to the system is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

8. Solve by using substitution or elimination by addition.

4x+7y= 5

-40x-70y=-49

Select the correct choice below and fill in the answer box within your choice.

a) The solution is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

9. Solve by using substitution or elimination by addition.

2x+7y=-4

4x+8y=-8

a) The solution is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

10. Solve by using substitution or elimination by addition.

4x-3y= 4

-8x+6y=-8

Select the correct choice below and fill in the answer box within your choice.

a) The unique solution to the system is ___ (Type an ordered pair)

b) There are an infinite number of solutions.

c) There is no solution

11. At $0.47 per bushel, the daily supply for wheat is 475 bushels, and the daily demand is 576 bushels. When the price is raised to $0.86 per bushel, the daily supply increases to 605 bushels, and the daily demand decreases to 381 bushels. Assume that the price-supply and price demand equations are linear.

a. Find the price supply equation

P=___ (Type an expression using q as the variable. Round to three decimal places as needed.)

12. A company markets exercise DVDs that sell for $14.95, including shipping and handling. The monthly fixed costs (advertising rent, etc. ) are $14.620 and the variable costs (material, shipping etc) are $6.45 per DVD.

a. Find the cost equation ___and the revenue equation___

b. How many DVDs must be sold each month for the company to break even?

13. The United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing 1 pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $23.00 for shipping a 3-pound package and $79.25 for a 18-pound package. Find the base price and the surcharge for each additional pound.

The Base price is $___

14. The animals in an experiment are to be kept under a strict diet. Each animal should receive 35 grams of protein and 6 grams of fat. The laboratory technician is able to purchase two food mixes: Mix A has 30% protein and 8% fat; mix B has 50% protein and 5% fat. How many grams of each mix should be used to obtain the right diet for one animal?

One animal’s diet should consist of__ grams of Mix A

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