🧮 algebra

1. **State the problem:** Solve the quadratic equation $$x^2 - 12x + 7 = 0$$ and find the value of $$jk$$ where one solution is written as $$j - \sqrt{k}$$. 2. **Recall the quadrat

1. **State the problem:** We want to find an expression equivalent to $$\frac{1}{\frac{1}{x+2} + \frac{1}{x+3}}$$ for $$x > 3$$.

1. **Problem 36:** Given foci at $(-3,-11)$ and $(-3,0)$ and transverse axis endpoints at $(-3,-9)$ and $(-3,-2)$, identify the conic and find its equation. 2. The foci share the s

1. **State the problem:** Solve the equation $$\left(\frac{1}{64}\right)^{2+5x} - 4^{3-2x} = 64^{0} - \left(\frac{1}{320}\right)^{64}.$$\n\n2. **Recall important rules and formulas

1. 题目要求求一条直线的方程，该直线垂直于直线 $3x - 4y = 5$ 并且经过点 $(-2, 1)$。 2. 首先，求已知直线的斜率。将方程 $3x - 4y = 5$ 改写为斜截式：

1. 题目要求求一条直线的方程，该直线垂直于直线 $3x - 4y = 5$，且经过点 $(-2, 1)$。 2. 首先，求已知直线的斜率。将方程 $3x - 4y = 5$ 改写为斜截式：

1. Considere a função $$h(x) = \frac{(2x^2+16)(x^2+3x-4)}{|5-3x|\cdot(-x^2+9)} + (\sqrt{2} - 8x)$$ e resolva a condição $$h(x) \leq 0$$. 2. Resolva em $$\mathbb{R}$$ as condições:

1. **State the problem:** We need to show that for the function $g(x) = 2x$, the expression $g(x+3) - g(x-1)$ equals 8. 2. **Recall the function definition:** $g(x) = 2x$ means tha

1. **State the problem:** Solve the equation $8y + 7 + 7y + 8 = 90$ for $y$. 2. **Combine like terms:** Group the terms with $y$ and the constant terms.

1. **Stating the problem:** Vi skal undersøge påstandene fra fire elever om løsninger til ligningen $$4x + 3y = 100$$ hvor $$x$$ og $$y$$ er hele tal større end 0. 2. **Formlen:**

1. **State the problem:** Simplify the expression $$1 - 5 - 2 - 3y - 3y$$ by combining like terms. 2. **Identify like terms:** Like terms are terms that have the same variable rais

1. **State the problem:** Two thirds of the children were pediatricians, and 40 children were non-pediatricians. We need to find the total number of children. 2. **Set up the equat

1. **Enunciado do problema:** Calcular o valor da expressão $$1^{21} \times 6^{5} \div 2^{5} \times 3^{4} \times (2^{3})^{2}$$ passo a passo. 2. **Fórmulas e regras importantes:**

1. **Problem:** Determine which statement about the cost per ounce of Bag A and Bag B is true. 2. **Formula:** Cost per ounce = \frac{Cost}{Ounces}

1. The problem asks for the constant of proportionality $\frac{y}{x}$ for a line passing through the origin and the point $(1,40)$. 2. The constant of proportionality in a direct v

1. The problem asks what the number 30 means in the context of the graph point (1, 30), where 1 represents grams of hamster food and 30 represents days. 2. The point (1, 30) means

1. El problema no está explícito, pero parece que quieres resolver una ecuación cuadrática usando la fórmula general para ecuaciones de la forma $ax^2 + bx + c = 0$. 2. La fórmula

1. **State the problem:** Simplify the expression $21 - (-2x - 8)$. 2. **Recall the rule:** Subtracting a negative expression is equivalent to adding its opposite. So, $a - (-b) =

1. **State the problem:** Solve the system of equations using the equal value method: $$y = x^2 - x - 2$$

1. **Problem Statement:** Find the sum of the infinite geometric sequence with first term 20 and common ratio $\frac{1}{2}$. Determine if the sum exists and calculate it if possibl

1. The problem is to find the expanded form of the function $f(x) = (x-2)(x+3)$. 2. We use the distributive property (also known as FOIL for binomials) which states: