🧮 algebra

1. The problem is to solve the equation for the variable 3. 2. Since 3 is a constant and not a variable, it cannot be solved for.

1. **State the problem:** Solve the equation \( \frac{x + 7}{x^2 + 3x - 10} - \frac{7}{x^2 + 10x + 25} = \frac{x - 7}{x^2 + 3x - 10} \). 2. **Factor the denominators:**

1. **State the problem:** Solve the equation $3x - (5 - 3x) = 8$ for $x$. 2. **Apply the distributive property:** Remove the parentheses by distributing the minus sign:

1. **State the problem:** We are given the parabola equation $$(x + 4)^2 = -4(y + 7)$$ and need to find the vertex, focus, focal diameter, and directrix. 2. **Identify the form:**

1. **State the problem:** Find the zeros of the function $f(x) = 2x^2 - 10.2x + 5.8$. Zeros are values of $x$ where $f(x) = 0$. 2. **Formula used:** To find zeros of a quadratic $a

1. **Stating the problem:** We want to understand what a proof is and see an example of finding a proof in mathematics. 2. **What is a proof?** A proof is a logical argument that s

1. The problem asks to find the values of all nine filled-in expressions or equations (assuming a grid or matrix of nine items). 2. Since the user did not provide explicit expressi

1. **State the problem:** Evaluate the expression $$9^{-\frac{3}{2}}$$. 2. **Recall the rules:** For any positive number $a$ and rational exponent $m/n$, $$a^{\frac{m}{n}} = \sqrt[

1. The problem asks to solve for the first option among a, b, c, or d. Since no specific problem statement or options are given, I will demonstrate how to solve a typical algebraic

1. **Énoncé du problème :** Résoudre l'inéquation $2x + 3 > 6x - 1$. 2. **Formule et règle importante :** Lorsqu'on divise ou multiplie une inéquation par un nombre négatif, il fau

1. The problem asks for the equation of the vertical asymptote of a reciprocal-type curve. 2. A vertical asymptote occurs where the function approaches infinity or negative infinit

1. **State the problem:** We need to find the excluded value for the function represented by the graph. 2. **Analyze the graph:** The graph shows a reciprocal-shaped curve with a v

1. **State the problem:** We need to find the value of $x$ such that the expressions for the top-left and top-right are equal: $$\sqrt{100^2 - x^2} = \sqrt{89.4^2 - (x-20)^2}$$

1. **State the problem:** We are given two equations: $$y = 0.4 + 3.25$$

1. **State the problem:** We are given the linear function $y=0.4x + 3.25$ and want to understand its properties. 2. **Formula and explanation:** This is a linear equation in slope

1. **Problem statement:** We need to find all possible combinations of the number of saftevand cups ($x$), kakao cups ($y$), and pieces of chokolade ($z$) that sum up to 90 kr. 2.

1. **State the problem:** We are given the expression for the total candies in $b$ bags as $$bg + by$$ and asked to find an equivalent expression for the total candies in 1 bag. 2.

1. The problem asks to find an equivalent expression for the total number of candies in 1 bag, given the total for $b$ bags is $bg + by$. 2. The original expression is $bg + by$, w

1. **State the problem:** We are given the inequality $$2(p + 6) > 20$$ where $p$ represents the number of pages Mr. Vann assigned. 2. **Analyze the inequality:** The expression $2

1. **State the problem:** Solve the equation $$\frac{1}{2}x - \frac{x}{4} + \frac{6}{2} = -\frac{1}{9}x + \frac{3 - x}{3}$$ for $x$. 2. **Write down the equation clearly:**

1. **State the problem:** Solve the equation $$\frac{4}{3} - x + \frac{7}{6} - \frac{3x + 1}{2} = -\frac{7}{9}x + \frac{3 - x}{3}$$ for $x$. 2. **Combine like terms and find a comm