Modeling with Systems — Unit test Answers

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the time in seconds. A high-speed camera is ready to film the person between 15 m and 10 m above the ground. For which interval of time should the camera film the person?

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

Aramis is adjusting a satellite because he finds it is not focusing the incoming radio waves perfectly. The shape of his satellite can be modeled by , where x and y are modeled in inches. He realizes that the static is a result of the feed antenna shifting slightly off the focus point. Where should the feed antenna be placed?

The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is –16 ft/s2, which equation models the height of the projectile correctly?h(t) = at2 + vt + h0

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is the area of the original square. What was the side length of the original square?A = s2

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

Which equation demonstrates the multiplicative identity property?

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

Which statement about the following equation is true?2x2 – 9x + 2 = –1

A projectile is fired straight up from ground level with an initial velocity of 112 ft/s. Its height, h, above the ground after t seconds is given by h = –16t2 + 112t. What is the interval of time during which the projectile's height exceeds 192 feet?

What is one of the solutions to the following system?

Which equation represents a graph with a vertex at (–3, 2)?

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

A company plans to sell pens for $2 each. The company’s financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). What is the minimum number of pens the company must sell to make a profit?