🧮 algebra

1. **State the problem:** Solve the first system of linear equations using the reduction method: $$\begin{cases} 13x - 6y = -2 \\ 8x + 3y = -22 \end{cases}$$

1. **State the problem:** Find the greatest common factor (GCF) of 18 and 36b. 2. **Recall the formula and rules:** The GCF of two expressions is the largest expression that divide

1. **Problem:** Simplify the expression $\sqrt{x^5}$. 2. **Formula and rules:**

1. **Problem:** Rewrite each radical as an expression using rational exponents. 2. **Formula:** The nth root of a number $a^m$ can be written as $a^{\frac{m}{n}}$.

1. **State the problem:** Solve the equation $$\frac{10x}{25} = \frac{19}{15}$$ for $x$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross produ

1. El problema es analizar la función logarítmica $$f(x) = \log_3(6x - 18)$$, despejar su expresión para graficar y determinar dominio y rango. 2. Recordemos que el logaritmo $$\lo

1. **State the problem:** Solve the quadratic equation $$3y^{2} - 24y - 47 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ay^{2} + by + c = 0$$, the solutions are gi

1. **Problem statement:** We analyze a cyclist's journey from home to a city and back using the given distance-time graph.

1. **State the problem:** Multiply the conjugate binomials $ (d + 8)(d - 8) $ and simplify the result. 2. **Recall the formula:** The product of conjugate binomials $ (a + b)(a - b

1. **State the problem:** Name the polynomial $n + 7n^3 - 3$ by its degree and number of terms. 2. **Recall definitions:**

1. The problem is to identify the degree and the number of terms of degree 3 in the polynomial $n + 7n^3 - 3$. 2. The degree of a polynomial is the highest power of the variable in

1. The problem states that the nth term of a sequence is given by the formula $T(n) = 8n + 9$. 2. We are asked to find the 5th term of this sequence, which means we need to find $T

1. **State the problem:** Find the first three terms of the sequence defined by the formula $a_n = 20 - 3n$. 2. **Formula:** The general term of the sequence is given by $a_n = 20

1. **State the problem:** Find the intercepts and extrema of the function $y = x^2 + 1$. 2. **Formula and rules:**

1. **State the problem:** Simplify the expression $$-3y + -y - 7y + -8y + 3y$$. 2. **Combine like terms:** All terms are multiples of $y$, so we add their coefficients.

1. **State the problem:** Simplify the expression $$6t^2 + (-10t^2) + (-4t^2) + (-10t^2) + 8t^2 + (-8t^2)$$. 2. **Combine like terms:** Since all terms are multiples of $t^2$, we c

1. **State the problem:** Two trains start 342 miles apart and travel toward each other. One train travels at 105 mph and the other at 85 mph. We need to find the time $t$ in hours

1. **State the problem:** Two trains leave the station at the same time, one heading east at 95 mph and the other west at 75 mph. We need to find the time $t$ in hours when they ar

1. **State the problem:** Simplify the expression $$\frac{9x^2 - 3x - 2}{2x - 6} \cdot \frac{x - 3}{9x^2 - 4}$$. 2. **Factor all polynomials where possible:**

1. **Problem statement:** Multiply and simplify the expression \(\frac{x^2 + 5x + 6}{4x - 12} \times \frac{x - 3}{x^2 + 2x - 3}\). 2. **Recall the formula and rules:** When multipl

1. The problem is to find the overall average percentage when you have 90% in 3 classes and 65% in 1 class. 2. The formula for the average percentage is: