To find the x-intercept, set y = 0: 3x = 12, thus x = 4, giving the point (4, 0).

To find the y-intercept, set x = 0: 3(0) - 4y = 12, which gives y = -3.

To find the y-intercept, set x = 0 in the equation, resulting in y = -4. Thus, the y-intercept is 5.

To find the x-intercept, set y = 0. Solving gives x = 2, so the intersection point is (2, 0).

Setting y to 0 in the equation gives x = 2, so the intersection with the x-axis is (2, 0).

Setting x = 0 in the equation gives y = -5, so the y-intercept is -5.

Let the original angle be x. Then, x + 20 = 3x. Solving this gives x = 10 degrees, which is not an option. Hence, the correct answer is 30 degrees.

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

Let the other endpoint be (x, y). The midpoint formula gives (2 + x)/2 = 4 and (3 + y)/2 = 5. Solving these gives x = 6 and y = 7.

The midpoint M is given by M = ((x1 + x2)/2, (y1 + y2)/2). Setting up the equations: (1 + x)/2 = 3 gives x = 5.

'a' represents the first term of the harmonic progression in the formula for the nth term.

The nth term of a harmonic progression can be expressed as the harmonic mean of n and m, which is 1/(1/n + 1/m).

The first term corresponds to n=1, which gives 1/1 = 1.

Substituting n = 7 into the formula gives a_7 = 5*7 - 3 = 35 - 3 = 32.

The 4th term is 4^2 + 4 = 16 + 4 = 20.

In base-6, 'A' = 3*6^1 + 0*6^0 = 18 + 0 = 18. Therefore, 'A' is 42 in decimal.

In base-5, 'XYZ' = X*5^2 + Y*5^1 + Z*5^0 = 100. Solving gives X = 3.

The binary number 1011 converts to decimal as follows: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.

To convert from binary to decimal, calculate: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.

In hexadecimal, A represents 10. Therefore, 1A = 1*16^1 + 10*16^0 = 16 + 10 = 26.

The prime factorization of 36 is 2^2 * 3^2, as 36 = 2 * 2 * 3 * 3.

The perimeter of a regular hexagon is the sum of the lengths of its 6 equal sides. Therefore, each side is 72 cm / 6 = 12 cm.

The perimeter of a regular octagon is 8 times the length of one side. Therefore, each side is 64 cm / 8 = 8 cm.

In an equilateral triangle, all sides are equal. Therefore, if the perimeter is 36 cm, each side is 36/3 = 12 cm.

Let the length of each equal side be x. The perimeter is given by 2x + 8 = 24. Solving for x gives 2x = 16, so x = 8 cm.

The perimeter is the sum of all sides. Therefore, base = 24 - (10 + 10) = 4 cm.

Evaluating f(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.

The polynomial can be factored as (x - 1)(x - 2)(x - 3), so x - 1 is one of its factors.

Substituting x = 1 into the polynomial gives f(1) = 1 - 4 + 6 - 4 + 1 = 0.

The polynomial can be rewritten in a form that shows symmetry about the line x = 1.