The inverse function is defined as h(x) = 4x + 48. To derive it from f(x) = 1/4x - 12, substitute y = f(x) and rearrange the equation to isolate x as shown, leading to h(x).
The attached graph illustrates the region. The centroid's coordinates are (5/3, 1). The centroid's coordinates are determined by averaging the coordinates of the area; Oₓ = (Aₓ+Bₓ+Cₓ)/3 = (0+1+4)/3 = 5/3 and O(y) = (A(y) + B(y) + C(y)) = (0+3+0)/3=3/3=1.
Short answer: 195
First, you multiply 65 by 3, yielding 195 miles.
Then, multiplying 55 by 2 gives you 110 miles.
By summing both distances, you arrive at 305.
From 500, if you subtract 305, you find =195.
In February, 423 daytime minutes were utilized. Let x represent the base plan charges and y denote the cost per daytime minute. In December, the equation is x + 510y = 92.25. In January, it is x + 397y = 77.56. When we eliminate eq(2) from eq(1), we find 0 + 113y = 14.69, leading to y being \frac{14.69}{113}, thus y = 0.13. Substituting (3) into (1) gives x + 510(0.13) = 92.25, further simplifying to x + 66.3 = 92.25, which results in x = 25.95. Hence, for February: base plan + (daytime minutes)(0.13) = 80.9, which simplifies to (daytime minutes)(0.13) = 54.95, yielding daytime minutes = 422.69.
