🧮 algebra

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

1. The problem asks to identify the type of function between options a) polynomial function and b) rational function. 2. Definitions:

1. The problem asks to identify the type of function for each given case: a) polynomial function, b) rational function, c) square root function, d) other. 2. Definitions:

1. **State the problem:** Find the roots of the cubic function $$f(x) = x^3 - 2x^2 + 4x - 8$$ and express it in intercept form. 2. **Number of roots:** A cubic polynomial has exact

1. The problem is to find the domain of the function $f(x) = \sqrt{2 - 3x + 3}$.\n\n2. The domain of a square root function requires the expression inside the root to be greater th

1. We beginnen met het uitleggen van wat een vergelijking is: een vergelijking is een wiskundige uitspraak waarin twee uitdrukkingen gelijk aan elkaar zijn, bijvoorbeeld $ax + b =

1. **State the problem:** Simplify the expression $x^2 - 9$. 2. **Recognize the formula:** This is a difference of squares, which follows the rule:

1. **Stating the problem:** We have two options for total cost depending on the number of visits. Option 1 increases linearly from about $30 at 0 visits to $100 at 14 visits. Optio