🧮 algebra

1. **State the problem:** Mrs Lim starts with 35 liters of water. She uses $\frac{3}{7}$ of it to wash dishes, then uses $\frac{1}{4}$ of the remaining water to water flowers. We n

1. **State the problem:** Divide 560 among 3 people such that the second person gets twice as much as the first, and the third gets twice as much as the second. 2. **Set variables:

1. **State the problem:** We have 1 litre of fruit drink made by mixing cordial and water in the ratio 1:7. 2. **Initial quantities:** Since the total is 1 litre and the ratio is 1

1. **State the problem:** Simplify the expression $$\frac{\sin x \cdot x^{2}}{|\theta x m x|} + \frac{\sin x}{|\theta x m x|^{2}}.$$\n\n2. **Identify the components:** The expressi

1. El problema es factorizar la expresión $6x^2 + 3x$. 2. Para factorizar, buscamos el factor común entre los términos. Recordemos que la factorización por factor común usa la prop

1. **State the problem:** Find the midpoint of the segment connecting the complex numbers $z_1 = 0 + 4i$ and $z_2 = 0 - 5i$ in the complex plane. 2. **Formula for midpoint:** The m

1. **State the problem:** Solve the equation $$-2y + 1 = -9$$ for the variable $y$. 2. **Isolate the term with $y$:** Subtract 1 from both sides to move the constant term.

1. **State the problem:** Solve the equation $$-8 = 3d + 4$$ for the variable $$d$$. 2. **Isolate the term with $$d$$:** Subtract 4 from both sides to move the constant term.

1. **State the problem:** Simplify the expression $5p^0 + (7p)^0$. 2. **Recall the rule:** Any nonzero number raised to the power of 0 is 1, i.e., $a^0 = 1$ for $a \neq 0$.

1. **State the problem:** Simplify the expression $$\frac{4(x^2 y)^3 \times 2xy^2}{2x^2 y}$$. 2. **Recall the exponent and multiplication rules:**

1. **State the problem:** Simplify the expression $$\sqrt{x} \cdot \sqrt{4x} + \sqrt{100x^2} - \sqrt{9} \sqrt{x}$$. 2. **Recall the properties of square roots:**

1. **State the problem:** We have a population model for coyotes given by $$P = 1024(1.078)^n$$ where $n$ is the number of years since 2005. 2. **Find the initial population in 200

1. **State the problem:** You want to find out how long it takes to read a 540-page book if you read 30 pages per hour. 2. **Formula used:** Time = \frac{Total Pages}{Pages per Hou

1. Let's verify each fraction operation step-by-step. 2. For the first line: $\frac{3}{4} \times \frac{5}{6} = \frac{15}{24} = \frac{5}{8}$ (simplified).

1. **State the problem:** Solve the equation $-4 = h - 20$ for $h$. 2. **Formula and rules:** To isolate $h$, add 20 to both sides of the equation to cancel out the $-20$ on the ri

1. **State the problem:** We need to graph the quadratic function $$y = -x^2 - 10x - 21$$ and plot 5 points including the roots and the vertex. 2. **Formula and rules:** The quadra

1. **State the problem:** Solve the equation $$3.4d = 17.34$$ for the variable $$d$$. 2. **Formula and rules:** To isolate $$d$$, divide both sides of the equation by $$3.4$$.

1. **State the problem:** We need to graph the quadratic function $$y = x^2 + 8x + 7$$ and plot 5 points including the roots and the vertex. 2. **Formula and rules:** The quadratic

1. المشكلة: تبسيط الكسر \( \frac{8}{10} \). 2. القاعدة: لتبسيط كسر، نقسم البسط والمقام على القاسم المشترك الأكبر (GCD).

1. The problem is to find the domain and range of a combined function, which typically means a function formed by operations like addition, subtraction, multiplication, division, o

1. The problem asks to create a function $t(n)$ to model the growth of Lin's tetra population, where $n$ is the number of months since she bought the tetras. 2. From the table, the