🧮 algebra

1. **Stating the problem:** We want to find the unit rate, which is the amount of one quantity per one unit of another quantity. 2. **Formula:** The unit rate is found by dividing

1. **Problem Statement:** We are given a piecewise function $c(m)$ that represents cost based on miles driven $m$: $$

1. **State the problem:** We are given a table showing the number of vegetable plants ($x$) and flowers ($y$) planted in a garden. We need to determine if the table shows a proport

1. **Problem (2a):** Find the ratio of First Class seats to Premium seats to Economy seats given 14, 70, and 168 seats respectively. 2. **Formula and rule:** To find the simplest r

1. Тодорхойлж байна: Өгөгдсөн муруй нь $y = 4x + 1$. 2. Өгөгдсөн шулуун нь $32x - y = 15$.

1. **Problem (a):** Luc uses $\frac{3}{4}$ of a tin per door and needs to paint 7 doors. Find the least number of tins needed. 2. **Formula:** Total paint needed $= 7 \times \frac{

1. The problem is to understand where the condition $x=0$ comes from when solving for zeros of a function. 2. When solving for zeros of a function, we are finding the values of $x$

1. The problem is to simplify the expression $$\frac{n+x}{x} - \frac{x}{x}$$. 2. Recall the rule that $$\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$$ when the denominators are the sa

1. The problem is to understand the expression $x^x$ and rewrite it using exponential and logarithmic functions for $x > 0$. 2. We start with the expression:

1. Let's start by stating the problem: "Solve for zeros" means finding the values of the variable (usually $x$) that make the function equal to zero. 2. The general formula or rule

1. Let's clarify step 7 in detail. 2. Step 7 involves applying the formula or rule that was introduced earlier in the problem.

1. **Nyatakan masalah:** (a) Permudahkan ekspresi $\frac{8\sqrt{h} + 5\sqrt{k}}{\sqrt{h} - \sqrt{k}}$.

1. **Problem 22:** Given a rectangle with length $x + 4$ and width $x - 2$, we need to: a) Write the expression for the perimeter.

1. Тодорхойлолт: f(x) функц нь хоёр хэсэгтэй өгөгдсөн: $$f(x) = \begin{cases} x+1, & \text{хэрэв } x \leq -1 \\ x^2, & \text{хэрэв } x > -1 \end{cases}$$

1. The problem asks to identify which equations represent inverse variation. Inverse variation means $y$ varies inversely as $x$, so $y = \frac{k}{x^n}$ for some $n > 0$.

1. **State the problem:** Simplify the expression $\frac{1}{3} U_n + 1 - U_n + 3$. 2. **Rewrite the expression:** Combine like terms involving $U_n$ and constants separately:

1. **State the problem:** Simplify the expression $$\frac{1}{3} (U_n + 1) - U_n + 3$$. 2. **Write the expression clearly:** $$\frac{1}{3} (U_n + 1) - U_n + 3$$.

1. **State the problem:** Find the slope of the line passing through the points $(2,3)$ and $(5,9)$. 2. **Formula:** The slope $m$ of a line through points $(x_1,y_1)$ and $(x_2,y_

1. **State the problem:** Simplify the expression $$\frac{\frac{1}{3}U_n + 1}{U_n + 3}$$ where $U_n$ is a variable or sequence term. 2. **Write the expression clearly:**

1. **Problem Statement:** We have two lines intersecting at point $(0, 2)$ dividing the plane into 4 sections. We want to determine which section is shaded based on the given point

1. The problem is to analyze the system of inequalities: $$y \geq 4x + 2$$