By subtracting 3 from both sides, the equation becomes 2x = 4, and dividing by 2 results in x = 2. This demonstrates a basic technique for solving linear equations.

Dividing 12 by 3 gives 4 because 3 multiplied by 4 equals 12. This is a fundamental division problem.

Fifty percent represents half, so 50% of 100 is 50. This problem tests understanding of basic percentages.

Dividing 1 by 4 gives 0.25, which is the decimal equivalent of the fraction 1/4. This conversion is commonly used to bridge fractions and decimals.

The perimeter of a square is 4 times the length of one side. Multiplying 4 by 4 results in a perimeter of 16 units.

Dividing both sides of the equation by 3 gives x - 2 = 5, and adding 2 to both sides results in x = 7. This is an application of basic algebraic manipulation.

Convert both fractions to have a common denominator of 12: 3/4 becomes 9/12 and 2/3 becomes 8/12. Their sum is 17/12.

The factors common to both 24 and 36 include 1, 2, 3, 4, 6, and 12, with the largest being 12. Thus, the GCD of 24 and 36 is 12.

Adding 5 to both sides results in 2y = 8, and dividing by 2 gives y = 4. This problem reinforces basic techniques in solving linear equations.

The slope is determined by dividing the change in y by the change in x: (8 - 2)/(4 - 1) equals 6/3, which simplifies to 2.

With a cat to dog ratio of 3:5, 15 cats represent 3 parts; hence, one part equals 5. Multiplying 5 by 5 (for dogs) gives 25.

When multiplying exponential terms with the same base, add the exponents: 2^3 * 2^2 equals 2^(3+2) = 2^5, which is 32.

First, distribute 5 to get 5x + 15, then subtract 2x to simplify the expression to 3x + 15. This applies the distributive property effectively.

The square root of 81 is 9 because 9 x 9 equals 81. This exercise is centered around recognizing perfect squares.

The decimal 0.75 is equivalent to 75/100, which simplifies to 3/4 when divided by 25. This problem reinforces conversion between decimals and fractions.

By expressing y from the second equation as x - 1 and substituting into the first equation, you obtain 3x = 11, leading to x = 11/3 and y = 8/3. This method showcases solving systems of equations using substitution.

Substitute x = 3 into the function to calculate f(3): 2(9) - 3(3) + 1 equals 18 - 9 + 1, which simplifies to 10. This evaluates a quadratic function at a specific point.

Finding a common denominator leads to (7x)/12 = 7; multiplying both sides by 12 gives 7x = 84, so x = 12. This problem tests skills in combining fractions and solving linear equations.

Using the formula V = πr²h, substitute r = 3 and h = 5 to get V = 3.14 × 9 × 5, which equals 141.3. This reinforces the application of geometric formulas.

Cross-multiplying the proportion gives 5x = 60, hence solving for x results in x = 12. This problem emphasizes the concept of proportional reasoning.