A joint venture is a temporary partnership formed for a specific project or goal, distinct from a permanent partnership.

A limited partner contributes capital but does not participate in the management of the business, thus limiting their liability.

A limited partnership consists of at least one general partner who has unlimited liability and one or more limited partners who have limited liability.

Partnership by estoppel occurs when a person represents themselves as a partner, leading others to believe they are part of the partnership, thus creating legal recognition.

The profit-sharing ratio refers to the ratio in which partners agree to share the profits of the partnership.

A silent partner invests capital but does not engage in the daily operations of the business.

The Fibonacci sequence is significant because it appears in various natural phenomena and patterns, illustrating the connection between mathematics and nature.

Infinity is often described as a limit that can never be reached, representing an unbounded quantity in mathematics.

Mathematical induction is a method of proof that involves proving a base case and then showing that if the statement holds for an arbitrary case n, it holds for n+1.

The conclusion emphasizes that digital sum is fundamental and has numerous applications across various domains.

The conclusion of the passage asserts that digital sum continues to be a fundamental concept in the field of technology.

The passage indicates that access to quality education is a significant factor in reducing inequality.

The passage suggests that education plays a crucial role in mitigating social inequalities, highlighting its importance.

A consistent system can either have one solution or infinitely many solutions.

Dependent systems have infinitely many solutions as they represent the same line.

A polynomial that includes a variable in the denominator is not a polynomial function.

A cubic function has one end rising and the other falling, characteristic of odd-degree polynomials.

Since the leading coefficient is negative and the degree is even, both ends of the polynomial go down.

The leading coefficient is defined as the coefficient of the term with the highest degree in the polynomial.

8 ≡ 15 (mod 8) is false; the correct answer is 5 ≡ 10 (mod 5) is true.

The standard equation of a circle with center (0, 0) and radius r is x^2 + y^2 = r^2. Here, r = 5, so r^2 = 25.

Parallel lines have the same slope. The equation 2x + 3y = 12 has the same slope as 2x + 3y = 6.

Parallel lines have the same slope. The slope of y = -3x + 4 is -3, so any line with the same slope, like y = -3x + 1, is parallel.

All options are valid, but 5x ≡ 10 (mod 5) simplifies to 0 ≡ 0, which is trivially true.

Using the power of a product rule, (x^3 * y^2)^2 = x^(3*2) * y^(2*2) = x^6 * y^4.

Distributing 2 gives 2 * x + 2 * 3 = 2x + 6.

Distributing gives 3x + 12 - 2x + 2 = x + 14.

Using the property of exponents that states a^m * a^n = a^(m+n), we combine the exponents: 2x + (x + 1) = 3x + 1.

log_10(100) = 2 and log_10(10) = 1, so 2 + 1 = 3.

Since 1000 is 10^3, log_10(1000) = 3.