Subtracting 3 from both sides gives 2x = 4, and dividing by 2 yields x = 2. This straightforward linear equation tests basic algebraic manipulation.

First, add the numbers inside the parentheses: 2 + 5 equals 7. Multiplying 7 by 3 results in 21, following the correct order of operations.

In the slope-intercept form y = mx + b, the coefficient m represents the slope. Here, m is 2, so the slope is 2.

Combining like terms by adding the coefficients, 4x + 5x becomes 9x. This tests the basic property of addition in algebra.

x^2 - 9 is a difference of squares and factors into (x - 3)(x + 3). This technique is a fundamental factoring method in algebra.

For a quadratic equation ax^2 + bx + c = 0, the product of the roots is given by c/a. Here, c = 6 and a = 1, so the product is 6.

Adding the equations eliminates y, giving 2x = 8 and thus x = 4. Substituting back, we find y = 2.

The discriminant is calculated using the formula b^2 - 4ac. With a = 1, b = 4, and c = 1, the discriminant is 16 - 4 = 12, indicating two distinct real roots.

Multiply the coefficients (3 and 2) to get 6 and add the exponents (2 + 3) to obtain x^5. The correct simplified product is 6x^5.

Substitute 4 into the function: f(4) = 2(4) + 3 = 8 + 3 = 11. This exercise reinforces function evaluation.

Completing the square for x^2 + 6x + 8 transforms it into vertex form. The correct conversion is (x + 3)^2 - 1, which clearly depicts the vertex of the parabola.

Squaring both sides of the equation yields x + 5 = 9, and subtracting 5 gives x = 4. This ensures the solution fits within the domain of the square root function.

The quadratic factors into two binomials that multiply to give 2x^2 + 7x + 3. Expanding (2x + 1)(x + 3) confirms it matches the original expression.

Substituting x = -3 into f(x) gives (-3)^2, which is 9. Squaring a negative number results in a positive outcome.

Since 27 equals 3 raised to the power of 3, setting 3^x = 3^3 directly implies that x = 3. This problem tests the understanding of exponent rules.

Completing the square transforms the circle's equation into (x - 2)^2 + (y + 3)^2 = 12. The radius is the square root of 12, which simplifies to 2√3.

To find the inverse, swap x and y in the equation and solve for y. This process results in the inverse function f❻¹(x) = 2x + 3.

Adding 5 to both sides gives 2x > 8, and dividing by 2 results in x > 4. The strict inequality excludes the equality case.

Using the formula aₙ = a₝ + (n - 1)d, substitute a₝ = 3, d = 4, and n = 10 to obtain 3 + 9×4 = 39. This is a typical application in sequences.

Factor the numerator as (x - 2)(x + 2) and cancel the common factor with the denominator. Substituting x = 2 into the simplified expression x + 2 yields 4.