🧮 algebra

1. **State the problem:** We need to solve the equation $$3^x - 3^y = 234$$ for the variables $x$ and $y$. 2. **Analyze the equation:** The equation involves exponential terms with

1. The problem is to evaluate the expression $6 \div 2(1+2)$.\n\n2. According to the order of operations (PEMDAS/BODMAS), first solve the parentheses.\n\n3. Calculate inside the pa

1. The problem is to evaluate the expression $6 \div 2(1+2)$. 2. According to the order of operations (PEMDAS/BODMAS), we first solve expressions inside parentheses.

1. Let's solve an example logarithm problem: Find $x$ if $\log_2(x) = 3$. 2. The logarithm formula states that $\log_b(a) = c$ means $b^c = a$.

1. Let's start by stating the problem: factoring a function means expressing it as a product of simpler functions or polynomials. 2. The most common type of factoring is factoring

1. The problem is to simplify the expression $x^2 + x^2$. 2. The formula used here is the addition of like terms: $a^n + a^n = 2a^n$.

1. **State the problem:** Solve the equation $16 - 2t = 5t + 9$ for $t$. 2. **Write down the equation:**

1. **State the problem:** We are given three equations involving apple, banana bunch, and coconut half: - apple + banana bunch + banana bunch = 18

1. **State the problem:** Simplify the expression $6 \div 2(1+2)$. 2. **Evaluate inside the parentheses first:** $1+2=3$. So the expression becomes $6 \div 2(3)$.

1. **State the problem:** We have a total of $p=342$ peanuts divided equally into 6 bags. We want to find how many peanuts are in each bag. 2. **Identify the operation:** Since the

1. The problem asks which scenario corresponds to the algebraic expression $\frac{365}{y}$. 2. The expression $\frac{365}{y}$ means "365 divided by $y$."

1. Let's clarify how we get the number 6 in the context of a problem. 2. Suppose the problem involves solving an equation or simplifying an expression that results in 6.

1. **State the problem:** We need to find how many degrees the minute hand of a clock moves from 11:10 to 11:45. 2. **Formula and rules:** The minute hand completes a full circle (

1. The problem is to solve the exponential equation $$7^x = 343$$ for the variable $x$. 2. Recall that $343$ can be expressed as a power of $7$ because $7^3 = 343$.

1. The problem is to solve the equation $$7^x = 343$$ for the variable $x$. 2. We recognize that 343 is a power of 7. Specifically, $$343 = 7^3$$.

1. **Problem stated:** Find the complex roots of $f(x)=-\frac{1}{x-2}-\ln(x-4)$ and its asymptotes. 2. **Formula and domain rules:** A root is found by solving $f(x)=0$.

1. **Problem statement:** Simplify each expression given in parts 8 and 9. ---

1. The problem asks to identify which equation corresponds to the given graph. 2. The graph is a straight line with positive slope, crossing the y-axis at (0, 6) and the x-axis at

1. **State the problem:** Put the equation of the line $$5x + y = -4$$ into slope-intercept form, which is $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 2.

1. **Problem statement:** Write the given expressions as the square of a binomial. 2. **Formula used:** A perfect square trinomial can be written as $$(ax + b)^2 = a^2x^2 + 2abx +

1. **Problemstellung:** Untersuche, ob die Gleichung $(-a - b)^2 = (a + b)^2$ oder $(-a - b)^2 = -(a + b)^2$ gilt.