🧮 algebra

1. **Problem:** Solve the equation $|x^2 - 14| = 5x$ for $x > 0$. 2. **Formula and approach:** Since the equation involves an absolute value, we consider two cases:

1. Énoncé du problème : Comparer les nombres $A = \frac{x}{x+1}$ et $B = \frac{y}{y+1}$ avec $0 < x < y$. 2. Formule et règles importantes : Pour comparer deux fractions de la form

1. **Énoncé du problème :** Comparer les nombres $A = \frac{x}{x+1}$ et $B = \frac{y}{y+1}$ avec $0 < x < y$. 2. **Formule et règles importantes :** Pour comparer deux fractions de

1. **Problem Statement:** We are given a polynomial curve with specific behavior: it starts high near $y=300$ at $x=0$, descends to a minimum between $x=5$ and $x=10$, rises to a l

1. The problem is to solve the equation $x^2 = x + 2$ for $x$. 2. We start by rewriting the equation to set it equal to zero: $$x^2 - x - 2 = 0$$

1. **State the problem:** Simplify the expression $\frac{3X+24}{-6}$. 2. **Formula and rules:** When dividing a sum by a number, you can divide each term separately by that number:

1. **State the problem:** Simplify the expression $\frac{1}{3}x \cdot 0.36x$. 2. **Recall the multiplication rule for coefficients and variables:** When multiplying terms, multiply

1. The problem asks to write three expressions equivalent to the given expression. 2. The original expression is $7.26 \times 5x \times 7$.

1. The problem involves solving the inequality $$2 \leq |x| - |x| + 5 \geq$$ but the expression is incomplete and unclear. 2. Since the inequalities are incomplete, we cannot deter

1. **State the problem:** Solve the equation $p - 1 = 5p + 3p - 8$ for $p$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $4m - 4 = 4m$ for $m$. 2. **Write down the equation:**

1. **State the problem:** Find the points on the ellipse $$64x^2 + y^2 = 64$$ that are farthest from the point $ (1,0) $. 2. **Rewrite the ellipse equation:** Divide both sides by

1. **State the problem:** Simplify the expression $$6 \left( \frac{1}{4} = \frac{1}{2} \right) - 2^3 \times 0.75$$. Note that the equal sign inside the parentheses seems to be a mi

1. The problem is to find the equation of the line passing through the points $(-1, 2)$ and $(3, 4)$. 2. The formula for the slope $m$ of a line through two points $(x_1, y_1)$ and

1. The problem is to solve the system of non-linear equations given by the points: $(-1, 2), (1, -2), (1, 1), (3, -1)$

1. The problem asks to represent the relation shown in the arrow diagram as a set of ordered pairs. 2. The arrow diagram shows arrows from numbers to houses: 3 to House Q, 4 to Hou

1. El problema es calcular la expresión $$\log_{\sqrt{7}} \sqrt[7]{343} + \log_{3\sqrt{4}} \sqrt[3]{16} + \log_{4\sqrt{3}} \sqrt[4]{27}$$. 2. Recordemos que $$\log_a b = \frac{\log

1. **State the problem:** Factor the polynomial $4x^3 + 6x^2 - 18x$ completely. 2. **Identify the greatest common factor (GCF):** Look at the coefficients 4, 6, and -18. The GCF of

1. **State the problem:** Simplify the expression $2m^4 \times 5m^2$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying terms with the same base, a

1. The problem is to understand how to find specific features or points on a graph. 2. To find points on a graph, you need to know the function equation, for example, $y=f(x)$.

1. **State the problem:** Solve the equation $$\frac{1}{x+y} + \frac{1}{x-y} = 0$$ for $x$ and $y$. 2. **Use a common denominator:** The denominators are $x+y$ and $x-y$. The commo