🧮 algebra

1. **State the problems:** Solve the quadratic equations from 29 to 36. 2. **Recall the quadratic formula:** For any quadratic equation $ax^2 + bx + c = 0$, the solutions are given

1. The problem is to simplify the expression $X \times 30 \times X \times 15$. 2. We start by recognizing that multiplication is associative and commutative, so we can rearrange th

1. The problem is to understand what 42% means and how to express it as a decimal and a fraction. 2. The percent symbol (%) means "per hundred," so 42% means 42 out of 100.

1. **Problem statement:** We are given a function $f(x)$ with vertical asymptotes at $x = -1$ and $x = 1$, and a horizontal asymptote at $y = 0$. We need to solve the inequality $f

1. **State the problem:** We are given a function $f$ with vertical asymptotes at $x=-2$ and $x=2$, and a horizontal asymptote at $y=0$. We need to solve the inequality $f(x)<0$ us

1. **State the problem:** Solve the linear equation $7x - 8 = 57$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add or subtract

1. El problema consiste en identificar el error en las multiplicaciones dadas en los dos apartados. 2. Para multiplicar polinomios, se debe aplicar la propiedad distributiva: cada

1. **State the problem:** Solve the equation $2x + 4 = 16$ for $x$. 2. **Formula and rules:** To solve a linear equation, isolate the variable on one side by performing inverse ope

1. **State the problem:** We are given the function $c(x) = \sqrt{4x + 1}$ and a graph with points including $(0,1)$ that matches this function. We want to confirm or rewrite the e

1. The problem asks to find the improper fraction equivalent to the mixed number $4 \frac{3}{5}$. 2. A mixed number consists of a whole number and a fraction. To convert it to an i

1. **State the problem:** Aron planted vegetables where \(\frac{5}{12}\) were carrots, \(\frac{3}{12}\) were cucumbers, and the rest were tomatoes. We need to find the fraction of

1. The problem asks to find another way to write the fraction $\frac{5}{6}$. 2. The fraction $\frac{5}{6}$ means 5 divided by 6, which can be written as $5 \div 6$.

1. The problem asks which pair of fractions are equivalent. 2. Two fractions are equivalent if their cross products are equal, i.e., for fractions $\frac{a}{b}$ and $\frac{c}{d}$,

1. **State the problem:** Determine the domain on which the function is increasing. 2. **Identify the function:** From the description, the function is a downward-opening parabola

1. The problem asks to determine the domain on which the quadratic function is increasing. 2. The graph is a parabola opening upwards with vertex at approximately $(2, -4)$.

1. **State the problem:** Find the slope of the line passing through the points $(6,4)$ and $(-3,-2)$. 2. **Formula for slope:** The slope $m$ of a line through points $(x_1,y_1)$

1. **Problem:** Write the expression $(2^3)^4$ as a power with base 2. 2. **Formula:** When raising a power to another power, multiply the exponents: $\left(a^m\right)^n = a^{m \cd

1. **State the problem:** Find the sum of the arithmetic series $$\sum_{i=1}^{18} (14 - 6i)$$. 2. **Formula used:** The sum of an arithmetic series with $n$ terms, first term $a_1$

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then d

1. **State the problem:** Find the set $A=\{x \in \mathbb{Z} \mid (x-1)(x-2)(x+\frac{1}{2})=0\}$. This means we want all integer values of $x$ that satisfy the equation. 2. **Use t

1. Planteamos el problema: realizar las divisiones indicadas. 2. La fórmula general para dividir un polinomio por un monomio es dividir cada término del polinomio entre el monomio,