🧮 algebra

1. We are asked to express each given rational function as partial fractions. 2. The general approach for partial fractions is to decompose a rational function \( \frac{P(x)}{Q(x)}

1. The problem asks for the equation of a straight line passing through the point $(1, 5)$ and parallel to the line $y = -2x + 3$. 2. Recall that parallel lines have the same slope

1. **Stating the problem:** Find the points of intersection between the two functions $$f_1(x) = x^2 - 4$$ and $$f_2(x) = x + 2$$. 2. **Formula and approach:** To find intersection

1. **State the problem:** Factorise the expression $5X^2 - 25XY$. 2. **Identify common factors:** Both terms have a common factor of $5X$.

1. The problem is to simplify the expression $a2$. 2. Assuming $a2$ means $a \times 2$, the expression can be rewritten as $2a$.

1. **State the problem:** Solve the equation $2x + 3x = 10$. 2. **Combine like terms:** Since both terms on the left side have $x$, add their coefficients: $2x + 3x = (2 + 3)x = 5x

1. **State the problem:** We know that $y$ varies directly as $x$ and inversely as the square of $z$. Given $y=8$ when $x=4$ and $z=1$, find $y$ when $x=9$ and $z=3$. 2. **Write th

1. Let's start by stating the problem: You want to understand how to combine like terms to solve equations. 2. Combining like terms means adding or subtracting terms that have the

1. The problem presents a 3-column numeric table with values and asks for calculations related to percentages: 50%, 55%, and 56%. 2. Since the exact question is not explicitly stat

1. **State the problem:** We are given that $y$ varies directly as $x$ and inversely as the square of $z$. This means the relationship can be written as: $$y = \frac{kx}{z^2}$$

1. **State the problem:** Solve the equation $$3x \cdot x \cdot x + 2x \cdot x + 4 \ln(x) = 0$$ for $x$. 2. **Rewrite the equation:** Simplify the powers of $x$: $$3x^3 + 2x^2 + 4

1. **State the problem:** Solve the equation $$x^2 + \log x + 24 = 0$$ for $x$. 2. **Important note:** The logarithm function $\log x$ is defined only for $x > 0$.

1. **State the problem:** Solve for $m$ in the equation $2^m = 64$. 2. **Recall the formula and rules:** The equation $a^x = b$ can be solved by expressing $b$ as a power of $a$ if

1. समस्या: एक चुनाव में 10 प्रतिशत मतदाताओं ने मत नहीं दिया, 60 मतदाता ने मत पत्र खाली छोड़ा, विजेता को मतदाता सूची के 47 प्रतिशत मत मिले और वह अपने प्रतिद्वंदी से 308 मत अधिक प्रा

1. **Problem statement:** Simplify the expression $$A = \left( \frac{x + \sqrt{x}}{\sqrt{x} + 1} \right) \times \left( \frac{\sqrt{x} - x}{\sqrt{x} - 1} \right) \times \left( 1 + \

1. المشكلة: حل المعادلة $2x + 3 = 7$. 2. القاعدة: لحل المعادلات الخطية، نريد عزل المتغير $x$ على أحد جانبي المعادلة.

1. Bài 1 yêu cầu rút gọn biểu thức: $$\sqrt{a^2} + \sqrt{(-7a)^2}$$ với $a > 0$. 2. Công thức quan trọng: $$\sqrt{x^2} = |x|$$, nhưng vì $a > 0$, nên $|a| = a$.

1. Vamos resolver a expressão $$\left(\left(\frac{1}{2}\right)^3\right)^{-4} \times \left(1 + 2^{\frac{1}{3}}\right)^{-12} \div \left(1 + 2^{\frac{2}{3}}\right)^{-11}$$

1. **State the problem:** Solve the equation $$3^x = 27$$. 2. **Recall the formula and rules:** We know that 27 can be expressed as a power of 3 because $$27 = 3^3$$.

1. **State the problem:** We need to graph the two linear equations $y=3x$ and $y=-x+400$ on the same coordinate plane. 2. **Recall the form of linear equations:** Both equations a

1. **Problem:** Find the equation of the parabola with directrix $y = -\frac{1}{2}$ and vertex at $(0,0)$. 2. **Formula and rules:** The vertex form of a parabola with vertical axi