🧮 algebra

1. **State the problem:** Solve the equation $$\frac{2}{y} + \frac{8}{y} - \frac{1}{y} = 9$$ for $y$. 2. **Combine like terms:** Since all terms on the left have the same denominat

1. **State the problem:** We need to find the value of $k$ such that the compound inequality $$4 - \frac{x}{3} > 3x - k > -13$$ holds true. 2. **Rewrite the compound inequality as

1. **State the problem:** Solve the quadratic equation $$x^2 - 10x + 34 = 0$$ for $x$. 2. **Formula used:** The quadratic formula for solving $ax^2 + bx + c = 0$ is:

1. **State the problem:** Solve the quadratic equation $$60x^2 + 25x - 15 = 0$$ by factoring. 2. **Formula and rules:** To solve by factoring, we first factor the quadratic express

1. **Stating the problem:** We have six numbers with the following information: - Lowest number = 37

1. **Problem statement:** We have two branches of a company with 100 and 80 employees respectively. The arithmetic means of their monthly salaries are 4570 and 6750 respectively. W

1. **State the problem:** Solve the equation by factoring: $$4x(3x + 1) = 1$$ 2. **Rewrite the equation:** Expand the left side:

1. The problem asks to find the value(s) of $d$ that complete the square for each quadratic expression. 2. The formula to complete the square for $x^2 + bx + c$ is to find $d = \le

1. **State the problem:** Solve the system of equations for $m_{1f}$ and $m_{2f}$ in terms of $m$ and $\theta$: $$-2\theta m_{1f} + 2\theta m_{2f} = -\theta m - 2m$$

1. **State the problem:** Solve the system of linear equations for $m_{1f}$ and $m_{2f}$ given: $$-2\theta m_{1f} + 2\theta m_{2f} = -\theta m - 2 m$$

1. **State the problem:** Solve the system of equations for $m_{1f}$ and $m_{2f}$: $$2\cdot(h+\theta h)\cdot(m - m_{1f}) + \theta h \cdot (m + m_{2f}) = -\left(2 m_{1f} \cdot h + \

1. **Problem (a): Explain why Eva's calculation is incorrect for $5 + 3 \times 2^2 = 32$.** 2. According to the order of operations (PEMDAS/BODMAS), we first calculate the exponent

1. **State the problem:** Multiply $3^{-2}$ by $9^{-3}$. 2. **Recall the properties of exponents:**

1. **State the problem:** Solve the system of linear equations: $$4x - 3y = 12$$

1. Masalani bayon qilamiz: Didymus korporatsiyasida faqat ikki xil xodimlar bor: kumush va oltin. Oltin xodimlarning o'rtacha maoshi kumush xodimlarning o'rtacha maoshidan 56000 ga

1. **State the problem:** Solve the inequality $3x + 7 \geq 2x$. 2. **Isolate the variable:** Subtract $2x$ from both sides:

1. **State the problem:** Solve the quadratic equation $$x^2 - 3x + 2 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by

1. Muammo: Berilgan ifodani soddalashtirish. 2. Soddalashtirish uchun algebraik qoidalar va amallarni qo'llaymiz: yig'indi va ayirmalarni birlashtirish, ko'paytma va bo'linmalarni

1. **State the problem:** Decompose the rational expression $$\frac{x^2 + x + 1}{(x-1)(x+2)}$$ into partial fractions. 2. **Formula and rules:** For partial fraction decomposition,

1. **Problem:** Given the product of $a$ and $\sqrt{b}$ is 31.59, and $\log a = 2.6182$, find $b$ using logarithms to 4 significant figures. 2. **Formula and rules:**

1. **Problem:** Simplify the expression $$\frac{(a^{-2} b^{3})^{2}}{a^{2} b^{-1}}$$. 2. **Formula and rules:** When raising a power to another power, multiply exponents: $$(x^m)^n