🧮 algebra

1. The problem states that Alexandra paid 7 dollars to park for 3 hours, and the parking garage charges a constant hourly rate. 2. We need to find an equation relating $p$, the num

1. The problem states that there are 2 supervisors for every 18 baby unicorns. 2. We want to write an equation relating $n$, the number of supervisors, and $u$, the number of baby

1. The problem states that $x$ and $y$ are proportional, meaning they satisfy the equation $y = rx$ where $r$ is the constant of proportionality. 2. To find $r$, we use the formula

1. The problem asks which table has a constant of proportionality between $y$ and $x$ equal to $\frac{1}{5}$. This means we want to check if $y = kx$ where $k = \frac{1}{5}$. 2. Th

1. The problem asks us to find which table has a constant of proportionality between $y$ and $x$ equal to 1.5. 2. The constant of proportionality $k$ means that $y = kx$ for all pa

1. The problem asks to find which table has a constant of proportionality between $y$ and $x$ equal to 2. 2. The constant of proportionality $k$ means $y = kx$. Here, $k=2$, so $y

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