Answer:
i'm pretty sure f(x) = g(x)
Step-by-step explanation:
Answer: Statements 1 and 2 shows that the coach blowing the whistle happened first.
Step-by-step explanation: The coach blowing the whistle as the first event can be seen only from statements 1 and 2 only.
From statement 1, "the referee blew the whistle" was followed by "the team ran onto the field."
From statement 2, "before the team ran onto the field" shows clearly that one event took place "BEFORE" the one being reported and the one that occurred before this one was "the referee blew the whistle."
Statement 3 which is "the referee blew the whistle, BUT..." indicates that the whistle was meant to prevent the team from from running onto the field. So if the referee blew the whistle, but the team ran onto the field, it means the whistle blowing was not supposed to make them run onto the field.
Statement 4, which states that "the referee blew the whistle BECAUSE the team ran onto the field" indicates that, the reason for blowing the whistle was because the team ran onto the field which clearly shows that the team ran onto the field first before the referee blew the whistle.
Statement 5, "WHILE the team ran onto the field..." clearly shows that both events took place at the same moment, and so the referee blowing the whistle could not have occurred first.
Answer: The fire is 3.5 miles from tower B
Step-by-step explanation: Please refer to the attached diagram. The triangle in the attached diagram illustrates the clues given in the question. Both rangers are standing at points A and B respectively with a distance of 5 miles between them, which is line AB. Also, one ranger spots a fire from a tower at an angle of 42 degrees, which is point A. Another ranger spots the same fire from another tower, but from an angle of 64 degrees, which is point B. The fire is at point C on the triangle. Now we have a triangle with only one side known (5 miles) and three angles known (the third angle is computed as 180 - {64+42} which equals 74) which are 64 degrees, 42 degrees and 74 degrees.
The distance from the fire to tower B is calculated using the law of sines. (Note that this is not a right angled triangle, hence we cannot use trigonometric ratios). The law of sines is expressed as follows;
a/SinA = b/SinB or
a/SinA = c/SinC
Depending on the sides and angles we are given and the ones we are to calculate.
The distance from the fire to tower B is line BC, labeled as a in our diagram. Using the law of sines
a/SinA = c/SinC
(Note also that a is directly facing angle A, c is directly facing angle C, and so on)
a/SinA = c/SinC
a/Sin 42 = 5/Sin 74
By cross multiplication we now have
a (Sin 74) = 5 (Sin 42)
Divide both sides of the equation by Sin 74 and we now arrive at
a = 5 (Sin 42)/Sin 74
a = 5 (0.6691)/0.9613
a = 3.3455/0.9613
a = 3.4802
{rounded to the nearest tenth of a mile, a equals 3.5}
Therefore the distance from tower B to the fire is approximately 3.5 miles