🧮 algebra

1. **State the problem:** Solve the quadratic equation $$x^2 - 25 = 0$$ and sketch its graph. 2. **Formula and rules:** The standard form of a quadratic equation is $$ax^2 + bx + c

1. The problem is to solve the equation $2x + 3 = 7$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides and then di

1. The problem is to find the reciprocal (1 divided by each value) of each number in the given list. 2. The formula to find the reciprocal of a number $x$ is:

1. The problem is to find an algebraic expression that represents the pattern 4, 8, 16, 32, 64, ... 2. This is a geometric sequence where each term is obtained by multiplying the p

1. **Problem Statement:** A farmer buys 54 bags of fertilizer A and 34 bags of fertilizer B. Fertilizer A contains 3 kg nitrogen, 1 kg potassium, 2 kg potash per bag. Fertilizer B

1. **State the problem:** Evaluate the expression $$\left(\frac{25}{36}\right)^{\frac{3}{2}}$$ where the exponent is a fractional power. 2. **Recall the rule for fractional exponen

1. **Problem statement:** Find the value of each expression if the result is a real number; otherwise, state NOT REAL. 2. **Recall the rules:**

1. Problemet handlar om att beräkna hur mycket färg som behövs för att måla 10000 träklossar. 2. Först måste vi beräkna ytan på en träkloss. Eftersom dimensionerna inte är givna i

1. **State the problem:** Simplify and analyze the expression $$x + \frac{1}{3x - 5} - \frac{8}{3} x \sqrt{8 + \frac{9x - 5}{24}}.$$\n\n2. **Rewrite the expression:**\n$$x + \frac{

1. The problem asks to rewrite each logarithmic equation in exponential form. 2. Recall the definition of logarithm: if $\log_b a = c$, then the exponential form is $b^c = a$.

1. **Problem:** A firm's production was 4000 units in 2000 and planned to be 10000 units in 2010. Assuming linear increase, estimate production in 2004. 2. **Formula:** For linear

1. **Problem Statement:** Find the break-even point for the company given the original data and then determine the break-even points for the two scenarios:

1. **Problem:** Find the inverse function $f^{-1}(x)$ of $f(x) = \frac{3x - 7}{4x + 3}$. 2. **Formula and rules:** To find the inverse function, swap $x$ and $y$ in the equation $y

1. **Problem Statement:** Find the inverse function $f^{-1}(x)$ of $f(x) = \frac{3x - 7}{4x + 3}$. 2. **Formula and Rules:** To find the inverse function, swap $x$ and $y$ in the e

1. The problem is to simplify the algebraic expression $8ab + 5a$. 2. We look for common factors in each term. The terms are $8ab$ and $5a$.

1. The problem is to simplify the algebraic expression $8ab + 5a$. 2. We look for common factors in each term. The terms are $8ab$ and $5a$.

1. **State the problem:** Simplify the algebraic expression $8ab + 5a$. 2. **Identify common factors:** Look for common factors in each term. Here, both terms have a factor of $a$.

1. **State the problem:** Reduce the expression $$\frac{3a^2 + 3ab}{3a^2 + 6ab + 3b^2}$$ to its lowest terms. 2. **Identify the formula and rules:** To simplify a rational expressi

1. The problem is to isolate and simplify the second term from a given expression containing three terms. 2. Let's assume the expression is $a + b + c$, where $a$ is the first term

1. The problem is to create a rational function similar to the example given: $$f(x) = \frac{2}{x^{2} - 64}$$ which factors as $$(x+8)(x-8)$$ and has vertical asymptotes at $x = -8

1. Das Problem lautet: Löse die Gleichung $$2x + 3 = 7$$. 2. Die verwendete Formel ist die lineare Gleichung in der Form $$ax + b = c$$, wobei wir $x$ isolieren wollen.