Modeling with Systems — Quiz Answers

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The local community theater sold a total of 240 tickets for Saturday night’s performance. They sold 180 more full-price tickets than discount tickets. Which system of equations can be used to model this situation?

A
f minus d is equal to 240 f is equal to 180 d
B
f minus d is equal to 240 f is equal to 180 plus d
C
f plus d is equal to 240 f minus d is equal to 180
D
f plus d is equal to 240 f is equal to 180
2
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A company plans to sell a new type of vacuum cleaner for 280 dollars each. The company’s financial planner estimates that the cost, y , of manufacturing the vacuum cleaners is a quadratic function with a y -intercept of 11 comma 000 and a vertex of open paren 500 comma 24 comma 000 close paren Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?

A
y is equal to 280 x y is equal to negative 0 point 0 5 2 times open paren x minus 500 close paren squared plus 24 comma 000
B
y is equal to 280 x y is equal to negative 0 point 0 5 2 times open paren x minus 500 close paren squared plus 11 comma 000
C
y is equal to 280 x y is equal to 0 point 0 5 2 x squared plus 11 comma 000
D
y is equal to 280 x y is equal to 0 point 0 5 2 times open paren x minus 500 close paren squared plus 24 comma 000
4

The first equation in the system models the height, h , of a falling volleyball as a function of time, t The second equation models the height, h , of the hands of a player jumping up to spike the ball as a function of time, t Which statement describes the situation modeled by this system? h is equal to 14 minus 16 t squared h is equal to 7 plus 24 t minus 16 t squared

A
The volleyball is 7 feet above the ground at the instant the player begins her jump.
B
The volleyball is 14 feet above the ground at the instant the player begins her jump.
C
The volleyball is 16 feet above the ground at the instant the player begins her jump.
D
The volleyball is 24 feet above the ground at the instant the player begins her jump.
5

A lighthouse is located at open paren 1 comma 2 close paren in a coordinate system measured in miles. A sailboat starts at open paren negative 7 comma 8 close paren and sails in a positive x -direction along a path that can be modeled by a quadratic function with a vertex at open paren 2 comma negative 6 close paren Which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?

A
open paren x minus 1 close paren squared plus open paren y minus 2 close paren squared is equal to 25 y is equal to negative 14 over 81 times open paren x plus 7 close paren squared plus 8
B
open paren x minus 1 close paren squared plus open paren y minus 2 close paren squared is equal to 5 y is equal to negative 14 over 81 times open paren x plus 7 close paren squared plus 8
C
open paren x minus 1 close paren squared plus open paren y minus 2 close paren squared is equal to 25 y is equal to 14 over 81 times open paren x minus 2 close paren squared minus 6
D
open paren x minus 1 close paren squared plus open paren y minus 2 close paren squared is equal to 5 y is equal to 14 over 81 times open paren x minus 2 close paren squared minus 6
6

A rectangular swimming pool has a perimeter of 96 ft. The area of the pool is 504 ft squared Which system of equations models this situation correctly, where l is the length of the pool in feet and w is the width of the pool in feet?

A
2 l plus 2 w is equal to 96 l w is equal to 504
B
2 l plus 2 w is equal to 96 open paren l plus w close paren squared is equal to 504
C
l plus w is equal to 96 l w is equal to 504
D
l plus w is equal to 96 open paren l plus w close paren squared is equal to 504
7

Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1 point 5 ft/s. When Graham’s arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?

A
h is equal to 18 plus 1 point 5 t h is equal to 5 plus 24 t plus 16 t squared
B
h is equal to 18 plus 1 point 5 t h is equal to 5 plus 24 t minus 16 t squared
C
h is equal to 18 plus 1 point 5 t h is equal to 5 plus 24 t
D
h is equal to 18 plus 1 point 5 t minus 16 t squared h is equal to 5 plus 24 t minus 16 t squared
8

The first equation in the system models the height in feet, h , of a falling baseball as a function of time, t The second equation models the height in feet, h , of the glove of a player leaping up to catch the ball as a function of time, t Which statement describes the situation modeled by this system? h is equal to 35 minus 16 t squared h is equal to 6 plus 18 t minus 16 t squared

A
The height of the baseball is 18 feet at the moment the player begins to leap.
B
The height of the baseball is 16 feet at the moment the player begins to leap.
C
The height of the baseball is 6 feet at the moment the player begins to leap.
D
The height of the baseball is 35 feet at the moment the player begins to leap.
10

A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at open paren 4 comma 2 close paren It passes through the point open paren 5 comma 4 close paren A linear road connects points open paren negative 3 comma 7 close paren and open paren 8 comma 2 close paren Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?

A
y minus open paren x minus 4 close paren squared is equal to 2 11 x plus 5 y is equal to 2
B
y minus 2 times open paren x minus 4 close paren squared is equal to 2 5 x plus 11 y is equal to 62
C
y minus 2 times open paren x minus 4 close paren squared is equal to 2 11 x plus 5 y is equal to 2
D
y minus open paren x minus 4 close paren squared is equal to 2 5 x plus 11 y is equal to 62

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