🧮 algebra

1. Let's start by understanding the problem: graphing in the Cartesian plane means plotting points using coordinates $(x,y)$ where $x$ is the horizontal position and $y$ is the ver

1. **State the problem:** Simplify the expression $f(2x-1)$ given the function $f(x) = -2 + 3x$. 2. **Recall the function definition:** The function is defined as $f(x) = -2 + 3x$.

1. **State the problem:** Find the next term in the sequence 4, 18, 85, 336, 1005, ? 2. **Analyze the sequence:** Let's look at the differences between terms to find a pattern.

1. The problem is to find a function that fits the given data points where $x$ ranges from 0 to 30 and $y$ values decrease approximately linearly. 2. We use the linear regression f

1. **State the problem:** We have two boxes, A and B, with a total mass of sand 250g.

1. The problem is to multiply the matrix \(\begin{bmatrix}a & b \\ c & d\end{bmatrix}\) by the scalar 1000. 2. The formula for scalar multiplication of a matrix is to multiply each

1. Énoncé du problème : Résoudre l'équation $\ln x^2 + 2 \ln x + 1 = 0$. 2. Rappel des propriétés des logarithmes :

1. Énoncé du problème : Résoudre l'équation $\ln x^2 + 2 \ln x + 1 = 0$. 2. Rappel des propriétés des logarithmes :

1. **State the problem:** We are given a rectangular land where the length is 10 meters longer than the breadth. The cost of fencing the land with 3 rounds at 50 per meter totals 1

1. The problem asks to solve part b of a question, but since the original question is not provided, I will assume it is a continuation of a previous problem. 2. To proceed, please

1. **State the problem:** Find the value of $k$ given that in the expansion of $(1 + kx)^{15}$, the coefficient of $x^3$ is $-29120$.

1. **State the problem:** Calculate the value of the expression $$\frac{(0.0050)^2 \cdot (0.8)^3}{(4 \times 25.783 \times 10^{-3})(5.013 \times 10^{-3})^3} \times (7.715 \times 10^

1. The problem involves expressions with sums of pairs of variables: $a+b$, $b+c$, and $c+a$. 2. We are given the expression $b+c, c+a, a+b = 2 b, c, a = 2(3abc - a^3 - b^3 - c^3)$

1. **State the problem:** We want to understand the function $y = x^x$. 2. **Formula and explanation:** The function $y = x^x$ is defined for $x > 0$ because the base and the expon

1. The problem asks for the number of generators of a cyclic group of order 800. 2. A cyclic group of order $n$ has exactly $\varphi(n)$ generators, where $\varphi$ is Euler's toti

1. 题目陈述：计算各项支出占总支出的百分比。 2. 公式：百分比 = $\frac{部分}{总数} \times 100$。

1. The problem states: Given the quadratic equation $$ax^2 + a = b$$ where $a$ and $b$ are integers, and one solution is $x=6$, find the other solution. 2. Rewrite the equation as

1. **Stating the problem:** We are given the cyclic sums $a+b$, $b+c$, $c+a$ and the cyclic sums $b+c$, $c+a$, $a+b$ equal to $2$, and we want to prove the identity:

1. **State the problem:** Solve the quadratic equation $$5x^2 = 12 - 17x$$ for $x$. 2. **Rewrite the equation in standard form:** Move all terms to one side to get zero on the othe

1. The problem is to understand the variable $x$ and its role in algebra. 2. In algebra, $x$ is commonly used as a variable representing an unknown value.

1. **State the problem:** Simplify the expression $-x \times 2y - xy \times -2x$. 2. **Recall multiplication rules:** When multiplying terms, multiply coefficients and variables se