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The solution to the problem \sqrt{25\%} + \sqrt{49\%} is 1.2, which is equivalent to 120%.

To find x, the exterior angle theorem is used, along with the knowledge that a right angle is 90 degrees, to solve for x, which equals 45 degrees.

The solution to the equation involving radicals and exponents is x = 77/120.

The water lily takes 47 days to cover half the pond, given that it doubles in size each day and covers the entire pond on day 48.

The equation 3^(x^2)/9^x = 81 is solved by rewriting the equation with the same base, simplifying the denominator, applying the quotient rule for exponents, equating the exponents, rearranging into a quadratic equation, and finally using the quadratic formula to find the two solutions, x = 1 + √5 and x = 1 - √5.

The unknown angle in a triangle, formed by two slanted lines and a vertical line, with two given angles of 80 degrees each, is calculated to be 20 degrees using the triangle angle sum property.

The equation x^2 + 3x + 7 = 6/(x^2 + 3x + 2) is solved by substituting u = x^2 + 3x, resulting in a quadratic equation in u. Factoring the quadratic equation yields two possible values for u, which are then substituted back into the substitution to find the solutions for x using the quadratic formula. One case results in two real solutions, while the other yields no real solutions.

The solution to the equation \sqrt{7 + \frac{3}{\sqrt{x}}} = 7 - \frac{9}{x} is x = \frac{9}{4}.

The solution involves finding an expression for X_n, a sum of reciprocals of powers of x, using the formula for a finite geometric series. Then, the expression for x^n is used to simplify the ratio x^n / X_n, ultimately resulting in x^(n+1).

To find x, supplementary angles 5x and 4x are used, along with the fact that the sum of the interior angles of a quadrilateral is 360 degrees. Solving the equation 9x = 180 yields x = 20.