Assign x as the hours Carlos drove and y as the hours Maria drove. The first equation is x + y = 4.4, from which we derive x = 4.4 - y. The second equation, representing their distances, is 55x + 50y = 233. Substituting the first equation into the second gives us 55(4.4 - y) + 50y = 233, resulting in a distance traveled of 3.5 m by Carlos in 2.6 hours.
The response is:
Therefore, option 1 is correct.
Hence, the final option is accurate.
Step-by-step breakdown:
Two functions are presented
. The domain represents the x values possible
. The range represents the y values achievable
. Thus, x can take any real number in functions f(x) and g(x)
. So, option 1 is correct.
For the range aspect
, f(x) can encompass any real number 
. However, for g(x), the range can only include positive numbers
. Consequently, the last option is accurate, while all other options are incorrect.
Answer:
The cabin is located 567 yards away.
Step-by-step solution:
The bearing angle of 21.2° corresponds to the interior angle near the cabin in the triangle.
Apply the tangent function:
Opposite side length: 220 yards
Adjacent side length: x (distance to cabin)
tan(21.2°) = opposite / adjacent
tan(21.2°) = 220 yards / x
Multiply both sides by x:
x × tan(21.2°) = 220 yards
Isolate x:
x = 220 yards / tan(21.2°)
x = 220 / 0.388
x = 567 yards
Hence, the cabin is 567 yards away.
