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).

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.

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

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

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.

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

Using Vieta's formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.

Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.

Let the original price be $100. After a 10% increase, the price becomes $110. After a 10% decrease, the price becomes $110 - $11 = $99. The net change is -1%, so the answer is 0%.

The interest earned is $400. Using SI = PRT, we have 400 = 2000 * R * 3. Solving for R gives R = 6.67%.

Using the simple interest formula, Total Amount = Principal + SI = 800 + (800 * 4 * 3) / 100 = $840.

Total amount = Principal + SI = 800 + (800 * 6/100 * 4) = $1040.

The probability of failing is 1 - P(passing) = 1 - 0.75 = 0.25.

The probability of either A or B occurring is P(A) + P(B) - P(A and B) = 0.2 + 0.5 - (0.2 * 0.5) = 0.7.

For independent events, P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

For mutually exclusive events, P(C or D) = P(C) + P(D) = 0.2 + 0.3 = 0.5.

The probability that it will not rain is 1 - 0.7 = 0.3.

6 and 7 are consecutive integers whose product is 42, not 72.

For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.

According to Vieta's formulas, the sum of the roots p and q is -b/a and the product is c/a.

For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0, leading to k = 4.

The constant ratio of consecutive terms in a geometric series is called the common ratio.

According to Vieta's formulas, the sum of the roots p + q is equal to -(-5) = 5.

A triangle with sides in the ratio 3:4:5 is a right-angled triangle, as it satisfies the Pythagorean theorem.

Using SI = PRT, we have 150 = P * 0.05 * 3. Solving for P gives P = 1000.

If all squares are rectangles, it implies that there are rectangles that are not squares, thus some rectangles are not squares.

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). By differentiating S_n with respect to n, we can find the common difference. The common difference is 3.