# A vendor sells hot dogs and bags of potato chips.

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A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 4 bags of potato chips for $10.25. Another customer buys 5 hot dogs and 3 bags of potato chips for $12.50. Find the cost of each item.

$ 1.25 for a hot dog; $ 1.75 for a bag of potato chips

$ 1.75 for a hot dog; $ 1.25 for a bag of potato chips

$ 1.75 for a hot dog; $ 1.50 for a bag of potato chips

$ 2.00 for a hot dog; $ 1.50 for a bag of potato chips

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A steel company produces two types of machine dies, part A and part B. The company makes a $2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let x = the number of part A produced in a week and y = the number of part B produced in a week. Write the objective function that describes the total weekly profit.

z = 2(x – 6) + 6(y – 2)

z = 8(x + y)

z = 2x + 6y

z = 6x + 2y

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Graph the inequality:

x2 + y2 1

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Two LORAN stations are positioned 248 miles apart along a straight shore. A ship records a time difference of 0.00086 seconds between the LORAN signals. (The radio signals travel at 186,000 miles per second.) Where will the ship reach shore if it were to follow the hyperbola corresponding to this time difference? If the ship is 200 miles offshore, what is the position of the ship?

44 miles from the master station, ( 186.9, 200)

80 miles from the master station, ( 200, 186.9)

80 miles from the master station, ( 186.9, 200)

44 miles from the master station, ( 200, 186.9)

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5 of 25

A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 70 inches, how deep is the mirror in the center?

1225

________________________________________1536 in.

256

________________________________________35 in.

1225

________________________________________18432 in.

1225

________________________________________128 in.

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6 of 25

A person with no more than $2000 to invest plans to place the money in two investments, telecommunications and pharmaceuticals. The telecommunications investment is to be no more than 4 times the pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x = amount to be invested in telecommunications and y = amount to be invested in pharmaceuticals.

x + y = 2000, y 4x, x 0, y 0

x + y 2000, 4x y, x 0, y 0

x + y 2000, x 4y, x 0, y 0

x + y = 2000, x 4y, x 0, y 0

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7 of 25

Eliminate the parameter. Find a rectangular equation for he plane curve defined by the parametric equations.

x = 3t, y = t + 7

y = 3x + 7

y = x/3 + 7

y = x/3 – 7

y = 3x – 7

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8 of 25

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants:

4x+1

________________________________________(x+6)(x-5)

A

________________________________________x+6 + B

________________________________________x-5

A

________________________________________x+6 + B

________________________________________x-5 + Cx+D

________________________________________(x+6)(x-5)

A

________________________________________x+6 + B

________________________________________x-5 + C

________________________________________(x+6)(x-5)

A

________________________________________x+6 + B

________________________________________x-5 + C

________________________________________(x+6)2(x-5)2

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9 of 25

Match the equation to the graph:

y2 = 16x

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10 of 25

The sum of the squares of two numbers is 10. The sum of the two numbers is 2. Find the two numbers.

-3 and 1

-1 and 3; or -3 and 1

-3 and -1; or 1 and 3

-1 and 3

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11 of 25

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solutions.

x + y = -3

-2 + y = -3

(0, -5)

(0, 0)

(-2, -1)

(-2, -3)

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12 of 25

Graph the polar equation and identify the directrix and vertex.

r = 9

________________________________________3-3cos

diretrix: 3 unit(s) above the pole at y = 3, vertex: (3/2, /2)

directrix: 3 unit(s) to the left of the pole at x = -3, vertex: (3/2, )

directrix: 3 unit(s) to the right of the pole at x = 3, vertex: (3/2, 0)

directrix: 3 unit(s) below the pole at y = -3, vertex: (3/2, 3/2)

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13 of 25

Solve the system by the substitution method:

x2 + y2 = 113

x + y = -15

{(7, 8), (8, 7)}

{(-7, -8), (-8, -7)}

{(-7, 8), (-8, 7)}

{(7, -8), (8, -7)}

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14 of 25

The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 38 feet and the height of the arch over the center of the roadway is 10 feet. Two trucks plan to use this road. They are both 8 feet wide. Truck 1 has an overall height of 9 feet and Truck 2 has an overall height of 8 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

Truck 1 can pass under the bridge, but Truck 2 cannot.

Both Truck 1 and Truck 2 can pass under the bridge.

Truck 2 can pass under the bridge, but Truck 1 cannot.

Neither Truck 1 nor Truck 2 can pass under the bridge.

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15 of 25

A baseball pitcher throws a baseball with an initial velocity of 133 feet per second at an angle of 20 to the hoizontal. The ball leaves the pitcher’s hand at a height of 5 feet. Find parametric equations that descrive the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball?

x = 124.98t; y = 16t2 + 45.49t + 5

2.729 sec;

1.422 sec;

4.983 feet

x = 124.98t; y = -16t2 + 45.49t + 5;

5.898 sec

1.422 sec

32.333 feet

x = 124.98t; y = -16t2 + 45.49t + 5

2.949 sec

1.422 sec

37.333 feet

x = 124.98t; y = -16t2 + 45.49t + 5;

5.457 sec

1.422 sec

263.668 feet

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16 of 25

Find the focus and directrix of the parabola with the given equation:

x2 = 36y

focus: (9, 0); y = 9

focus: (0, -9); x = -9

focus: (0, 9); y = -9

focus: (9, 0); x = 9

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17 of 25

Find a set of parametric equations for the rectangular equation:

y = 2x – 2

x = t/2; y = t – 1

y = 2t; 2x = t + 2

y = 2t2 – 2

x = t; y = 2t – 2

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18 of 25

Graph the ellipse and locate the foci:

x2

________________________________________9 + y2

________________________________________4 = 1

foci at (13, 0) and (-13, )

foci at (5, 0) and (-5, 0)

foci at (23, 0) and (-23, 0)

foci at (0, 5) and (0, -5)

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19 of 25

Write the equation in terms of a rotated x’y’-system using , the angle of rotation. Write the equation involving x’ and y’ in standard form.

x2 + 2xy + y2 – 8x + 8y = 0; = 45

x’2 = -42y’2

x’2 = -42y’

3x’2 – 42x’y’ + y’2 = 0

2x’2 – 2x’y’ + 2y’2 = 0

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20 of 25

Find the vertices and locate the foci for the hyperbola whose equation is given:

x2

________________________________________16 – y2

________________________________________100 = 1

vertices: (- 10, 0), ( 10, 0)

foci: ( -2, 0 ), (229, 0)

vertices: (- 4, 0), ( 4, 0)

foci: (- 10, 0), ( 10, 0)

vertices: (0, – 4), (0, 4)

foci: (-229, 0) , (229, 0)

vertices: (- 4, 0), ( 4, 0)

foci : (-229, 0), (229, 0)

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21 of 25

An experimental model for a suspension bridge is built. In one section, cable runs from the top of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers stand 50 inches apart. At a point between the towers and 17.5 inches along the road from the base of one tower, the cable is 0.56 inches above the roadway. Find the height of the towers.

8.25 in.

6.75 in.

5.75 in.

6.25 in.

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22 of 25

A vineyard produces two special wines, a white and a red. A bottle of the white wine requires 14 pounds of grapes and 1 hour of processing time. A bottle of red wine requires 25 pounds of grapes and 2 hours of processing time. The vineyard has on hand 2,198 pounds of grapes and can allot 160 hours of processing time to the production of these wines. A bottle of the white wine sells for $11.00, while a bottle of the red wine sells for $20.00. How many bottles of each type should the vineyard produce in order to maximize gross sales?

132 bottles of white and 14 bottles of red

76 bottles of white and 42 bottles of red

14 bottles of white and 132 bottles of red

42 bottles of white and 59 bottles of red

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23 of 25

Find a set of parametric equations for the rectangular equation:

y = 2x – 2

x = t/2; y = t – 1

y = 2t; 2x = t + 2

y = 2t2 – 2

x = t; y = 2t – 2

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24 of 25

Determine if the given ordered triple is a solution of the system:

x + y + z = -6

x – y + 4z = 13

4x + y + z = -18

(-4, -5, 3)

solution

not a solution

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25 of 25

Determine whether the given ordered pair is a solution of the system

(-2, 1)

x

________________________________________3

solution

not a solution