🧮 algebra

1. **Problem 27:** Given the system of equations: $$2a - c = 0$$

1. **State the problem:** Solve the system of equations: $$3x + 2y = 19$$

1. **State the problem:** We are given a rectangle with perimeter 40 cm and a relationship between length $l$ and width $w$: twice the length is five centimeters more than three ti

1. **State the problem:** We want to find the baseball ticket prices in 2009 using the previous equation or model given for ticket prices over the years. 2. **Recall the formula:**

1. **State the problem:** We need to find the equation of the line of fit in slope-intercept form $y=mx+b$ using the points $(2001, 17.60)$ and $(2002, 18.75)$. 2. **Formula for sl

1. Let's solve the quadratic equation $2x^2 - 4x - 6 = 0$ as another example. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$.

1. Let's solve a fraction problem: Simplify the expression $$\frac{6}{8} + \frac{3}{4}$$. 2. The formula to add fractions is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ wher

1. **State the problem:** We are given a system of linear equations:

1. 题目：计算分数加法 $\frac{2}{3} + \frac{4}{5}$。 2. 公式和规则：

1. **State the problem:** Simplify the product of the functions \(f(x)\) and \(g(x)\) given by $$

1. The problem asks for the new location of the point $(2, \frac{9}{16})$ on the function $f(x) = \left(\frac{3}{4}\right)^x$ after reflecting the function across the x-axis. 2. Re

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:**