🧮 algebra

1. State the problem. Problem: Rewrite the quadratic equation $$x^2 - 6 = 11x$$ in standard form and identify $a$, $b$, and $c$.

1. We are asked to find the value of $y$ in the equation $$-\frac{3}{7} y = \frac{2}{3}.$$ 2. To isolate $y$, we need to divide both sides of the equation by $-\frac{3}{7}$. The fo

1. **State the problem:** Solve for $t$ in the equation $5 = \frac{10.3}{1 + 12.8 e^{-0.036t}}$. 2. **Rewrite the equation:** Multiply both sides by the denominator to eliminate th

1. **State the problem:** Factor the polynomial expression $4x^3 - 20x^2$ completely. 2. **Identify the greatest common factor (GCF):** Both terms have a factor of $4x^2$.

1. **State the problem:** Solve for $x$ in the equation $100 = 85 \times 1.005^x$. 2. **Write the formula and explain:** We want to isolate $x$. The equation involves an exponentia

1. **Problem statement:** Given points $P(6|6)$ and $Q(8|3)$ on a parabola $p$ with equation $y = -0.25x^2 + bx + c$, find $b$ and $c$.

1. **Problem statement:** Given a parabola $p$ passing through points $P(6|6)$ and $Q(8|3)$ with equation form $y = -0.25x^2 + bx + c$, find $b$ and $c$.

1. El problema es dividir el polinomio $2x^2 + 3x$ entre el binomio $2x + 3$. 2. La división de polinomios se realiza como la división larga: dividimos el término de mayor grado de

1. The problem is to factor the polynomial expression $2x^3 - 6x$ by factoring out the common factor. 2. The formula used is factoring out the greatest common factor (GCF): $$a b +

1. **State the problem:** We need to find the equation of line K in the form $y = mx + c$. 2. **Identify points on the line:** From the graph description, line K passes through poi

1. **State the problem:** We are given the linear function $$y = -2x - 1$$ and a table with some known and unknown values: $$\begin{array}{c|ccccc}

1. Il problema è analizzare la funzione razionale $$y = \frac{x^2 + 1}{2x + 1}$$ e determinarne il dominio, i segni e i punti notevoli. 2. Il dominio è dato da tutti i valori di $x

1. Il problema chiede di trovare le intersezioni della funzione razionale fratta $$y=\frac{x^2+1}{2x+1}$$ con gli assi cartesiani. 2. Intersezione con l'asse y: si trova ponendo $$

1. **State the problem:** Solve the inequality $$\frac{x^2 + 1}{2x + 1} > 0$$ and determine the domain.

1. Let's start by stating the problem: You want to understand how to identify horizontal and vertical dilations and translations in a function. 2. The general form of transformatio

1. The problem is to understand and analyze the concept of a sequence (suite in French). 2. A sequence is an ordered list of numbers defined by a specific rule or formula.

1. **Problem Statement:** We are given the graph of $y = g(x)$ and asked to sketch the curve of $y = 10 - g(4x)$ on the same axes.

1. The problem appears to involve the expression $Z_1^0 Z + \sqrt{y} y xy^2 \frac{dx}{dy}$, but it is unclear what exactly is asked. Assuming you want to simplify or analyze the ex

1. **State the problem:** Solve the equation $14^x = -18$ for $x$. 2. **Understand the properties of exponential functions:** The function $14^x$ is an exponential function with ba

1. The problem is to analyze the function $f(x) = |2x - 3|$ and determine its domain and range. 2. The domain ($D$) of an absolute value function is all real numbers because you ca

1. Let's start by understanding question 8, where you want to know how we get 30000. 2. Usually, 30000 could be a result of multiplying or adding numbers in the problem. For exampl