🧮 algebra

1. We are given the equation $234x \times 434 = 223$ and need to find the value of $x$. 2. First, calculate the constant product $234 \times 434$:

1. Let's identify the context first: the expression was simplified to 2x in step 4. 2. Usually, this comes from combining like terms or simplifying a multiplication or division.

1. Stated problem: Solve the equation $$4(2^{2x}) - 25 = 0$$ for $x$. 2. Add 25 to both sides to isolate the exponential term:

1. The problem asks to expand the expression $-4x^2 + 24x - 4$. 2. This expression is already expanded as a quadratic polynomial with three terms: one quadratic term $-4x^2$, one l

1. The problem is to expand the expression "it". However, "it" is not a mathematical expression that can be expanded. 2. If you have a specific algebraic expression, polynomial, or

1. The problem is to analyze and simplify the quadratic expression $$-4x^2 + 24x - 4$$. 2. First, factor out the greatest common factor from all terms, which is $$-4$$.

1. **Question 9:** A line $y=mx+c$ is perpendicular to a line $y=px+q$ if the gradients satisfy $p=-\frac{1}{m}$. So from the options, none exactly matches this, but usually it is

1. **Find the gradient of the line through points R(4, 0) and S(-2, 1).** Gradient formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$.

1. Solve the equation $\frac{3x - 4}{3} = \frac{3x^2 + 5x - 12}{2}$ for $x$. Multiply both sides by 6 to clear denominators:

1. The problem states that Isaac and Victoria share money in the ratio $2:5$ and Victoria receives 6.60. 2. Let the total number of parts be $2 + 5 = 7$ parts.

1. We are given the formula $$R=\frac{x^2}{y}$$ and values $$x=2.9 \times 10^5$$ and $$y=6.2 \times 10^4$$. 2. Substitute the given values into the formula:

1. Stating the problem: We need to find the equation of a circle with center at the origin $(0,0)$ and radius $3$. 2. Recall the equation of a circle centered at the origin: $$x^2

1. **Problem:** Factor $x^2 + 5x + 6$. 2. **Strategy:** Look for two numbers that multiply to $6$ and add to $5$.

1. **Stating the problem**: We have a sequence starting at 3. Each term is generated from the previous as follows: - If the term is even, next term = term \div 2

1. Share 2.40 in the ratio 3:5. Total parts = 3 + 5 = 8.

1. The problem asks us to subtract two dates and express the difference in hours. 2. To do this, first find the difference in days between the two dates.

1. The problem is to solve inequalities, but no specific inequality was provided. 2. Please provide the inequalities you want to solve so I can assist properly.

1. **State the problem:** We want to show that $$\log_{16} (xy) = \frac{1}{2} \log_{4} x + \frac{1}{2} \log_{4} y$$ and then solve the simultaneous equations: (i) $$\log_{16} (xy)

1. The problem asks to simplify the expression $2x-6$ or solve/interpret it further if needed. 2. First, factor out the common factor from the terms: $$2x-6 = 2(x-3)$$.

1. **Problem statement:** A pump can fill a tank in 2 hours. Due to a leak, it takes 2.5 hours to fill the tank. We need to find how many hours the leak alone would take to empty t

1. Stating the problem: Calculate $$-30 + 5 \cdot (-2)^3$$ and verify if it equals $$-70$$. 2. Simplify powers and multiplication: