🧮 algebra

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

1. **State the problem:** Given $x=2$, $y=3$, and $z=-4$, find the value of the expression $2xy + yz + 3x$. 2. **Write the expression:**

1. **State the problem:** Simplify or factor the quadratic expression $x^2 - 13x + 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two number

1. **State the problem:** Given $x=2$, $y=3$, and $z=-4$, find the value of the expression $$2xy + y^2 + 3x$$. 2. **Write the formula:** The expression is $$2xy + y^2 + 3x$$.

1. **State the problem:** Simplify the expression $2x - 3(x+1)$. 2. **Use the distributive property:** Multiply $-3$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $6 - 6 \times \frac{1}{3}$. 2. **Recall the order of operations:** Multiplication and division are performed before addition and s

1. **State the problem:** Solve for $x$ in the equation $12^{4} \times 4^{2} = 16^{x}$. 2. **Rewrite the bases in terms of prime factors:**

1. **State the problem:** Simplify the expression $\left(x - \frac{2}{3}\right) \ln x \ln x$. 2. **Rewrite the expression:** Notice that $\ln x \ln x = (\ln x)^2$. So the expressio

1. **State the problem:** We want to find the cost in cents of $p$ pencils if $k$ pencils cost $c$ cents. 2. **Formula and explanation:** The cost per pencil is the total cost divi