🧮 algebra

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 $2$: $8 = 2^3$.

1. **State the problem:** Onacha spent $\frac{1}{4}$ of his salary on food. From the remainder, he spent $\frac{3}{9}$ on school fees and the rest on leisure. His salary was 5400.

1. **State the problem:** We want to find the exact time between 10:00 and 11:00 such that six minutes from now, the minute hand is exactly opposite the position where the hour han

1. **State the problem:** We are asked to find a number such that when 18 is added to it and then 15 is subtracted, the result is 22. 2. **Set up the equation:** Let the number be

1. **State the problem:** Rationalize the denominator and simplify the expression $$\frac{14}{3-\sqrt{2}}$$. 2. **Formula and rule:** To rationalize a denominator with a binomial i

1. The problem is to solve a simple algebraic equation suitable for grade 7 level: Solve for $x$ in the equation $$3x + 5 = 20$$. 2. The formula used here is to isolate the variabl

1. **Problem statement:** Given the demand function $P = 190 - 0.6x$ and total cost function $TC = 40 + 30x + 0.4x^2$, where $P$ is price per unit and $x$ is units produced and sol

1. The problem is to explain the concept of standard form in mathematics. 2. Standard form can refer to different things depending on the context, but commonly it means writing num

1. **State the problem:** Rearrange the formula $$y=\frac{3a-2}{a-1}$$ to make $a$ the subject. 2. **Start by multiplying both sides by the denominator to eliminate the fraction:**