🧮 algebra

1. The problem is to solve the equation $3k = 1$ for $k$. 2. The formula used here is to isolate the variable by dividing both sides of the equation by the coefficient of $k$.

1. **State the problem:** Find the coefficients $a$, $b$, $c$, and $d$ of the cubic curve $$y = ax^3 + bx^2 + cx + d$$ such that it touches the line $$y = x + 1$$ at the point $(0,

1. **State the problem:** Find the coefficients $a$, $b$, $c$, and $d$ of the cubic curve $$y = ax^3 + bx^2 + cx + d$$ such that it touches the line $$y = x + 1$$ at the point $(0,

1. **State the problem:** Calculate the value of $\sqrt{3,312,400} \times e^{-\ln(130)}$. 2. **Recall formulas and rules:**

1. **Problem statement:** We have an arithmetic series where the sum of the first 5 terms is 70 and the sum of the first 11 terms is 352. We need to find the first term $a$ and com

1. **Problem Statement:** Find the value of $k$ in each term of the expansion of $$\left(2x-\frac{1}{3}y\right)^{10}$$ corresponding to the given terms. 2. **Formula:** The general

1. Solve the inequality $6n - 12 > 30$. Start by adding 12 to both sides:

1. **State the problem:** Simplify the expression $x - 13 \_ 20$. 2. **Identify the operation:** The underscore symbol \_ is not a standard arithmetic operator. Assuming it is a ty

1. **State the problem:** Solve the system of equations:

1. **State the problem:** We need to find the ratio of dogs to cats in simplest form given 18 dogs and 8 cats. 2. **Write the ratio:** The ratio of dogs to cats is $$\frac{18}{8}$$

1. **State the problem:** Solve the equation $$x^2 + \frac{2^{x-5}}{3} - \frac{1}{3}x - \frac{2(x-25)}{15} = 2x + \frac{3}{5} + 2x + (x-1)^2$$. 2. **Rewrite and simplify the equati

1. Solve each equation and classify it. (a) Solve $$\frac{1}{2}x + 6 = \frac{3}{4}x - 2 - \frac{1}{4}x + 8$$

1. The problem is to simplify the expression $23\sqrt{94}$. 2. The expression consists of a coefficient 23 multiplied by the square root of 94.

1. The problem is to express a given number or expression as a fraction. 2. To convert a decimal or mixed number to a fraction, identify the place value of the last digit.

1. **State the problem:** We have a total investment of 20000 split into two parts: one part invested at 11% simple interest for 2 years, and the other part invested at 8% simple i

1. **State the problem:** Solve the equation $8x - 40 = 20x - 4$ for $x$. 2. **Write the formula and rules:** To solve linear equations, we isolate the variable $x$ by performing t

1. **State the problem:** Solve the inequality $$\frac{x^2+5x+6}{x+3} > 0$$. 2. **Factor the numerator:** The quadratic $x^2+5x+6$ factors as $$(x+2)(x+3)$$.

1. **State the problem:** We have a rectangle with sides $2x$ and $4x$, and the area $A$ satisfies the inequality $32 < A < 392$. 2. **Formula for area of a rectangle:**

1. **State the problem:** Solve the equation $6(x-4)=2x+4$ for $x$. 2. **Write down the formula and rules:** Use the distributive property to expand and then isolate $x$ by combini

1. **Nyatakan masalah:** Diberi fungsi kuadratik $$f(x) = 2(x^2 - x - 2)$$.

1. El problema trata sobre la agrupación y factorización de expresiones algebraicas. 2. La agrupación consiste en agrupar términos que tienen factores comunes para luego factorizar