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 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?
In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context? y is equal to 35 x y is equal to negative 0 point 0 5 times open paren x minus 400 close paren squared plus 9 comma 492
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 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 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?
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?
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
The width of a rectangular field is 20 feet less than its length. The area of the field is 12 comma 000 ft squared What is the length of the field?
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?
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