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Published on September 19, 2025
This problem involves identifying the translation that maps one figure onto another on a coordinate plane by comparing the coordinates of corresponding vertices.
The solution demonstrates how to find the value of RS by expanding the second equation, substituting the first equation, and simplifying the resulting equation.
To solve the equation 16/x = x^2/4, cross-multiply to get 64 = x^3, then take the cube root of both sides to find x = 4.
The solution to the equation (1/3)^(x+3) = 9^x is x = -1.
The equation |a - 5| = |5 - a| is proven by considering two cases: when (a - 5) is greater than or equal to zero and when (a - 5) is less than zero. In both cases, the equation holds true, demonstrating that the absolute value of the difference between a and 5 is equal to the absolute value of the difference between 5 and a for all values of a.
The partial fraction decomposition of the rational expression x/((x+1)(x-4)) is (1/5)/(x+1) + (4/5)/(x-4).
The system of equations is solved by substitution, expanding, simplifying, using the quadratic formula to find x values, and then substituting back into the equations to find the corresponding y values. The solutions are (3, 4) and (-4, -3).
The solution to the system of equations x + 2y = 5 and 3x - y = 1 is x = 1 and y = 2, found using the elimination method.
The solution for x in the equation involving fractions with (x-1) and (x+1) in the denominator is x = √2 and x = -√2.
The solution to the equation 3^(a^2 - 10a + 25)! = 729^4 is a = 3 or a = 7, found by equating exponents after expressing both sides with the same base and solving the resulting quadratic equation.
The solution to the equation 4a³ = 2⁵ is a = 2.