🧮 algebra

1. **State the problem:** Solve the quadratic equation using the Bhaskara formula (quadratic formula). 2. **Formula:** For a quadratic equation $ax^2 + bx + c = 0$, the solutions a

1. The problem is to find the roots of the function $y(x) = 2(x-1)^2$. 2. Roots of a function are the values of $x$ for which $y(x) = 0$.

1. **Stating the problem:** Find the equations of the lines passing through given points and express them in slope-intercept form $y = mx + b$. 2. **Line R through points $(-2,1)$

1. **State the problem:** Solve the equation $5kx^2 + 6x = 2(x+4)$ for $x$. 2. **Rewrite the equation:** Expand the right side:

1. **Problem Statement:** Find the values of $x$ such that the area of the triangle with vertices $(x,4)$, $(2,-6)$, and $(5,4)$ is 35 square units. 2. **Formula for Area of Triang

1. El problema es simplificar la expresión en un solo cálculo. 2. Para simplificar expresiones algebraicas, se deben aplicar las propiedades de las operaciones y combinar términos

1. **State the problem:** We need to find the slope $m$ and the y-intercept $c$ of the line $T$ given its graph points. 2. **Identify two points on the line:** From the graph, appr

1. Planteamos el problema: Factorizar la función $$f(x) = x^4 - 2x^3 - 3x^2 + 4x + 4$$ y luego aplicar el teorema de Bolzano para encontrar intervalos donde la función cambia de si

1. **Planteamiento del problema:** Dada la función cuadrática $$f(x) = 2x^2 - 4x - 30$$, primero la factorizaremos y luego aplicaremos el Teorema de Bolzano para encontrar un inter

1. **State the problem:** Solve the quadratic equation $$80x^{2} + 9x + 30 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^{2} + bx + c = 0$$ is

1. El problema es convertir una expresión algebraica dada en su forma factorizada. 2. La factorización consiste en expresar un polinomio como el producto de polinomios más simples.

1. **Planteamiento del problema:** Resolver la función $f(x) = x^3 - 5x^2 + 7x - 3$, es decir, encontrar los valores de $x$ para los cuales $f(x) = 0$. 2. **Fórmula y reglas import

1. **State the problem:** Solve for $x$ in the equation $$x = 200000 + 70000 + \frac{2139}{100} \times x.$$\n\n2. **Rewrite the equation:** Combine the constants on the right side:

1. **State the problem:** We need to find the values of $m$ (slope) and $c$ (y-intercept) for the line $Q$ given its equation in the form $y = mx + c$. 2. **Identify points on the

1. **State the problem:** Simplify the expression $x - (-3)$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. Formally, $a - (

1. **Problem statement:** Simplify and arrange the polynomial $P(x) = 3x^3 + 5x - 12 - x^2 + x^3 - 6x^2 - 2x$ in ascending powers of $x$. 2. **Combine like terms:**

1. **Problem statement:** Given two polynomials: $$P(x) = 3x^3 + 5x - 12 - x^2 + x^3 - 6x^2 - 2x$$

1. Bài toán yêu cầu rút gọn biểu thức phân số $$\frac{2x^3 - 7x^2 - 12x + 45}{3x^3 - 19x^2 + 33x - 9}$$. 2. Công thức rút gọn phân số đại số là phân tích tử số và mẫu số thành các

1. The problem states that the function $f$ is composed of two pieces: a polynomial piece and an exponential piece. 2. The graph shows the polynomial piece on the left side for $x

1. **State the problem:** Solve the quadratic equation $$64x^2 + 5x + 25 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is

1. **State the problem:** Solve the system of linear equations: $$5(x + 1) - 2(y - 3) = 21$$