🧮 algebra

1. **State the problem:** We need to translate the statement "a varies inversely with b" into an equation. 2. **Recall the formula for inverse variation:** If a quantity $a$ varies

1. **Problem:** Translate "w is directly proportional to v" into an equation. 2. **Formula:** Direct variation means $w = kv$ where $k$ is the constant of proportionality.

1. The problem is to add more steps to a solution, but since no specific problem was given, I will demonstrate adding steps to a simple algebraic equation solving process. 2. Consi

1. **State the problem:** We have a line $n$ passing through points $(-2,5)$ and $(1,-1)$.

1. **Énoncé du problème** : Résoudre dans $\mathbb{R}$ les équations suivantes : (E1) : $\frac{6x - 2}{3x + 4} = 2$

1. The question asks: "Where did the second 5 come from?" This usually refers to an expression or equation where the number 5 appears twice. 2. To answer this, we need to see the o

1. Let's start with a basic Grade 10 Indonesian mathematics topic: solving linear equations. 2. Problem: Solve the equation $3x + 5 = 20$ for $x$.

1. The user asks for questions suitable for grade 7. 2. Since the request is for questions and not a specific math problem, I will provide a sample algebra question appropriate for

1. **Statement of the problem:** Factor the expression $$A = (x+1)(-x+5) + (x+1)(-6+4x)$$ into a product of two factors. 2. **Formula and rules:** Use the distributive property to

1. **State the problem:** Jada and Diego baked some cookies. They gave away fractions of the cookies, threw some away, and after several steps, 15 cookies remained. We need to find

1. Statement of the problem: State the given function $f(x)=3e^{-4x}+5$ for $x\in\mathbb{R}$.

1. Problem statement: Given $f(x)=3e^{-4x}+5$ for $x\in\mathbb{R}$.\n2. What is asked: (i) State the range of $f$.\n(ii) Find $f^{-1}$ and state its domain.\n3. Formula and importa

1. The problem is to simplify the fraction $\frac{4}{9}$ and check if it can be expressed as $\frac{2}{3}$.\n\n2. The formula for simplifying fractions is to divide the numerator a

1. **State the problem:** Show that the equation $4x^2 + 4y^2 + 7x - 11y = 0$ represents a circle. 2. **Recall the general form of a circle's equation:**

1. **State the problem:** Magda buys 6 apples and 4 oranges for a total cost of 4.18. Each orange costs 0.52. We need to find the cost of one apple. 2. **Define variables:** Let th

1. **State the problem:** Simplify the algebraic expression $$\frac{2p}{2p+2} + \frac{7}{5p-20}$$. 2. **Identify common factors and factor denominators:**

1. **Stating the problem:** Diketahui fungsi $f(x) = \sqrt{x + 4}$ dan $g(x) = x^2$. Kita diminta untuk menentukan komposisi fungsi $(f \circ g)(x)$ dan menyelidiki domain dari $(f

1. The problem shows three pairs of numbers connected by arrows with numbers in parentheses, indicating a transformation or operation between the numbers. 2. Let's analyze the firs

1. **State the problem:** Find the equation of the perpendicular bisector of the line segment joining points $A(1,-5)$ and $B(9,1)$ in the form $y=mx+c$. 2. **Find the midpoint of

1. **State the problem:** We are given the function $$f(x) = 3e^{-4x} + 5$$ for all real numbers $$x \in \mathbb{R}$$.

1. **Problem 1:** Find $x$ such that $2^{2x-3} = 8$. 2. We know that $8$ can be written as a power of $2$: $8 = 2^3$.