Subtracting 3 from both sides of the equation yields x = 4. This is the only value that satisfies the given equation.

2 raised to the power of 3 means multiplying 2 by itself three times, which equals 8. This is a basic exponentiation concept.

By substituting x = 3 into the expression, 5(3 - 2) simplifies to 5(1), which is 5. This straightforward substitution confirms the answer.

The line is written in slope-intercept form, y = mx + b, where m is the slope. In this case, the coefficient of x is 2, which is the slope.

Dividing both sides of the equation 3y = 12 by 3 isolates y, giving y = 4. This is the clear and direct solution.

The quadratic factors neatly into (x - 2)(x - 3) = 0. Setting each factor equal to zero yields the solutions x = 2 and x = 3.

x^2 - 9 is a difference of two squares, where 9 can be written as 3^2. Its factorization is therefore (x - 3)(x + 3).

Substituting x = 4 into the function gives f(4) = 3(4) + 2, which equals 14. This is a simple evaluation of a linear function.

First, divide both sides by 2 to get 3x - 4 = 5, then add 4 to obtain 3x = 9. Dividing by 3 gives the solution x = 3.

The equation 0x = 0 holds true for every value of x since zero times any number equals zero. Therefore, there are infinitely many solutions.

The square root of 49 is the number that when multiplied by itself gives 49. Since 7 × 7 = 49, the value is 7.

By applying the power rule of differentiation, the derivative of x^2 is calculated as 2x. This rule states that the derivative of x^n is n*x^(n-1).

Since 10 raised to the power of 2 equals 100, log₝₀(100) is 2. This follows directly from the definition of a logarithm.

Multiplying both sides by (x - 2) gives 3 = x - 2. Adding 2 to both sides results in x = 5, which is the unique solution.

Adding 5 to both sides of the inequality yields 2x < 12, and dividing both sides by 2 gives x < 6. This is the correct interval solution for the inequality.

By using the substitution method, express x from the second equation as x = y + 1 and substitute it into the first equation to get 2(y + 1) + 3y = 12. Solving yields y = 2 and then x = 3, which is the correct solution.

First, factor 3 from the numerator to obtain 3(x² - 4) and cancel the common factor with the denominator 3x. Recognizing x² - 4 as a difference of squares allows further factorization to (x - 2)(x + 2)/x.

A quadratic has exactly one real solution when its discriminant is zero. Setting k² - 36 = 0 and selecting the positive value results in k = 6.

The nth term of an arithmetic sequence is determined by the formula a + (n-1)d. Substituting a = 4, d = 3, and n = 10 gives 4 + 9×3 = 31.

First, calculate the radius using the formula r = Circumference/(2π). With an approximate radius of 5, the area is computed as πr² ≈ 3.14×25, which is around 78.5.