🧮 algebra

1. El problema es encontrar la función dada: $f(x) = -2x + 5$. 2. Esta es una función lineal de la forma $f(x) = mx + b$, donde $m$ es la pendiente y $b$ es la ordenada al origen.

1. The problem is to find the sign of the function $f(x) = \ln\left(\frac{2x-3}{3x+4}\right)$.\n\n2. Recall that the natural logarithm function $\ln(y)$ is defined only for $y > 0$

1. **State the problem:** Make $x$ the subject of the formula given by $$9y = \frac{5 - 2x}{2}$$ 2. **Start by eliminating the denominator:** Multiply both sides by 2 to get rid of

1. Problema C1: Determinați numerele reale a, b, c, știind că polinoamele $f = X^3 + aX^2 + bX + c$ și $g = (X - 2)(X - 3)(X + 1)$ sunt egale. 2. Pentru a determina coeficienții $a

1. **Stating the problem:** Given an arithmetic progression (a_n) with the conditions:

1. **State the problem:** We need to graph the function $f(x) = -(x - 3)^2$ and plot the vertex and another point on the parabola. 2. **Identify the vertex:** The function is in ve

1. **State the problem:** Solve the equation $$\frac{6x + 1 - x}{6x} + \frac{3}{x} = 1 + \frac{11}{3}$$ for $x$. 2. **Simplify the numerator in the first fraction:**

1. **State the problem:** Graph the function $f(x) = -x^2 + 8$ and plot the vertex and another point on the parabola. 2. **Formula and rules:** This is a quadratic function in the

1. Il problema chiede come calcolare il segno di una funzione, cioè determinare dove la funzione è positiva, negativa o nulla. 2. Per calcolare il segno di una funzione $f(x)$, si

1. Il problema richiede di analizzare la funzione razionale $$f(x) = \frac{x+1}{x-1}$$ e rappresentarne il grafico. 2. La funzione è una frazione con numeratore $$x+1$$ e denominat

1. The problem is to generate a function or expression based on the user's request "Can you generate it?" which is ambiguous but implies generating a mathematical function. 2. Sinc

1. **State the problem:** Simplify the expression $(2k-3)x^3$. 2. **Understand the expression:** This is a product of a binomial $(2k-3)$ and a monomial $x^3$.

1. **Problem Statement:** Solve the system of simultaneous equations using the substitution method. 2. **General Idea:** The substitution method involves solving one equation for o

1. **Stating the problem:** We want to solve simultaneous equations using the elimination method. For example, solve the system: $$\begin{cases} 2x + 3y = 8 \\ 4x - y = 2 \end{case

1. The problem is to transform the given quadratic equations into standard form $ax^2 + bx + c = 0$. 2. Recall that the standard form of a quadratic equation is $ax^2 + bx + c = 0$

1. **State the problem:** We want to factor the expression $$3^{2x} + 3^x - 6$$ into the form $$(3^x + a)(3^x + b)$$ and find the values of $a$ and $b$. 2. **Rewrite the expression

1. **State the problem:** Zahra's EMSAT score was 820 initially, and it increased by 20% in her second attempt. We need to find her new EMSAT score. 2. **Formula used:** To calcula

1. **State the problem:** Zahra's EMSAT score was 820 initially, and it increased by 20% in her second attempt. We need to find her new EMSAT score. 2. **Formula used:** To calcula

1. **State the problem:** We have a rectangle ABCD with sides labeled as follows: - AB = $2x + 5y$

1. Let's understand the problem: The user is asking if division is basically "KFC" which stands for "Keep, Flip, Change". 2. The "Keep, Flip, Change" rule is a method used to divid

1. Let's start by understanding fractions and the operations you mentioned: addition, subtraction, multiplication, and division. 2. **Addition and Subtraction of Fractions:**