To factor the given quadratic equation, we look for two numbers that multiply to 6 (3 multiplied by the constant term 2) and add up to -7 (the coefficient of the middle term).

The two numbers that fit these criteria are -6 and -1.

Now, we can rewrite the equation by factoring the quadratic expression:

3x² - 7x + 2 = (3x - 1)(x - 2) = 0

We then set each factor equal to zero to solve for x:

3x - 1 = 0 => x = 1/3
x - 2 = 0 => x = 2

Thus, the solution to the quadratic equation 3x² - 7x + 2 = 0 is x = 1/3 and x = 2, which corresponds to option C.

Let x and y be the two numbers.

Write the system of linear equations using the given information:
x + y = 24
x - y = 10

Add the two equations together to eliminate y:
2x = 34

Divide by 2 to solve for x:
x = 17

Now substitute x into the first equation:
17 + y = 24

Subtract 17 from both sides of the equation to solve for y:
y = 7

Thus, the two numbers are 17 and 7, which corresponds to option C.

To find the inverse of a function, we swap the x and y coordinates (x and f(x), respectively) and then solve for the new f(x):

1. Replace f(x) with y:
y = 3x - 2

2. Swap x and y:
x = 3y - 2

3. Solve for y:
x + 2 = 3y
y = (x + 2) / 3

The inverse of the function f(x) = 3x - 2 is f^(-1)(x) = (x + 2) / 3, which corresponds to option C.

A system of equations has no solution if the two lines are parallel (meaning they have the same slope but different y-intercepts). Let's analyze the options:

A) y = 2x + 1 and y = 2x + 2
These two lines have the same slope (2), and different y-intercepts (1 and 2). Thus, they are parallel and have no solution.

B) y = x - 3 and y = -x + 1
These two lines have different slopes (1 and -1), so they are not parallel and will have a solution.

C) 3x + 6y = 9 and 2x - 3y = 4
To check for parallel lines, put both equations in the slope-intercept form (y = mx + b). For the first equation:
6y = -3x + 9
y = -1/2x + 3/2

For the second equation:
3y = -2x + 4
y = -2/3x + 4/3

These two lines have different slopes (-1/2 and -2/3), so they are not parallel and will have a solution.

D) y = 2x - 5 and y = -3x + 8
These two lines have different slopes (2 and -3), so they are not parallel and will have a solution.

Thus, the system of equations with no solution is option A, y = 2x + 1 and y = 2x + 2.

To find the difference f(x) - g(x), we need to subtract the corresponding terms of f(x) and g(x):

f(x) - g(x) = (5x² - 3x + 1) - (2x² + x - 3)

Subtract g(x) from f(x):

3x² - 4x + 4

Thus, f(x) - g(x) = 3x² - 4x + 4, which corresponds to option A.