Question

1. (x^{2}-53 = 91). what is the positive solution to the given equation? a) 144 b) 72 c) 38 d) 12
2. during a portion of a flight, a small airplanes cruising - speed varied between 150 miles per hour and 170 miles per hour. which inequality best represents this situation, where (s) is the cruising speed, in miles per hour, during this portion of the flight? a) (sleq20) b) (sleq150) c) (sleq170) d) (150leq sleq170)
3. an object was launched upward from a platform. the graph shown models the height above ground, (y), in meters, of the object (x) seconds after it was launched. for which of the following intervals of time was the height of the object increasing for the entire interval? a) from (x = 0) to (x = 2) b) from (x = 0) to (x = 4) c) from (x = 2) to (x = 3) d) from (x = 3) to (x = 4)

Explanation:

Step1: Solve the equation $x^{2}-53 = 91$

Add 53 to both sides: $x^{2}=91 + 53=144$.

Step2: Find the value of $x$

Take the square - root of both sides. Since we want the positive solution, $x=\sqrt{144}=12$.

Step3: Analyze the speed inequality problem

The speed $s$ varies between 150 and 170 miles per hour. The inequality representing this is $150\leq s\leq170$.

Step4: Analyze the height - time graph problem

The height of the object is increasing when the slope of the graph is positive. From the graph, the height is increasing from $x = 0$ to $x=2$.

Answer:

1. D. 12
2. D. $150\leq s\leq170$
3. A. From $x = 0$ to $x = 2$