🧮 algebra

1. **State the problem:** Solve the equation $4x - 8 + 5 = 1 - 3x - 9 + 12x$ for $x$. 2. **Simplify both sides:**

1. **State the problem:** Find the product of the binomials $$(7m + 8n)(7m - 8n)$$. 2. **Recall the formula:** This is a difference of squares pattern, which states:

1. The problem asks for the number of values of $x$ such that $f(x) = 0$ where $f(x) = ax^3 + bx^2 + cx + d$ is a cubic function. 2. A cubic function can have up to 3 real roots be

1. **State the problem:** Jordan uses 24 pints of paint in total. One quarter ($\frac{1}{4}$) of this paint is green, and the rest is blue. We need to find how many pints of blue p

1. **Stel het probleem vast:** We willen weten hoeveel kilogram suiker er in de voorraadpot zit als deze tot 3 cm onder de rand gevuld is.

1. **State the problem:** In the library, the number of fiction books is $\frac{2}{5}$ the number of nonfiction books. The total number of books is 56. We need to find how many boo

1. Problema: Simplificar la expresión $ (2x)^3 $ usando las leyes de exponentes. 2. Fórmula: Para un producto elevado a una potencia, se eleva cada factor a esa potencia: $$ (ab)^n

1. **State the problem:** Solve the linear equation $-2x - 3 = 5x + 11$ for $x$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $3x(x + 1) = -5$ for $x$. 2. **Rewrite the equation:** Expand the left side:

1. **State the problem:** A container holds 0.7 liters of a mixture of oil and vinegar. Three-fourths ($\frac{3}{4}$) of the mixture is vinegar. We need to find how many liters of

1. **State the problem:** We need to determine which of the given input-output pairs satisfy the function $y = x^3$. 2. **Recall the function:** The function is defined as $y = x^3

1. **Problem:** Factor the polynomial $3x^2 + 14x - 5$ completely. 2. **Formula and rules:** To factor a quadratic $ax^2 + bx + c$, find two numbers that multiply to $a \times c$ a

1. **State the problem:** Calculate the value of $\frac{2}{3} \times 8$. 2. **Formula used:** Multiplication of a fraction by a whole number is done by multiplying the numerator by

1. Stating the problem: Solve for $x$ in the proportion $$\frac{2}{5} = \frac{x}{20}$$. 2. Formula used: In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross products are equal,

1. **Problem statement:** Calculate the combined transformation matrix and the image of point $P(3,-2)$ after two successive transformations given by matrices

1. The problem asks for the percentage of Claudia's total yearly work time spent on the project "Customer Survey" given she spends $x$ percent of her monthly work time on the proje

1. **Problem Statement:** Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers 24 and 36 using factorization. 2. **Formula and Rules:**

1. **State the problem:** We have a hospital with two wards, A and B. Ward A has 40% of the beds and contributes 60% of the total turnover of 120 million. Ward B has the remaining

1. **Stating the problem:** The ratio of female to male employees is initially 2:5. After hiring 6 more women, the ratio becomes 7:10. We need to find the total number of employees

1. Problemet: Vi ska beräkna med hur många procent priset på halsbandet ökade från utropspriset 6300 till slutpriset 12000. 2. Formeln för procentuell ökning är:

1. We beginnen met het opstellen van een vergelijking voor het vraagstuk. 2. Stel dat de vergelijking de vorm heeft $ax + b = c$, waarbij $a$, $b$, en $c$ getallen zijn en $x$ de o