In a certain town, the wind speed, x, in km/h on a certain day is described by two statements: If 2 times the wind speed is incr
eased by 2, the wind speed is still less than 46 km/h. Twice the wind speed minus 27 is greater than 11 km/h. Part A: Create a compound inequality to represent the wind speed range. (3 points) Part B: Can the wind speed in this town be 20 km/h? Justify your answer by solving the inequalities in Part A. (3 points) Part C: The average wind speed in another town is 23 km/h, but the actual wind speed is within 4 km/h of the average. Write and solve an inequality to find the range of wind speed in this town.
<span>1) if 2 times the wind speed is increased by 2, the wind speed is still less
than 46 km/h.
=> 2x + 2 < 46
2) Twice the wind speed minus 27 is greater than 11 km/h.
=> 2x - 27 > 11
Part A: Create a compound inequality to represent the wind speed range.
(3 points)
from 2x + 2 < 46
=> 2x < 44
=> x < 22
from 2x - 27 > 11
=> 2x > 11 + 27
=> 2x > 38
=> x > 19
The set of inequalities is
2x + 2 <46 2x - 27 > 11
The solution is x < 22 and x > 19, which is:
19 < x < 22 <----- answer
Part B: Can the wind speed in this town be 20 km/h? Justify
your answer by solving the inequalities in Part A. (3 points)
Yes, the wind speed can be 20 km/h, because the solution of the inequality is the range (19,22).
Part C:
The average wind speed in another town is 23 km/h, but the actual wind
speed is within 4 km/h of the average. Write and solve an inequality to
find the range of wind speed in this town.
The easiest method is to find the x-intercepts of the quadratic function by substituting y=0 in the function and solving it to find the possible values of x. The number of all possible values of x is the number of x-intercepts of the graph.
