🧮 algebra

1. **State the problem:** Solve the inequality $$\frac{x - 2}{2} + \frac{x + 3}{5} < \frac{1}{10}$$. 2. **Identify the formula and rules:** To solve inequalities involving fraction

1. Stated problem: Rozwiąż nierówność a) $$\frac{x+1}{3} + \frac{x+2}{4} > \frac{1}{12}$$ 2. Użyjemy wspólnego mianownika, którym jest 12, aby uprościć nierówność.

1. **State the problem:** Solve the quadratic equation $4x^2 + 11x + 6 = 0$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Solve the quadratic equation $2x^2 + 5x + 3 = 0$. 2. **Formula used:** The quadratic formula is given by

1. **State the problem:** Simplify or factor the quadratic expression $2x^2 + 5x + 0$. 2. **Identify the expression:** The expression is $2x^2 + 5x + 0$, which can be rewritten as

1. **State the problem:** Simplify the expression $$\frac{5}{4} \times \frac{2}{3} \div \frac{1}{5} + \frac{2}{5} \div \frac{1}{10} \times \frac{3}{4} + \frac{1}{2} \times \frac{4}

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} y - x = 28 \\ y + x = 156 \end{cases}$$

1. **State the problem:** Factor the quadratic expression $x^2 + 11x + 24$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multi

1. **State the problem:** We are given the sequence 16, 36, 64, 81, 100 and asked to find the next two terms. 2. **Analyze the sequence:** Let's look for a pattern. Notice that the

1. **State the problem:** We need to solve the system of equations:

1. **State the problem:** The factory fills 750 ml containers using 900 litres of juice in one day. There are 4 times as many 100 ml containers filled as 750 ml containers each day

1. The problem states that the function $s$ is in the form $$y = ax^2 + c$$ where $a < 0$ and $c > 0$. 2. Important rules for quadratic functions in this form:

1. **State the problem:** Simplify the expression $2(m + 3)(m + 5) + 4(2m + 3)$. 2. **Use the distributive property:** Expand each product.

1. **State the problem:** Simplify the expression $5(x^0 y)$. 2. **Recall the rule:** Any nonzero number or variable raised to the zero power equals 1, i.e., $x^0 = 1$.

1. The problem asks to describe the transformation from the graph of $g(x) = x^2$ to $h(x) = -\left(\frac{x}{2}\right)^2$. 2. The original graph $g(x) = x^2$ is a parabola opening

1. Problema: Factorizar la expresión $a(x+1) + b(x+1)$. 2. Fórmula: Para factorizar expresiones con un factor común, usamos $A\cdot C + B\cdot C = (A+B)\cdot C$.

1. **State the problem:** Solve the system of equations using elimination: $$-7x + 10y = 6$$

1. **State the problem:** Solve the system of equations using elimination: $$-9x - 4y = -4$$

1. El problema parece ser evaluar o simplificar expresiones con potencias y números dados. 2. Para el primer ejercicio: "9 8 7 6 4 5^1" interpretamos que se quiere evaluar $5^1$ y

1. **Problem statement:** Given the function $f(x) = \frac{\ln(2x - 3)}{3x + 4}$, find its domain, zeros, sign, parity, symmetry, asymptotes, extrema, inflection points, and sketch

1. **State the problem:** Simplify the expression $$\frac{2^3 \times 2^2}{3^4}$$. 2. **Recall the laws of exponents:** When multiplying powers with the same base, add the exponents