🧮 algebra

1. **State the problem:** Marion thinks of a number less than 15. She multiplies it by 3, subtracts 4, then divides the result by 5, and the final answer is 7. 2. **Set up the equa

1. The problem is to calculate the product of two fractions: $\frac{5}{8} \times \frac{2}{3}$ and simplify the result. 2. The formula for multiplying fractions is:

1. The problem is to multiply two fractions: $\frac{7}{8} \times \frac{5}{2}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}

1. **Problem Statement:** We need to define a piecewise function $f(x)$ representing the cost of electricity for up to 700 units, where the cost per unit changes based on the numbe

1. The problem is to solve the equation or expression given by the user, but since no specific equation or expression was provided, I cannot solve a particular problem. 2. Please p

1. **Stating the problem:** We want to find the expression for $\tan^{-1}(\sqrt{x-3})$ or understand its behavior. 2. **Understanding the function:** The function is the inverse ta

1. The problem is to solve a GCSE level algebra question. Since no specific problem was given, let's consider a common example: Solve for $x$ in the equation $2x + 3 = 11$. 2. The

1. **Problem Statement:** Given the ratio $$(x - 2y + 8z) : (y - 3z + 4w) : (4x + 5z - 7w) = 3 : 4 : 7,$$

1. **Stating the problem:** Given the ratio $$ (x - 2y + 8z) : (y - 3z + 4w) : (4x + 5z - 7w) = 3 : 4 : 7 $$

1. **Énoncé du problème :** Simplifier l'expression $$P = \frac{2(x + 3y)}{5} - \frac{x + 3y}{2} + \frac{1}{5}$$

1. **State the problem:** Solve the system of linear equations: $$2x + 2y + 2z = 15$$

1. The problem is to find the new value after a 30% increase on 4000. 2. The formula to calculate the increased value is:

1. **State the problem:** Theo starts with 18 and saves 4.5 each week.

1. **Stating the problem:** We have rent values for the years 2013 and 2014, and we want to find the rent for 2015. 2. **Given data:**

1. Diberikan fungsi $f(x) = 3x + 1$. Kita diminta mencari nilai $f(1 - 2x)$. 2. Substitusikan $1 - 2x$ ke dalam fungsi $f(x)$, sehingga

1. **State the problem:** We are given two linear equations: $$y = 2kx + 3$$

1. **State the problem:** We need to check if the population in 2021, calculated by adding the same absolute increase from 2001 to 2011, matches the claim that the population incre

1. Vamos trabalhar com a função quadrática, que tem a forma geral $$f(x) = ax^2 + bx + c$$, onde $a$, $b$ e $c$ são números reais e $a \neq 0$. 2. A tarefa é: para a função $$f(x)

1. **State the problem:** We need to divide the polynomial $2x^3 + 3x - 5$ by the binomial $x - 1$. 2. **Formula and method:** Polynomial division can be done using long division o

1. **State the problem:** We need to find the equation of Line B in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 2. **Identify points on the line:** Fr

1. The problem is to simplify the expression $5^{\log_5(2)}$. 2. We use the property of logarithms and exponents: $a^{\log_a(b)} = b$ for any positive $a \neq 1$.