🧮 algebra

1. **State the problem:** We need to find the equation of a line that goes through the point $(6, -4)$ and is perpendicular to the line given by the equation $$6 = 4y + 3x$$. 2. **

1. **State the problem:** We need to find the equation of the line that passes through the points $(3, -5)$ and $(-2, 7)$. 2. **Formula used:** The equation of a line can be found

1. **State the problem:** Solve the inequality $$|x + 9| - 3 \geq -2$$. 2. **Isolate the absolute value:** Add 3 to both sides:

1. **State the problem:** Solve the equation $$-9|a - 1| + 3 = -42$$ for $a$. 2. **Isolate the absolute value term:** Subtract 3 from both sides:

1. Let's understand the fraction $\frac{8}{5}$. A fraction represents a part of a whole or a division of two numbers. 2. The fraction $\frac{8}{5}$ means 8 divided by 5.

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$12x + 30y = 180$$. 2. **Recall the intercept definitions:**

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$-x + y = 3$$. 2. **Recall the intercept definitions:**

1. The problem asks to identify which point on a number line corresponds to the value $-0.135$. 2. We know the points are labeled A, B, C, and D, and the value $-0.135$ lies betwee

1. **Stating the problem:** Simplify or analyze the given fractions and expressions involving large numerators and denominators. 2. **Understanding the fractions:** Each term is a

1. **State the problem:** We want to find the product of $y$ to the second power and $y$ to the sixth power, i.e., calculate $y^2 \times y^6$. 2. **Recall the exponent multiplicati

1. **Problemos aprašymas:** Turime taškus A($-2$, $-4$), B($6$, $4$), C($-5$, $1$) ir D($4$, $-2$) koordinačių plokštumoje OXY.

1. **State the problem:** We are given the vertex of a quadratic relation as $ (6, -4) $ and the value of $ a = 3 $. We need to find the equation in vertex form. 2. **Recall the ve

1. **State the problem:** We need to find the equation of a parabola with vertex $(3,-2)$ and y-intercept $7$. 2. **Recall the vertex form of a parabola:** The equation of a parabo

1. **State the problem:** Calculate the value of the expression $$(6\times \left(5^4\right))^2 \times 6 \times 10^{-6}$$.

1. **State the problem:** We want to find the partial fraction decomposition of the rational function

1. **State the problem:** We want to decompose the rational function

1. Để giải thích tại sao lại có số $24$ trong đoạn cuối, ta cần xem xét ngữ cảnh hoặc bài toán gốc mà bạn đang nói đến. 2. Thông thường, số $24$ xuất hiện trong các bài toán liên q

1. **Đặt lại bài toán:** Cho $$A = \frac{\sqrt{x} + 5}{2\sqrt{x} - 4}$$ và $$B = \frac{x}{x - 4} + \frac{1}{\sqrt{x} - 2} + \frac{1}{\sqrt{x} + 2}$$ với $$x > 0$$, $$x \neq 4$$. Câ

1. **Problem Statement:** We are given the implicit curve defined by the equation $$ (x^2 + y^2 - 1)^3 - x^2 y^3 = 0 $$.

1. **Problem statement:** Evaluate the expression $$\log_{\sqrt{a}} \frac{1}{y}$$. 2. **Recall the logarithm change of base and properties:**

1. **Problem statement:** Given $\log_a y = m$, express each of the following in terms of $m$: a) $\log_y a$