🧮 algebra

1. **Problem 1:** Find the first term $a$ of an AP where the 43rd term $T_{43} = 26$ and the common difference $d = \frac{1}{2}$. 2. The formula for the $n$th term of an AP is

1. The problem states: "The ratio of twenty-seven and nine is equal to the thirty percent of ten."\n\n2. Let's translate the words into a mathematical statement.\n\n- "The ratio of

1. The problem states: "The ratio of twenty-seven and nine is equal to the thirty percent of ten."\n\n2. Let's translate the words into a mathematical statement.\n\n3. The ratio of

1. **State the problem:** We start with a plane priced at 67000000. The price is first reduced by 20%, then increased by 5%. We want to calculate the amounts after each change and

1. The problem states: "One thousand less twelve percent of it is eight hundred eighty." We need to convert this into a mathematical equation. 2. Let the unknown number be $x$.

1. The problem is to understand the role of the natural logarithm (ln) in the geometric mean. 2. The geometric mean of $n$ positive numbers $x_1, x_2, \ldots, x_n$ is defined as:

1. Let's clarify the problem: You mentioned that the coefficients of the equations and the numbers in the matrix are not the same. 2. In systems of linear equations, the coefficien

1. **State the problem:** Jack had some stickers, say $x$. Ben had 470 more stickers than Jack, so Ben had $x + 470$ stickers. 2. Ben gave 735 stickers to Jack. After this, Jack's

1. Let's start by stating the problem: solving an equation means finding the value(s) of the variable that make the equation true. 2. The general approach depends on the type of eq

1. The problem is to solve the equation given by the user. Since the user only wrote "equation," we need a specific equation to proceed. 2. To solve an equation, we typically isola

1. Let's start by understanding the problem: You asked to solve it using Singaporean Maths, which emphasizes model drawing and step-by-step problem solving. 2. Since the exact prob

1. **State the problem:** We need to find the length of Beth's ribbon given the relationships between the lengths of Joan's, Sandra's, and Beth's ribbons and their total length. 2.

1. **State the problem:** We are given two linear equations: $$y = 2x + 1$$

1. **Stating the problem:** We are given several algebraic expressions involving fractions and variables $u$, $x$, $p$, and constants such as 7. The goal is to simplify and underst

1. **State the problem:** Lisa took 4 chemistry tests with an arithmetic mean of 82. She then scores 97 on her 5th test. We need to find the new arithmetic mean for all five exams.

1. **Első feladat:** Kata 39 600 forintot költött reklámozásra. Egy sütemény elkészítése 400 forintba kerül, és 900 forintért árulja. 2. A cél, hogy a reklámköltséget legalább viss

1. **Problem statement:** (a) Find the time the journey ends if it starts at 09:15 and lasts 5 hours 54 minutes.

1. Állítsuk fel a problémát: Egy gazda birtokát négy fia között osztotta el. András a nyáj negyedét kapja, Béla a harmadát, Csaba az András és Béla része után meghatározott részt,

1. **State the problem:** We have line k with equation $y=\frac{5}{4}x$ and want to find the equation of line n, which is perpendicular to line k and passes through the point $(4,7

1. **Problem Statement:** We need to find the price of a basic subscription and a premium subscription given the revenue function and contour lines on the graph. 2. **Understanding

1. **State the problem:** We need to find the range of the giant panda's mass $p$ in grams at birth, given it is between $\frac{1}{950}$ and $\frac{1}{850}$ times its mother's mass