🧮 algebra

1. The problem asks which table shows a constant of proportionality between $y$ and $x$ equal to 0.9. 2. The constant of proportionality means $y = kx$ where $k$ is constant. Here,

1. **State the problem:** We have a geometric sequence defined by the first term $a_1 = 8$ and the common ratio $r = -1.5$. We want to find the sum of the first 20 terms, denoted a

1. **Problem statement:** A hotel has 320 rooms and 32 cleaners. With all cleaners working, it takes 2 hours to clean all rooms. On Monday, 20% of cleaners were not available. Will

1. Таван хүний насны нийлбэр нь 80 гэж өгөгдсөн. 2. Хамгийн бага нь 6 настай.

1. The problem is to identify which number among 98, 70, 35, 20, and 10 fits a certain pattern or condition. 2. Since no specific condition is given, let's analyze the numbers for

1. The problem is to convert the inequality $10x + 32y \geq 5000$ into slope-intercept form. 2. The slope-intercept form for a line is given by the formula:

1. **State the problem:** Given that $2^a=5$ and $5^b=7$, find the value of $2^{ab+1}$. 2. **Understand the problem:** We want to find $2^{ab+1}$. Notice that $ab+1 = ab + 1$, so w

1. **Problem Statement:** We want to find how many t-shirts and tickets must be sold to raise at least 5000 for charity.

1. **Problem statement:** We have a function $f$ defined for all real numbers such that $$f(x+y) = f\left(\frac{x}{2}\right) + f\left(\frac{y}{2}\right)$$ for all real $x,y$. We ar

1. The problem asks to add 9 to the square root of 3. 2. The square root of 3 is written as $\sqrt{3}$.

1. The problem is to simplify or work with an expression involving a square root without expanding it. 2. When dealing with square roots, the key rule is to keep the radical form i

1. **State the problem:** We need to simplify the expression $3\sqrt{6} + 9$. 2. **Recall the components:** The term $3\sqrt{6}$ is a product of 3 and the square root of 6, which i

1. **Énoncé du problème :** Calculer le déterminant de la matrice $A = \begin{pmatrix} 1 & 2 & 5 \\ 1 & 1 & 1 \\ 1 & -2 & -2 \end{pmatrix}$ et montrer qu'elle est inversible.

1. **State the problem:** Simplify the expression $$\sqrt[4]{2x^2} \cdot \sqrt[4]{8y^3}$$ and verify the given equality. 2. **Recall the property of radicals:** For the same root i

1. The problem is to solve the equation or expression given previously (not specified here, so assuming a generic solve request). 2. Since the original problem is not restated, let

1. **State the problem:** Simplify the expression $$2\pi^{1/2}(8 - 2t) \div 8\sqrt{\pi}$$. 2. **Recall the rules:**

1. The problem states that the points $(3,2)$ and $(-3,2)$ are maximum points, and the minimum value is $-6$ occurring at $x=0$. 2. We want to find a function $y=f(x)$ that satisfi

1. **State the problem:** Solve for $x$ in the equation $3x + 5 = 27$. 2. **Formula and rules:** To solve a linear equation, isolate the variable $x$ by performing inverse operatio

1. **State the problem:** Solve the linear equation $3x + 5 = 27$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtra

1. **State the problem:** Solve for $x$ in the equation $2(x + 4) = 16$. 2. **Use the distributive property:** Multiply 2 by each term inside the parentheses.

1. **Problem statement:** A contractor employs 20 men to finish a project in 50 days. After 15 days, 10 men leave, and the remaining 10 men increase their working hours from 6 hour