🧮 algebra

1. **State the problem:** We are given the line equation $y=\frac{3}{2}x-1$ and need to find the equation of the line perpendicular to it that passes through the point $(3,4)$. 2.

1. **State the problem:** We need to graph the quadratic function $$f(x) = -4x^2$$ on a Cartesian coordinate plane. 2. **Recall the formula and properties:** The function is a quad

1. The problem is incomplete as no specific expression or equation is provided to find the value for. 2. To solve any algebraic or arithmetic problem, we first need the exact expre

1. **State the problem:** Solve for $x$ in the equation $\frac{x}{13} = \frac{7}{91}$.\n\n2. **Formula and rule:** To solve for $x$ in a proportion $\frac{a}{b} = \frac{c}{d}$, cro

1. **State the problem:** Graph the inequality $3x - 4y > 12$ using intercepts. 2. **Rewrite the inequality as an equation to find intercepts:**

1. **State the problem:** Simplify the expression $$\frac{c^{-3} d^{5}}{c^{2} d^{-1}}$$. 2. **Recall the laws of exponents:**

1. **State the problem:** Simplify the expression $\frac{b^{-2}}{b^{6}}$. 2. **Recall the rule for dividing powers with the same base:** When dividing powers with the same base, su

1. مسئله: حل معادله $2x + 3 = 7$. 2. فرمول: برای حل معادله خطی، هدف این است که $x$ را تنها کنیم.

1. **Problem statement:** Find the equation of line L perpendicular to the line $2y + x = 1$ and passing through point $(2, -1)$.

1. The problem is to understand what an improper divisor is. 2. In mathematics, a divisor (or factor) of a number is a number that divides it exactly without leaving a remainder.

1. مسئله: جملات داده شده به صورت کسرهایی با صورت و مخرج مشخص هستند: $$\frac{3}{1}, \frac{6}{1}, \frac{6}{1}, \frac{7}{1}, \frac{15}{2}, \frac{39}{5}, \frac{8}{1}, \frac{57}{8}$$

1. **Énoncé du problème :** Trouver la fonction $f(x) = \frac{x^2}{\ln(x) - 1}$. 2. **Domaine de définition :** La fonction est définie pour $x > 0$ car $\ln(x)$ est défini uniquem

1. The problem is to understand why $q^2$ can divide the expression $3p(p-1)$. 2. To say that $q^2$ divides $3p(p-1)$ means that when you divide $3p(p-1)$ by $q^2$, the result is a

1. The problem is to understand how to order terms by their exponents from biggest to smallest. 2. When dealing with expressions involving exponents, the exponent indicates the pow

1. The problem is to understand how to write a polynomial in standard form. 2. A polynomial is an expression consisting of variables and coefficients, combined using addition, subt

1. **State the problem:** Expand the expression $$(2a - 1)^6$$ using the binomial theorem. 2. **Formula used:** The binomial theorem states that

1. **State the problem:** Expand the expression $$(4a - b)^3$$. 2. **Formula used:** The cube of a binomial $$(x - y)^3$$ expands as $$x^3 - 3x^2y + 3xy^2 - y^3$$.

1. **State the problem:** Simplify or expand the expression $$(4^a - b)^3$$. 2. **Formula used:** We use the binomial expansion formula for cubes: $$(x - y)^3 = x^3 - 3x^2y + 3xy^2

1. **State the problem:** An ice cream shop creates 25 new flavors and discards the 13 least popular ones. They produce 80 cartons of each remaining flavor. Each 2 cartons make 1 l

1. **State the problem:** Solve the quadratic equation $63x^2 = 175$ for $x$. 2. **Rewrite the equation:** To isolate $x^2$, divide both sides by 63:

1. The problem is to evaluate the expression $10 \div 2 (4 + 4)$. 2. According to the order of operations (PEMDAS/BODMAS), first solve the parentheses.