Answer:
[tex]Distance = 3.75x[/tex]
[tex]({\frac{f}{g})(x) = x + 4[/tex]
Step-by-step explanation:
(4)
Given
[tex]Average\ Speed= x[/tex]
[tex]Time = 225\ mins[/tex]
Required
Determine the distance
This is calculated as:
[tex]Distance = Average\ Speed * Time[/tex]
Convert time to hour
[tex]Time = \frac{225}{60}[/tex]
[tex]Time = 3.75[/tex]
So:
[tex]Distance = Average\ Speed * Time[/tex]
[tex]Distance = x * 3.75[/tex]
[tex]Distance = 3.75x[/tex]
(5)
[tex]f(x) = x^2 + 3x - 4[/tex]
[tex]g(x) = x - 1[/tex]
Required
Find [tex]({\frac{f}{g})(x)[/tex]
This is calculated as:
[tex]({\frac{f}{g})(x) = \frac{f(x)}{g(x)}[/tex]
So:
[tex]({\frac{f}{g})(x) = \frac{x^2 + 3x - 4}{x-1}[/tex]
Expand
[tex]({\frac{f}{g})(x) = \frac{x^2 - x +4x - 4}{x-1}[/tex]
Factorize
[tex]({\frac{f}{g})(x) = \frac{x( x- 1) +4(x - 1)}{x-1}[/tex]
[tex]({\frac{f}{g})(x) = \frac{(x-1) (x + 4)}{x-1}[/tex]
[tex]({\frac{f}{g})(x) = x + 4[/tex]
